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Current File : /var/www/html/kalemon/public/mbdbuds1/TG/Class-9/Math/assets/DataJS/ch1.js
var chpdata=[
  {
    "subject": "Mathematics",
    "chapter": "ch1",
    "chapterName": "Chapter 1 - Number Systems",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Decimal representation of a rational number cannot be",
          "ans": "(d) non-terminating non-repeating",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
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            "(a) terminating",
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            "(c) non-terminating repeating",
            "(d) non-terminating non-repeating"
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          "val": 1
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        {
          "heading": "Multiple Choice Question.",
          "qus": "Every rational number is",
          "ans": "(c) a real number",
          "code": "MCQ",
          "width": null,
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            "(c) a real number",
            "(d) a whole number"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The product of any two irrational numbers is",
          "ans": "(d) sometimes rational, sometimes irrational",
          "code": "MCQ",
          "width": null,
          "height": null,
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            "(c) always an integer",
            "(d) sometimes rational, sometimes irrational"
          ],
          "val": 3
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        {
          "heading": "Multiple Choice Question.",
          "qus": "The decimal expansion of the number 2 is",
          "ans": "(d) non-terminating non-recurring",
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          "width": null,
          "height": null,
          "optn": null,
          "options": [
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            "(c) non-terminating recurring",
            "(d) non-terminating non-recurring"
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          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is irrational number?",
          "ans": "(c) √7",
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          "pic": {
            "image": "ch1m5.jpg",
            "width": "360",
            "height": "100"
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          "val": 5
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        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is irrational number?",
          "ans": "(d) 0.4014001400014...",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m6.jpg",
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          "val": 6
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        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m7.jpg",
            "width": "500",
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          "ansimg": {
            "image": "ch1m7a.jpg",
            "width": "75",
            "height": "44"
          },
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "2√3 + √3 is equal to",
          "ans": "(c) 3√3",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2√6",
            "(b) 6",
            "(c) 3√3",
            "(d) 4√6"
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          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Every rational number is",
          "ans": "(c) a real number",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a natural number",
            "(b) an integer",
            "(c) a real number",
            "(d) a whole number"
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          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Between two rational numbers",
          "ans": "(c) there are infinitely many rational numbers",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) there is no rational number",
            "(b) there is exactly one rational number",
            "(c) there are infinitely many rational numbers",
            "(d) there are only rational numbers and no irrational numbers"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Decimal representation of a rational number cannot be",
          "ans": "(d) non-terminating non-repeating",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) terminating",
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          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The product of any two irrational numbers is",
          "ans": "(d) sometimes rational, sometimes irrational",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) always an irrational number",
            "(b) always a rational number",
            "(c) always an integer",
            "(d) sometimes rational, sometimes irrational"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The decimal expansion of the number √2 is",
          "ans": "(d) non-terminating non-recurring",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a finite decimal",
            "(b) 1.41421",
            "(c) non-terminating recurring",
            "(d) non-terminating non-recurring"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is irrational?",
          "ans": "√7",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m14.jpg",
            "width": "449",
            "height": "115"
          },
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is irrational?",
          "ans": "(d) 0.4014001400014...",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m15.jpg",
            "width": "175",
            "height": "109"
          },
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A rational number between √2 and √3 is",
          "ans": "(c) 1.5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m16.jpg",
            "width": "101",
            "height": "149"
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          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": " ",
          "ans": "(c) 2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
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          "pic": {
            "image": "ch1m17.jpg",
            "width": "101",
            "height": "149"
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          "val": 17
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        {
          "heading": "Multiple Choice Question.",
          "qus": "2√3 + √3 is equal to",
          "ans": "(c) 3√3",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2√6",
            "(b) 6",
            "(c) 3√3",
            "(d) 4√6"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": "(c) 5√6",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
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          "pic": {
            "image": "ch1m19.jpg",
            "width": "349",
            "height": "108"
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          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
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          "pic": {
            "image": "ch1m20.jpg",
            "width": "456",
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          "ansimg": {
            "image": "ch1m20a.jpg",
            "width": "96",
            "height": "59"
          },
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": "(d) 3 + 2√2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m21.jpg",
            "width": "347",
            "height": "174"
          },
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": "(b) 19",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 13",
            "(b) 19",
            "(c) 5",
            "(d) 35"
          ],
          "pic": {
            "image": "ch1m22.jpg",
            "width": "510",
            "height": "50"
          },
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": "(b) 2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) √2",
            "(b) 2",
            "(c) 4",
            "(d) 8"
          ],
          "pic": {
            "image": "ch1m23.jpg",
            "width": "250",
            "height": "51"
          },
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": "(c) 0.4142",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2.4142",
            "(b) 5.8282",
            "(c) 0.4142",
            "(d) 0.1718"
          ],
          "pic": {
            "image": "ch1m24.jpg",
            "width": "286",
            "height": "60"
          },
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m25.jpg",
            "width": "243",
            "height": "145"
          },
          "ansimg": {
            "image": "ch1m25a.jpg",
            "width": "61",
            "height": "41"
          },
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": "(b) 2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m26.jpg",
            "width": "258",
            "height": "103"
          },
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m27.jpg",
            "width": "246",
            "height": "168"
          },
          "ansimg": {
            "image": "ch1m27a.jpg",
            "width": "61",
            "height": "55"
          },
          "val": 27
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Value of (256)<sup>0.16</sup> × (256)<sup>0.09</sup> is",
          "ans": "(a) 4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4",
            "(b) 16",
            "(c) 64",
            "(d) 256.25"
          ],
          "val": 28
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is equal to x?",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch1m29.jpg",
            "width": "313",
            "height": "117"
          },
          "ansimg": {
            "image": "ch1m29a.jpg",
            "width": "94",
            "height": "54"
          },
          "val": 29
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery whole number is a natural number.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery integer is a rational number.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery rational number is an integer.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery natural number is a whole number.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThere are finitely many rational numbers between any two given rational numbers.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tAll irrational numbers are rational numbers.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tπ is a rational number.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tDifference of two irrational numbers is not always irrational number.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery real number is always rational or irrational number.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tSquare root of every positive integer is irrational number.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tProduct of two irrational numbers may or may not be irrational number.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf we add, subtract, multiply or divide two irrationals, the result may be rational or irrational.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "",
          "ans": "False",
          "code": "TF",
          "pic": {
            "image": "ch1tf13.jpg",
            "width": "275",
            "height": "50"
          },
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThere are infinitely many integers between any two integers.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 14
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tNumber of rational numbers between 15 and 18 is finite.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 15
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThere are numbers which cannot be written in the form <sup>p</sup>/<sub>q</sub>, q ≠ 0, p, q both are integers.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 16
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe square of an irrational number is always rational.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 17
        },
        {
          "heading": "State True or False.",
          "qus": "",
          "ans": "False",
          "code": "TF",
          "pic": {
            "image": "ch1tf18.jpg",
            "width": "525",
            "height": "59"
          },
          "val": 18
        },
        {
          "heading": "State True or False.",
          "qus": " ",
          "ans": "False",
          "code": "TF",
          "pic": {
            "image": "ch1tf19.jpg",
            "width": "525",
            "height": "59"
          },
          "val": 19
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "The collection of rational numbers is denoted by __________.",
          "ans": "Q",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "‘Rational’ comes from the word __________ and Q comes from the word __________.",
          "ans": "‘ratio’, ‘quotient’",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a number a can be written in the form <sup>p</sup>/<sub>q</sub>, where p and q are integers and q ≠ 0, then number ‘a’ is called a __________.",
          "ans": "‘rational number’",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "There are __________ rational numbers between any two given rational numbers.",
          "ans": "‘infinitely many’",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "The decimal expansion of a rational number is either __________ or __________ recurring.",
          "ans": "terminating, non-terminating",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A number whose decimal expansion is terminating or non-terminating recurring is __________ number.",
          "ans": "rational",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The decimal expansion of an irrational number is ________________.",
          "ans": "non-terminating non-recurring",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A number whose decimal expansion is non-terminating non-recurring is __________ number.",
          "ans": "irrational",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "",
          "ans": "zero",
          "code": "FIB",
          "pic": {
            "image": "ch1f9.jpg",
            "width": "310",
            "height": "40"
          },
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "",
          "ans": "never",
          "code": "FIB",
          "pic": {
            "image": "ch1f10.jpg",
            "width": "350",
            "height": "50"
          },
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The sum or difference of a rational number and irrational number is __________ number.",
          "ans": "irrational",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The product or quotient of non-zero rational number with an irrational number is __________ number.",
          "ans": "irrational",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "a<sup>m</sup> a<sup>n</sup> = __________, where a, m, n ∈ N or a &gt; 0, m, n, are rational numbers.",
          "ans": "a<sup>m + n</sup>",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a<sup>m</sup>)<sup>n</sup> = __________, where a, m, n ∈ N or a &gt; 0, m, n are rational numbers.",
          "ans": "a<sup>mn</sup>",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "",
          "ans": "a<sup>m – n</sup>",
          "code": "FIB",
          "pic": {
            "image": "ch1f15.jpg",
            "width": "450",
            "height": "50"
          },
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "a<sup>m</sup> b<sup>m</sup> = __________, where a, b, m ∈ N or a &gt; 0, b &gt; 0, m ∈ N.",
          "ans": "(ab)<sup>m</sup>",
          "code": "FIB",
          "val": 16
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1d1.jpg",
            "width": "490",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1d1a.jpg",
            "width": "352",
            "height": "501"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Locate 3.765 on number line by the method of successive magnification.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch1d2a.jpg",
            "width": "534",
            "height": "213"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1d3.jpg",
            "width": "220",
            "height": "30"
          },
          "ansimg": {
            "image": "ch1d3a.jpg",
            "width": "667",
            "height": "510"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1d4.jpg",
            "width": "230",
            "height": "30"
          },
          "ansimg": {
            "image": "ch1d4a.jpg",
            "width": "590",
            "height": "450"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find a rational number between 3 and 4.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch1s1a.jpg",
            "width": "270",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s2.jpg",
            "width": "290",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1s2a.jpg",
            "width": "290",
            "height": "310"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Convert the following rational number into their decimal representation.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s3.jpg",
            "width": "30",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s3a.jpg",
            "width": "90",
            "height": "210"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Convert the following rational number into their decimal representation.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s4.jpg",
            "width": "30",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s4a.jpg",
            "width": "100",
            "height": "230"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Convert the following rational number into their decimal representation.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s5.jpg",
            "width": "35",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s5a.jpg",
            "width": "100",
            "height": "210"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Convert the following rational number into their decimal representation.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s6.jpg",
            "width": "30",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s6a.jpg",
            "width": "120",
            "height": "240"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s7.jpg",
            "width": "181",
            "height": "42"
          },
          "ansimg": {
            "image": "ch1s7a.jpg",
            "width": "100",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s8.jpg",
            "width": "181",
            "height": "42"
          },
          "ansimg": {
            "image": "ch1s8a.jpg",
            "width": "115",
            "height": "150"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s9.jpg",
            "width": "189",
            "height": "42"
          },
          "ansimg": {
            "image": "ch1s9a.jpg",
            "width": "100",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s10.jpg",
            "width": "189",
            "height": "42"
          },
          "ansimg": {
            "image": "ch1s10a.jpg",
            "width": "130",
            "height": "150"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find three rational numbers between –1 and –2.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch1s11a.jpg",
            "width": "172",
            "height": "379"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find three rational numbers between 0.1 and 0.11.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch1s12a.jpg",
            "width": "260",
            "height": "330"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s13.jpg",
            "width": "40",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s13a.jpg",
            "width": "190",
            "height": "110"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s14.jpg",
            "width": "60",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s14a.jpg",
            "width": "310",
            "height": "321"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s15.jpg",
            "width": "60",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1s15a.jpg",
            "width": "200",
            "height": "404"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s16.jpg",
            "width": "30",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s16a.jpg",
            "width": "310",
            "height": "220"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s17.jpg",
            "width": "45",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1s17a.jpg",
            "width": "190",
            "height": "210"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s18.jpg",
            "width": "45",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1s18a.jpg",
            "width": "310",
            "height": "370"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 19,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s19.jpg",
            "width": "60",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1s19a.jpg",
            "width": "310",
            "height": "370"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rationalise the denominator of the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 20,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s20.jpg",
            "width": "70",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1s20a.jpg",
            "width": "200",
            "height": "250"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 21,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s21.jpg",
            "width": "100",
            "height": "40"
          },
          "ansimg": {
            "image": "ch1s21a.jpg",
            "width": "110",
            "height": "260"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 22,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s22.jpg",
            "width": "130",
            "height": "60"
          },
          "ansimg": {
            "image": "ch1s22a.jpg",
            "width": "200",
            "height": "470"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 23,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s23.jpg",
            "width": "130",
            "height": "60"
          },
          "ansimg": {
            "image": "ch1s23a.jpg",
            "width": "110",
            "height": "440"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 24,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s24.jpg",
            "width": "110",
            "height": "80"
          },
          "ansimg": {
            "image": "ch1s24a.jpg",
            "width": "110",
            "height": "456"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 25,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s25.jpg",
            "width": "80",
            "height": "70"
          },
          "ansimg": {
            "image": "ch1s25a.jpg",
            "width": "150",
            "height": "380"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 26,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s26.jpg",
            "width": "120",
            "height": "60"
          },
          "ansimg": {
            "image": "ch1s26a.jpg",
            "width": "280",
            "height": "300"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 27,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch1s27.jpg",
            "width": "70",
            "height": "70"
          },
          "ansimg": {
            "image": "ch1s27a.jpg",
            "width": "160",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Let <i>x</i> and <i>y</i> be rational and irrational numbers, respectively. Is <i>x</i> + <i>y</i> necessarily an irrational number? Give an example in support of your answer.",
          "ans": "Yes. Let <i>x</i> = 21, <i>y</i> = √2 be a rational number. <br>Now <i>x</i> + <i>y</i> = 21 + √2 = 21 + 1.4142 ... = 22.4142 ... <br>which is non-terminating and non-recurring. Hence <i>x</i> + <i>y</i> is irrational.",
          "code": "SATQ",
          "options": null,
          "val": 28,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Let <i>x</i> be rational and <i>y</i> be irrational. Is <i>xy</i> necessarily irrational? Justify your answer by an example.",
          "ans": "No. 0 × √2 = 0 which is not irrational.",
          "code": "SATQ",
          "options": null,
          "val": 29,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational: <br>−√2",
          "ans": "irrational number",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational:",
          "ans": "irrational number",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs2.jpg",
            "width": "32",
            "height": "41"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational: <br>(2 + √2)<sup>3</sup>",
          "ans": "irrational number",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational: <br>√4",
          "ans": "rational number",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational:",
          "ans": "rational number",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs5.jpg",
            "width": "48",
            "height": "26"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational: <br>5.7",
          "ans": "rational number",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 6
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs7.jpg",
            "width": "40",
            "height": "30"
          },
          "ansimg": {
            "image": "ch1vs7a.jpg",
            "width": "200",
            "height": "30"
          },
          "val": 7
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs8.jpg",
            "width": "40",
            "height": "30"
          },
          "ansimg": {
            "image": "ch1vs8a.jpg",
            "width": "620",
            "height": "30"
          },
          "val": 8
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs9.jpg",
            "width": "40",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1vs9a.jpg",
            "width": "290",
            "height": "50"
          },
          "val": 9
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational: <br>(1 + √5) − (4 + √5)",
          "ans": "(1 + √5) − (4 + √5) = 1 + √5 − 4 − √5 = −3, which is a rational number.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 10
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs11.jpg",
            "width": "40",
            "height": "30"
          },
          "ansimg": {
            "image": "ch1vs11a.jpg",
            "width": "150",
            "height": "30"
          },
          "val": 11
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs12.jpg",
            "width": "40",
            "height": "30"
          },
          "ansimg": {
            "image": "ch1vs12a.jpg",
            "width": "620",
            "height": "30"
          },
          "val": 12
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs13.jpg",
            "width": "40",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1vs13a.jpg",
            "width": "620",
            "height": "50"
          },
          "val": 13
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs14.jpg",
            "width": "50",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1vs14a.jpg",
            "width": "249",
            "height": "50"
          },
          "val": 14
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs15.jpg",
            "width": "50",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1vs15a.jpg",
            "width": "490",
            "height": "50"
          },
          "val": 15
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch1vs16.jpg",
            "width": "50",
            "height": "50"
          },
          "ansimg": {
            "image": "ch1vs16a.jpg",
            "width": "250",
            "height": "50"
          },
          "val": 16
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification: <br>0.5918",
          "ans": "Rational, as decimal expansion is terminating.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 17
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification: <br>(1 + √5)− (4 + √5)",
          "ans": "(1 + √5)− (4 + √5) = −3 , which is a rational number.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 18
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification: <br>10.124124...",
          "ans": "Rational, as decimal expansion is non-terminating recurring.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 19
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following number as rational or irrational with justification: <br>1.010010001...",
          "ans": "Irrational, as decimal expansion is non-terminating non-recurring.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 20
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch1_pbq",
    "gowf": "ch1_gowf",
    "afow": "ch1_afow",
    "cs": "ch1_cs",
    "afq": "ch1_afq",
    "fib": "ch1_fib",
    "grade": "Grade 9",
    "mcq": "ch1_mcq",
    "vsaq": "ch1_vsaq",
    "laq": "ch1_laq",
    "tf": "ch1_tf",
    "co": "ch1_co",
    "nf": "ch1_nf",
    "mtf": "ch1_mtf",
    "yn": "ch1_yn",
    "saq": "ch1_saq",
    "dtf": "ch1_dtf",
    "map": "ch1_map",
    "ctt": "ch1_ctt",
    "un": "ch1_un",
    "ctco": "ch1_ctco",
    "grf": "ch1_grf",
    "snc": "ch1_snc",
    "jtf": "ch1_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch2",
    "chapterName": "Chapter 2 - Polynomials",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which one of the following is a polynomial?",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch2m1.jpg",
            "width": "263",
            "height": "100"
          },
          "ansimg": {
            "image": "ch2m1a.jpg",
            "width": "109",
            "height": "51"
          },
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "√2 is a polynomial of degree",
          "ans": "(b) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2",
            "(b) 0",
            "(c) 1",
            "ch2m2.jpg"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Degree of the polynomial 4<i>x</i><sup>4</sup> + 0<i>x</i><sup>3</sup> + 0<i>x</i><sup>5</sup> + 5<i>x</i> + 7 is",
          "ans": "(a) 4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4",
            "(b) 5",
            "(c) 3",
            "(d) 7"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(b) 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) 4√2",
            "(d) 8√2 + 1"
          ],
          "pic": {
            "image": "ch2m4.jpg",
            "width": "270",
            "height": "30"
          },
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The value of the polynomial 5<i>x</i> - 4<i>x</i><sup>2</sup> + 3, when <i>x</i> = -1 is",
          "ans": "(a) -6",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) -6",
            "(b) 6",
            "(c) 2",
            "(d) -2"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If p(<i>x</i>) = <i>x</i> + 3, then p(<i>x</i>) + p(-<i>x</i>) is equal to",
          "ans": "(d) 6",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3",
            "(b) 2<i>x</i>",
            "(c) 0",
            "(d) 6"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Zero of the polynomial p(<i>x</i>) = 2<i>x</i> + 5 is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch2m7.jpg",
            "width": "220",
            "height": "88"
          },
          "ansimg": {
            "image": "ch2m7a.jpg",
            "width": "59",
            "height": "37"
          },
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "One of the zeroes of the polynomial 2<i>x</i><sup>2</sup> + 7<i>x</i> - 4 is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch2m8.jpg",
            "width": "220",
            "height": "80"
          },
          "ansimg": {
            "image": "ch2m8a.jpg",
            "width": "49",
            "height": "41"
          },
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If <i>x</i> – 1 is a factor of 3<i>x</i><sup>3</sup> + 4<i>x</i><sup>2</sup> – 3<i>x</i> + <i>k</i>. Then <i>k</i> = __________.",
          "ans": "(d) –4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3",
            "(b) –3",
            "(c) 4",
            "(d) –4"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "<i>x</i> – 2 is a factor of <i>x</i><sup>2</sup> + 3<i>x</i> – 10. Then <i>p</i>(2) = ___________.",
          "ans": "(c) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1",
            "(b) –1",
            "(c) 0",
            "(d) 2"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which one of the following is a polynomial?",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch2m11.jpg",
            "width": "274",
            "height": "114"
          },
          "ansimg": {
            "image": "ch2m11a.jpg",
            "width": "102",
            "height": "65"
          },
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "√2 is a polynomial of degree",
          "ans": "(b) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2",
            "(b) 0",
            "(c) 1",
            "ch2m12d.jpg"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Degree of the polynomial 4<i>x<i><sup>4</sup> + 0<i>x</i><sup>3</sup> + 0x<sup>5</sup> + 5<i>x<i> + 7 is",
          "ans": "(a) 4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4",
            "(b) 5",
            "(c) 3",
            "(d) 7"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Degree of the zero polynomial is",
          "ans": "(d) Not defined",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) Any natural number",
            "(d) Not defined"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(b) 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) 4√2",
            "(d) 8√2 + 1"
          ],
          "pic": {
            "image": "ch2m15.jpg",
            "width": "310",
            "height": "35"
          },
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The value of the polynomial 5<i>x</i> – 4<i>x</i><sup>2</sup> + 3, when <i>x</i> = –1, is",
          "ans": "(a) –6",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) –6",
            "(b) 6",
            "(c) 2",
            "(d) –2"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If <i>p</i>(<i>x</i>) = <i>x</i> + 3, then <i>p</i>(<i>x</i>) + <i>p</i>(–<i>x</i>) is equal to",
          "ans": "(d) 6",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3",
            "(b) 2<i>x</i>",
            "(c) 0",
            "(d) 6"
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Zero of the zero polynomial is",
          "ans": "(c) Any real number",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) Any real number",
            "(d) Not defined"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Zero of the polynomial <i>p</i>(<i>x</i>) = 2<i>x</i> + 5 is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch2m19.jpg",
            "width": "282",
            "height": "89"
          },
          "ansimg": {
            "image": "ch2m19a.jpg",
            "width": "62",
            "height": "42"
          },
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "One of the zeroes of the polynomial 2<i>x</i><sup>2</sup> + 7<i>x</i> – 4 is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch2m20.jpg",
            "width": "249",
            "height": "82"
          },
          "ansimg": {
            "image": "ch2m20a.jpg",
            "width": "55",
            "height": "39"
          },
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If <i>x</i><sup>51</sup> + 51 is divided by <i>x</i> + 1, the remainder is",
          "ans": "(d) 50",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) 49",
            "(d) 50"
          ],
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is",
          "ans": "(c) 2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) –3",
            "(b) 4",
            "(c) 2",
            "(d) –2"
          ],
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "<i>x</i> + 1 is a factor of the polynomial",
          "ans": "(b) <i>x</i><sup>3</sup> + <i>x</i><sup>2</sup> + <i>x</i> + 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i><sup>3</sup> + x<sup>2</sup> – <i>x</i> + 1",
            "(b) <i>x</i><sup>3</sup> + <i>x</i><sup>2</sup> + <i>x</i> + 1",
            "(c) <i>x</i><sup>4</sup> + <i>x</i><sup>3</sup> + <i>x</i><sup>2</sup> + 1",
            "(d) <i>x</i><sup>4</sup> + 3<i>x</i><sup>3</sup> + 3<i>x</i><sup>2</sup> + <i>x</i> + 1"
          ],
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "One of the factors of (25<i>x</i><sup>2</sup> – 1) + (1 + 5<i>x</i>)<sup>2</sup> is",
          "ans": "(d) 10<i>x</i>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 5 + <i>x</i>",
            "(b) 5 – <i>x</i>",
            "(c) 5<i>x</i> – 1",
            "(d) 10<i>x</i>"
          ],
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The value of 249<sup>2</sup> – 248<sup>2</sup> is",
          "ans": "(d) 497",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1<sup>2</sup>",
            "(b) 477",
            "(c) 487",
            "(d) 497"
          ],
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The factorisation of 4<i>x</i><sup>2</sup> + 8<i>x</i> + 3 is",
          "ans": "(b) (2<i>x</i> + 1) (2<i>x</i> + 3)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (<i>x</i> + 1) (<i>x</i> + 3)",
            "(b) (2<i>x</i> + 1) (2<i>x</i> + 3)",
            "(c) (2<i>x</i> + 2) (2<i>x</i> + 5)",
            "(d) (2<i>x</i> –1) (2<i>x</i> – 3)"
          ],
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is a factor of (<i>x</i> + <i>y</i>)<sup>3</sup> – (<i>x</i><sup>3</sup> + <i>y</i><sup>3</sup>)?",
          "ans": "(d) 3<i>xy</i>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> + 2<i>xy</i>",
            "(b) <i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> – <i>xy</i>",
            "(c) <i>xy</i>2",
            "(d) 3<i>xy</i>"
          ],
          "val": 27
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The coefficient of <i>x</i> in the expansion of (<i>x</i> + 3)<sup>3</sup> is",
          "ans": "(d) 27",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1",
            "(b) 9",
            "(c) 18",
            "(d) 27"
          ],
          "val": 28
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(c) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1",
            "(b) –1",
            "(c) 0",
            "ch2m29a.jpg"
          ],
          "pic": {
            "image": "ch2m29.jpg",
            "width": "313",
            "height": "117"
          },
          "val": 29
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch2m30.jpg",
            "width": "347",
            "height": "155"
          },
          "ansimg": {
            "image": "ch2m30a.jpg",
            "width": "51",
            "height": "40"
          },
          "val": 30
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If <i>a</i> +<i>b</i> + <i>c</i> = 0, then <i>a</i><sup>3</sup> + <i>b</i><sup>3</sup> + <i>c</i><sup>3</sup> is equal to",
          "ans": "(c) 3<i>abc</i>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) <i>abc</i>",
            "(c) 3<i>abc</i>",
            "(d) 2<i>abc</i>"
          ],
          "val": 31
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\t0 (zero) is not a polynomial.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tConstant term is not a polynomial.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tx<sup>2</sup> + 1 is a monomial.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tx<sup>3</sup> + 5 is a binomial.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t2x<sup>2</sup> + 5<i>x</i> + 7 is a binomial.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t3<i>x</i><sup>2</sup> + 9<i>x</i> + 11 is a trinomial.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t2<i>x</i> + 3 is a linear polynomial.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t5<i>x</i><sup>2</sup> + 3<i>x</i> + 4 is a quadratic polynomial.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t<i>x</i><sup>3</sup> + 1 is a cubic polynomial.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t<i>x</i> + 2 is a factor of <i>x</i><sup>3</sup> + 3<i>x</i><sup>2</sup> + 5<i>x</i> + 6. Then <i>p</i>(-2) = 0.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t<i>x</i> - 1 is not a factor of <i>x</i><sup>3</sup> - 2<i>x</i><sup>2</sup> + 3<i>x</i> - 4. Then <i>p</i>(1) ≠ 0.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA binomial can have at most two terms.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery polynomial is a binomial.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA binomial may have degree 5.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 14
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tZero of a polynomial is always 0.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 15
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA polynomial cannot have more than one zero.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 16
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe degree of the sum of two polynomials each of degree 5 is always 5.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 17
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "The constant polynomial 0 is called the ________________.",
          "ans": "zero polynomial",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Polynomials having only one term are called _____________.",
          "ans": "monomials",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Polynomials having only two terms are called _____________.",
          "ans": "binomials",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Polynomials having only three terms are called ____________.",
          "ans": "trinomials",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "The degree of a non-zero constant polynomial is ____________.",
          "ans": "zero",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A polynomial of degree one is called a ____________ polynomial.",
          "ans": "linear",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A polynomial of degree two is called a ____________ polynomial.",
          "ans": "quadratic",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A polynomial of degree three is called a __________ polynomial.",
          "ans": "cubic",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The degree of the zero polynomial is ____________.",
          "ans": "undefined",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A non-zero constant polynomial has ____________ zero.",
          "ans": "no",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Every real number is a zero of the ____________ polynomial.",
          "ans": "zero",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Dividend = Divisor × ____________ + Remainder",
          "ans": "Quotient",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "By factor theorem, <i>x</i> - a is a factor of <i>p</i>(<i>x</i>), if ____________.",
          "ans": "<i>p</i>(a) = 0",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "By factor theorem, <i>p</i>(a) = 0 if ____________ is a factor of <i>p</i>(<i>x</i>).",
          "ans": "<i>x</i> - a",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(<i>x</i> + <i>y</i>)<sup>2</sup> = ________________.",
          "ans": "<i>x</i><sup>2</sup> + 2<i>xy</i> + <i>y</i><sup>2</sup>",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(<i>x</i> - <i>x</i>)<sup>2</sup> = ________________.",
          "ans": "<i>x</i><sup>2</sup> - 2<i>xy</i> + <i>y</i><sup>2</sup>.",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "<i>x</i><sup>2</sup> - <i>y</i><sup>2</sup> = ________________.",
          "ans": "(<i>x</i> + <i>y</i>)(<i>x</i> - <i>y</i>)",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(<i>x</i> + a)(<i>x</i> + b) = ________________.",
          "ans": "<i>x</i><sup>2</sup> + (a + b)<i>x</i> + ab",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(<i>x</i> + <i>y</i> + <i>z</i>)<sup>2</sup> = ________________.",
          "ans": "<i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> + <i>z</i><sup>2</sup> + 2<i>xy</i> + 2<i>yz</i> + 2<i>zx</i>",
          "code": "FIB",
          "val": 19
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(<i>x</i> + <i>y</i>)<sup>3</sup> = ________________.",
          "ans": "<i>x</i><sup>3</sup> + <i>y</i><sup>3</sup> + 3<i>xy</i>(<i>x</i> + <i>y</i>)",
          "code": "FIB",
          "val": 20
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(<i>x</i> - <i>y</i>)<sup>3</sup> = ________________.",
          "ans": "<i>x</i><sup>3</sup> - <i>y</i><sup>3</sup> - 3<i>xy</i>(<i>x</i> - <i>y</i>)",
          "code": "FIB",
          "val": 21
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise: <br>2<i>x</i><sup>3</sup> - 3<i>x</i><sup>2</sup> - 17<i>x</i> + 30",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2d1a.jpg",
            "width": "490",
            "height": "576"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise: <br><i>x</i><sup>3</sup> - 6<i>x</i><sup>2</sup> + 11<i>x</i> - 6",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2d2a.jpg",
            "width": "360",
            "height": "420"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "If the polynomials az<sup>3</sup> + 4z<sup>2</sup> + 3z - 4 and z<sup>3</sup> - 4z + a leave the same remainder when divided by z - 3, find the value of a.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2d3a.jpg",
            "width": "430",
            "height": "390"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2d4.jpg",
            "width": "410",
            "height": "45"
          },
          "ansimg": {
            "image": "ch2d4a.jpg",
            "width": "350",
            "height": "486"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Prove that (a + b + c)<sup>3</sup> - a<sup>3</sup> - b<sup>3</sup> - c<sup>3</sup> = 3(a + b)(b + c)(c + a).",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2d5a.jpg",
            "width": "480",
            "height": "360"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Which of the following expressions are polynomial in one variable and which are not? State reasons for your answer.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s1.jpg",
            "width": "390",
            "height": "70"
          },
          "ansimg": {
            "image": "ch2s1a.jpg",
            "width": "660",
            "height": "160"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the value of the polynomial 3<i>x</i><sup>3</sup> - 4<i>x</i><sup>2</sup> + 7<i>x</i> - 5, when <i>x</i> = 3.",
          "ans": "When <i>x</i> = 3 <br>3<i>x</i><sup>3</sup> – 4<i>x</i><sup>2</sup> + 7<i>x</i> – 5 <br>= 3(3)<sup>3</sup> – 4(3)<sup>2</sup> + 7(3) – 5 <br>= 81 – 36 + 21 – 5 <br>= 61",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the value of the polynomial 3<i>x</i><sup>3</sup> - 4<i>x</i><sup>2</sup> + 7<i>x</i> - 5, when <i>x</i> = -3.",
          "ans": "When <i>x</i> = -3 <br>3<i>x</i><sup>3</sup> – 4<i>x</i><sup>2</sup> + 7<i>x</i> – 5 <br>= 3(-3)<sup>3</sup> – 4(-3)<sup>2</sup> + 7(3) – 5 <br>= -81 – 36 + (-21) – 5 <br>= -143",
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find <i>p</i>(0), <i>p</i>(1), <i>p</i>(-2) for the following polynomial: <br><i>p</i>(<i>x</i>) = 10<i>x</i> - 4<i>x</i><sup>2</sup> - 3",
          "ans": "Cosider <i>p</i>(<i>x</i>) = 10<i>x</i> – 4<i>x</i><sup>2</sup> – 3 <br>Put <i>x</i> = 0 ; <i>p</i> (0) = 10. (0) – 4(0)<i>2</i> – 3 = – 3 <br>Put <i>x</i> = 1 ; <i>p</i>(1) = 10. (1) – 4(1)<i>2</i> – 3 = 10 – 4 – 3 = 3 <br>Put <i>x</i> = – 2 ; <i>p</i>(– 2) = 10 (–2) – 4 (–2)<i>2</i> – 3 = – 20 – 16 – 3 = –39",
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find <i>p</i>(0), <i>p</i>(1), <i>p</i>(-2) for the following polynomial: <br><i>p</i>(y) = (y + 2)(y - 2)",
          "ans": "We have <i>p</i>(y) = (y + 2) (y – 2) <br>Put y = 0 ; <i>p</i>(0) = (0 + 2) (0 – 2) = 2 × (–2) = –4 <br>Put y = 1 ; <i>p</i>(1) = (1 + 2) (1 – 2) = 3 × (–1) = –3 <br>Put y = –2; <i>p</i>(–2) = (–2 +2) (–2 – 2) = (0) × (–4) = 0",
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Verify whether the following is true or false: <br>-3 is a zero of <i>x</i> - 3.",
          "ans": "Let <i>p</i>(<i>x</i>) = <i>x</i> – 3 <br>⇒ <i>p</i>(–3) = –3 – 3 = –6 ≠ 0 <br>Thus, –3 is not a zero of <i>p</i>(<i>x</i>). <br>The statement is false.",
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Verify whether the following is true or false:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s7.jpg",
            "width": "150",
            "height": "40"
          },
          "ansimg": {
            "image": "ch2s7a.jpg",
            "width": "340",
            "height": "150"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Verify whether the following is true or false:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s8.jpg",
            "width": "150",
            "height": "40"
          },
          "ansimg": {
            "image": "ch2s8a.jpg",
            "width": "360",
            "height": "160"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Verify whether the following is true or false: <br>0 and 2 are the zeroes of <i>t</i><sup>2</sup> - 2<i>t</i>.",
          "ans": "Let <i>p</i>(<i>t</i>) = <i>t</i><sup>2</sup> – 2<i>t</i> <br>⇒ <i>p</i>(0) = (0)<sup>2<sup> – 2(0) = 0 <br>and <i>p</i>(2) = (2)<sup>2</sup> – 2 × 2 = 0 <br>Hence, 0 and 2 are the zeroes of <i>p</i>(<i>t</i>). <br>The statement is true.",
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Verify whether the following is true or false: <br>-3 is a zero of y<sup>2</sup> + y - 6.",
          "ans": "Let <i>p</i>(y) = y<sup>2</sup> + y – 6 <br>⇒ <i>p</i>(–3) = (–3)<sup>2</sup> + (–3) – 6 = 9 – 3 – 6 = 6 – 6 = 0 <br>Thus, – 3, is a zero of p (y). <br>The Statement is true.",
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the zero of the polynomial of the following: <br><i>p</i>(<i>x</i>) = <i>x</i> - 4",
          "ans": "<i>p</i>(<i>x</i>) = <i>x</i> – 4 <br>For zero, <i>p</i>(<i>x</i>) = 0 <br>⇒ <i>x</i> – 4 = 0 <br>⇒ <i>x</i> = 4",
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the zero of the polynomial of the following: <br><i>g</i>(<i>x</i>) = 3 - 6<i>x</i>",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s12a.jpg",
            "width": "140",
            "height": "130"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the zero of the polynomial of the following: <br><i>p</i>(<i>x</i>) = 2<i>x</i> - 7",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s13.jpg",
            "width": "140",
            "height": "130"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the zero of the polynomial of the following: <br><i>h</i>(y) = 2y",
          "ans": "<i>h</i>(y) = 2y <br>For zero, <i>h</i>(y) = 0 <br>⇒ 2y = 0 <br>⇒ y = 0",
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "By remainder theorem, find the remainder, when <i>p</i>(<i>x</i>) is divided by <i>g</i>(<i>x</i>), where <i>p</i>(<i>x</i>) = <i>x</i><sup>3</sup> - 2<i>x</i><sup>2</sup> - 4<i>x</i> - 1, <i>g</i>(<i>x</i>) = <i>x</i> + 1.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s15a.jpg",
            "width": "410",
            "height": "180"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "By remainder theorem, find the remainder, when <i>p</i>(<i>x</i>) = <i>x</i><sup>3</sup> - 3<i>x</i><sup>2</sup> + 4<i>x</i> + 50, <i>g</i>(<i>x</i>) = <i>x</i> - 3.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s16a.jpg",
            "width": "316",
            "height": "180"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "By remainder theorem, find the remainder, when <i>p</i>(<i>x</i>) = 4<i>x</i><sup>3</sup> - 12<i>x</i><sup>2</sup> + 14<i>x</i> - 3, <i>g</i>(<i>x</i>) = 2<i>x</i> - 1.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s17a.jpg",
            "width": "370",
            "height": "430"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "By remainder theorem, find the remainder, when",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s18.jpg",
            "width": "240",
            "height": "40"
          },
          "ansimg": {
            "image": "ch2s18a.jpg",
            "width": "330",
            "height": "320"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Show that, <i>x</i> + 3 is a factor of 69 + 11<i>x</i> - <i>x</i><sup>2</sup> + <i>x</i><sup>3</sup>.",
          "ans": "By factor theorem, the polynomial (<i>x</i> + 3) will be a factor of <br><i>p</i>(<i>x</i>) = 69 + 11<i>x</i> – <i>x</i><sup>2</sup> + <i>x</i><sup>3</sup> if <i>p</i>(–3) = 0. <br>Now, <i>p</i>(–3) = 69 + 11 × (–3) – (–3)<sup>2</sup> + (–3)<sup>3</sup> <br>= 69 – 33 – 9 – 27 <br>= 69 – 69 = 0 <br>∴ (<i>x</i> + 3) divides <i>p</i>(<i>x</i>) completely. <br>Thus, (<i>x</i> + 3) is a factor of given polynomial.",
          "code": "SATQ",
          "options": null,
          "val": 19,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Show that, 2<i>x</i> - 3 is a factor of <i>x</i> + 2<i>x</i><sup>3</sup> - 9<i>x</i><sup>2</sup> + 12.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 20,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s20.jpg",
            "width": "200",
            "height": "250"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Determine the following polynomial has (<i>x</i> - 2) as a factor: <br>3<i>x</i><sup>2</sup> + 6<i>x</i> - 24",
          "ans": "Let <i>p</i>(<i>x</i>) = 3<i>x</i><sup>2</sup> + 6<i>x</i> – 24 <br><i>x</i> – 2 = 0 ⇒ <i>x</i> = 2 <br>Now, <i>x</i>(2) = 3 × (2)<sup>2</sup> + 6 × 2 – 24 = 12 + 12 – 24 = 0 <br>Thus, (<i>x</i> – 2) is a factor of <i>p</i>(<i>x</i>).",
          "code": "SATQ",
          "options": null,
          "val": 21,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Determine the following polynomial has (<i>x</i> - 2) as a factor: <br>4<i>x</i><sup>2</sup> + <i>x</i> - 2",
          "ans": "Let <i>p</i>(<i>x</i>) = 4<i>x</i><sup>2</sup> + <i>x</i> – 2, <i>x</i> – 2 = 0 ⇒ <i>x</i> = 2 <br><i>p</i>(2) = 4 × (2)<sup>2</sup> + 2 – 2 = 16 + 2 – 2 = 16 ≠ 0 <br>Thus, (<i>x</i> – 2) is not a factor of <i>p</i>(<i>x</i>).",
          "code": "SATQ",
          "options": null,
          "val": 22,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Check whether <i>p</i>(<i>x</i>) is a multiple of g(x) or not: <br><i>p</i>(<i>x</i>) = <i>x</i><sup>3</sup> - 5<i>x</i><sup>2</sup> + 4<i>x</i> - 3, <i>g</i>(<i>x</i>) = <i>x</i> - 2",
          "ans": "<i>p</i>(<i>x</i>) = <i>x</i><sup>3</sup> – 5<i>x</i><sup>2</sup> + 4<i>x</i> – 3 and <i>g</i>(<i>x</i>) = <i>x</i> – 2, <i>g</i>(<i>x</i>) = 0 ⇒ <i>x</i> – 2 = 0 ⇒ <i>x</i> = 2 <br><i>p</i>(2) = (2)<sup>3</sup> – 5(2)<sup>2</sup> + 4(2) – 3 <br>= 8 – 20 + 8 – 3 <br>= 16 – 23 <br>= –7 ≠ 0 <br>Since <i>p</i>(2) ≠ 0, <i>p</i>(<i>x</i>) is not a multiple of <i>g</i>(<i>x</i>) = <i>x</i> – 2",
          "code": "SATQ",
          "options": null,
          "val": 23,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Check whether <i>p</i>(<i>x</i>) is a multiple of <i>g</i>(<i>x</i>) or not: <br><i>p</i>(<i>x</i>) = 2<i>x</i><sup>3</sup> - 11<i>x</i><sup>2</sup> - 4<i>x</i> + 5, <i>g</i>(<i>x</i>) = 2<i>x</i> + 1",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 24,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s24a.jpg",
            "width": "490",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If <i>x</i> + 1 is a factor of a<i>x</i><sup>3</sup> + <i>x</i><sup>2</sup> - 2<i>x</i> + 4<i>a</i> - 9, find the value of <i>a</i>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 25,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s25.jpg",
            "width": "390",
            "height": "230"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: <br><i>x</i><sup>2</sup> + 9<i>x</i> + 18",
          "ans": "<i>x</i><sup>2</sup> + 9<i>x</i> + 18 <br>= <i>x</i><sup>2</sup> + 6<i>x</i> + 3<i>x</i> + 18 <br>= <i>x</i>(<i>x</i> + 6) + 3(<i>x</i> + 6) <br>= (<i>x</i> + 3) (<i>x</i> + 6)",
          "code": "SATQ",
          "options": null,
          "val": 26,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: <br>6<i>x</i><sup>2</sup> + 7<i>x</i> - 3",
          "ans": "6<i>x</i><sup>2</sup> + 76<i>x</i> – 3 <br>= 6<i>x</i><sup>2</sup> + 9<i>x</i> – 2<i>x</i> – 3 <br>= 3<i>x</i>(2<i>x</i> + 3) – 1 (2<i>x</i> + 3) <br>= (2<i>x</i> + 3) (3<i>x</i> – 1)",
          "code": "SATQ",
          "options": null,
          "val": 27,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: <br>2<i>x</i><sup>2</sup> - 7<i>x</i> - 15",
          "ans": "2<i>x</i><sup>2</sup> - 7<i>x</i> - 15 <br>= 2<i>x</i><sup>2</sup> – 10<i>x</i> + 3<i>x</i> – 15 <br>= 2<i>x</i>(<i>x</i> – 5) + 3(<i>x</i> – 5) <br>= (<i>x</i> – 5) (2<i>x</i> + 3)",
          "code": "SATQ",
          "options": null,
          "val": 28,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: <br>84 - 2s - 2s<sup>2</sup>",
          "ans": "84 - 2s - 2s<sup>2</sup> <br>= – 2s<sup>2</sup> – 2s + 84 <br>= – 2s<sup>2</sup> – 14s + 12s + 84 <br>= – 2s(s + 7) + 12(s + 7) <br>= (s + 7) (– 2s + 12) <br>= 2(s + 7) (6 – s)",
          "code": "SATQ",
          "options": null,
          "val": 29,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: <br><i>x</i><sup>3</sup> + <i>x</i><sup>2</sup> - 4<i>x</i> - 4",
          "ans": "Let <i>p</i>(<i>x</i>) = <i>x</i><sup>3</sup> + <i>x</i><sup>2</sup> - 4<i>x</i> - 4 <br>= <i>x</i><sup>2</sup> (<i>x</i> + 1) – 4 (<i>x</i> + 1) <br>= (<i>x</i> + 1) (<i>x</i><sup>2</sup> – 4) <br>= (<i>x</i> + 1) [<i>x</i><sup>2</sup> – (2)<sup>2</sup>] <br>= (<i>x</i> + 1) (<i>x</i> + 2) (<i>x</i> – 2)",
          "code": "SATQ",
          "options": null,
          "val": 30,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: <br>3<i>x</i><sup>3</sup> - <i>x</i><sup>2</sup> - 3<i>x</i> + 1",
          "ans": "Let <i>p</i>(<i>x</i>) = 3<i>x</i><sup>3</sup> – <i>x</i><sup>2</sup> – 3<i>x</i> + 1 <br>= <i>x</i><sup>2</sup>(3<i>x</i> – 1) – 1(3<i>x</i> – 1) <br>= (x2 – 1) (3x – 1) <br>= (<i>x</i><sup>2</sup> – 12) (3<i>x</i> – 1) <br>= (<i>x</i> + 1) (<i>x</i> – 1) (3<i>x</i> – 1)",
          "code": "SATQ",
          "options": null,
          "val": 31,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Using suitable identity, evaluate the following: <br>103<sup>3</sup>",
          "ans": "103<sup>3</sup> = (100 + 3)<sup>3</sup> <br>= (100)<sup>3</sup> + (3)<sup>3</sup> + 3 (100) (3) (100 + 3) <br>= 1000000 + 27 + 92700 <br>= 1092727",
          "code": "SATQ",
          "options": null,
          "val": 32,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Using suitable identity, evaluate the following: <br>101 × 102",
          "ans": "101 × 102 = (100 + 1) (100 + 2) <br>= (100)<sup>2</sup> + (1 + 2) × 100 + (1 × 2) <br>= 10302",
          "code": "SATQ",
          "options": null,
          "val": 33,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Using suitable identity, evaluate the following: <br>999</sup>2</sup>",
          "ans": "999<sup>2</sup> = (1000 – 1)<sup>2</sup> <br>= (1000)<sup>2</sup> + (1)<sup>2</sup> – 2 × 1 × 1000 <br>= 1000000 + 1 – 2000 <br>= 998001",
          "code": "SATQ",
          "options": null,
          "val": 34,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following: <br>4<i>x</i><sup>2</sup> + 20<i>x</i> + 25",
          "ans": "4<i>x</i><sup>2</sup> + 20<i>x</i> + 25 <br>= (2<i>x</i>)<sup>2</sup> + 2. (2<i>x</i>) (5) + (5)<sup>2</sup> <br>= (2<i>x</i> + 5)<sup>2</sup> [∵ (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>]",
          "code": "SATQ",
          "options": null,
          "val": 35,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following: <br>9y<sup>2</sup> - 66yz + 121z<sup>2</sup>",
          "ans": "9y<sup>2</sup> – 66yz + 121z<sup>2</sup> <br>= (3y)<sup>2</sup> – 2. (3y) (11z) + (11z)<sup>2</sup> <br>= (3y – 11z)<sup>2</sup> [∵ a<sup>2</sup> – 2ab + b<sup>2</sup> = (a – b)<sup>2</sup>]",
          "code": "SATQ",
          "options": null,
          "val": 36,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 37,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s37.jpg",
            "width": "140",
            "height": "50"
          },
          "ansimg": {
            "image": "ch2s37a.jpg",
            "width": "460",
            "height": "290"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Expand the following: <br>(4<i>a</i> – <i>b</i> + 2<i>c</i>)<sup>2</sup>",
          "ans": "(4<i>a</i> – <i>b</i> + 2<i>c</i>)<sup>2</sup> <br>= [4<i>a</i> + (–<i>b</i>) + 2<i>c</i>]<sup>2</sup> <br>= (4<i>a</i>)2 + (–<i>b</i>)2 + (2<i>c</i>)<sup>2</sup> + 2(4<i>a</i>) (–<i>b</i>) + 2 (–<i>b</i>) (2<i>c</i>) + 2 (2<i>c</i>) (4<i>a</i>) <br>[∵ (<i>x</i> + <i>y</i> + <i>z</i>)<sup>2</sup> = <i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> + <i>z</i><sup>2</sup> + 2<i>xy</i> +2<i>yz</i> +2<i>zx</i>] <br>= 16<i>a</i><sup>2</sup> + <i>b</i><sup>2</sup> + 4<i>c</i><sup>2</sup> – 8<i>ab</i> – 4<i>bc</i> + 16<i>ca</i>",
          "code": "SATQ",
          "options": null,
          "val": 38,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Expand the following: <br>(3<i>a</i> - 5<i>b</i> - <i>c</i>)<sup>2</sup>",
          "ans": "(3<i>a</i> – 5<i>b</i> – <i>c</i>)<sup>2</sup> <br>= [3<i>a</i> + (–5<i>b</i>) + (–<i>c</i>)]<sup>2</sup> <br>= 9<i>a</i><sup>2</sup> + 25<i>b</i><sup>2</sup> + <i>c</i><sup>2</sup> + 2 (3<i>a</i>) (–5<i>b</i>) + 2 (–5<i>b</i>) (–<i>c</i>) + 2 (–<i>c</i>) (3<i>a</i>) <br>[∵ (<i>x</i> + <i>y</i> + <i>z</i>)<sup>2</sup> = <i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> + <i>z</i><sup>2</sup> + 2<i>xy</i> +2<i>yz</i> +2<i>zx</i>] <br>= 9<i>a</i><sup>2</sup> + 25<i>b</i><sup>2</sup> + <i>c</i><sup>2</sup> – 30<i>ab</i> + 10<i>bc</i> – 6<i>ca</i>",
          "code": "SATQ",
          "options": null,
          "val": 39,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Expand the following: <br>(-<i>x</i> + 2<i>y</i> - 3<i>z</i>)<sup>2</sup>",
          "ans": "(–<i>x</i> + 2<i>y</i> – 3<i>z</i>)<sup>2</sup> <br>= [(–<i>x</i>) +2<i>y</i> + (–3<i>z</i>)]<sup>2</sup> <br>= (–<i>x</i>)<sup>2</sup> + (2<i>y</i>)<sup>2</sup> + (–3<i>z</i>)<sup>2</sup> + 2 (–<i>x</i>) (2<i>y</i>) + 2 (2<i>y</i>) (–3<i>z</i>) + 2 (–3<i>z</i>) (–<i>x</i>) <br>= <i>x</i><sup>2</sup> + 4<i>y</i><sup>2</sup> + 9<i>z</i><sup>2</sup> – 4<i>xy</i> – 12<i>yz</i> + 6<i>zx</i>",
          "code": "SATQ",
          "options": null,
          "val": 40,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following: <br>9<i>x</i><sup>2</sup> + 4<i>y</i><sup>2</sup> + 16<i>z</i><sup>2</sup> + 12<i>xy</i> - 16<i>yz</i> - 24<i>xz</i>",
          "ans": "9<i>x</i><sup>2</sup> + 4<i>y</i><sup>2</sup> + 16<i>z</i><sup>2</sup> + 12<i>xy</i> - 16<i>yz</i> - 24<i>xz</i> <br>= (3<i>x</i>)<sup>2</sup> + (2<i>y</i>)<sup>2</sup> + (–4<i>z</i>)<sup>2</sup> + 2(3<i>x</i>) (2<i>y</i>) + 2(2<i>y</i>) (–4<i>z</i>) + 2 (–4<i>z</i>) (3<i>x</i>) <br>[∵ (<i>a</i> + <i>b</i> + <i>c</i>)<sup>2</sup> = <i>a</i><sup>2</sup> + <i>b</i><sup>2</sup> + <i>c</i><sup>2</sup> + 2<i>ab</i> + 2<i>bc</i> + 2<i>ca</i>] <br>= (3<i>x</i> + 2<i>y</i> – 4<i>z</i>)<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 41,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following: <br>25<i>x</i><sup>2</sup> + 16<i>y</i><sup>2</sup> + 4<i>z</i><sup>2</sup> - 40<i>xy</i> + 16<i>yz</i> - 20<i>xz</i>",
          "ans": "25<i>x</i><sup>2</sup> + 16<i>y</i><sup>2</sup> + 4<i>z</i><sup>2</sup> - 40<i>xy</i> + 16<i>yz</i> - 20<i>xz</i> <br>= (–5<i>x</i>)<sup>2</sup> + (4<i>y</i>)<sup>2</sup> + (2<i>z</i>)<sup>2</sup> + 2(–5<i>x</i>) (4<i>y</i>) + 2 (4<i>y</i>) (2<i>z</i>) + 2(2<i>z</i>) (–5<i>x</i>) <br>= (–5<i>x</i> + 4<i>y</i> + 2<i>z</i>)<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 42,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following: <br>16<i>x</i><sup>2</sup> + 4<i>y</i><sup>2</sup> + 9<i>z</i><sup>2</sup> - 16<i>xy</i> - 12<i>yz</i> + 24<i>xz</i>",
          "ans": "16<i>x</i><sup>2</sup> + 4<i>y</i><sup>2</sup> + 9<i>z</i><sup>2</sup> - 16<i>xy</i> - 12<i>yz</i> + 24<i>xz</i> <br>= (4<i>x</i>)<sup>2</sup> + (–2<i>y</i>)<sup>2</sup> + (3z)2 + 2 (4x) (–2y) + 2 (–2y) (3z) + 2 (3z) (4x) <br>= (4x – 2y + 3z)2",
          "code": "SATQ",
          "options": null,
          "val": 43,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Expand the following: <br>(3a - 2b)<sup>3</sup>",
          "ans": "(3a – 2b)<sup>3</sup> <br>= (3a)<sup>3</sup> – (2b)<sup>3</sup> – 3(3a) (2b) (3a – 2b) [∵ (a – b)<sup>3</sup> = a<sup>3</sup> – b<sup>3</sup> – 3ab(a – b)] <br>= 27a<sup>3</sup> – 8b<sup>3</sup> – 18ab × 3a + 18ab × 2b <br>= 27a<sup>3</sup> – 8b<sup>3</sup> – 54a<sup>2</sup>b + 36ab<sup>2</sup> <br>= 27a<sup>3</sup> – 54a<sup>2</sup>b + 36ab<sup>2</sup> – 8b<sup>3</sup>",
          "code": "SATQ",
          "options": null,
          "val": 44,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Expand the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 45,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s45.jpg",
            "width": "71",
            "height": "51"
          },
          "ansimg": {
            "image": "ch2s45a.jpg",
            "width": "290",
            "height": "170"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Expand the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 46,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s46.jpg",
            "width": "80",
            "height": "53"
          },
          "ansimg": {
            "image": "ch2s46a.jpg",
            "width": "350",
            "height": "230"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following: <br>1 – 64a<sup>3</sup> – 12a + 48a<sup>2</sup>",
          "ans": "1 – 64a<sup>3</sup> – 12a + 48a<sup>2</sup> <br>= (1)<sup>3</sup> – (4a)<sup>3</sup> – 3. (1)<sup>2</sup> (4a) + 3(4a)<sup>2</sup> (1) <br>= (1 – 4a)<sup>3</sup> [∵ a<sup>3</sup> – b<sup>3</sup> – 3a<sup>2</sup>b + 3ab<sup>2</sup> = (a – b)<sup>3</sup>] <br>= (1 – 4a) (1 – 4a) (1 – 4a)",
          "code": "SATQ",
          "options": null,
          "val": 47,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the following:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 48,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s48.jpg",
            "width": "191",
            "height": "54"
          },
          "ansimg": {
            "image": "ch2s48a.jpg",
            "width": "540",
            "height": "230"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Without actually calculating the cubes, find the value of:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 49,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s49.jpg",
            "width": "142",
            "height": "57"
          },
          "ansimg": {
            "image": "ch2s49a.jpg",
            "width": "360",
            "height": "360"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Without actually calculating the cubes, find the value of: <br>(0.2)<sup>3</sup> - (0.3)<sup>3</sup> + (0.1)<sup>3</sup>",
          "ans": "(0.2)<sup>3</sup> - (0.3)<sup>3</sup> + (0.1)<sup>3</sup> <br>= (0.2)<sup>3</sup> + (– 0.3)<sup>3</sup> + (0.1)<sup>3</sup> <br>Take a = 0.2, b = – 0.3 and c = 0.1 <br>Observe that a + b + c = 0.2 + (– 0.3) + 0.1 = 0 <br>If a + b + c = 0, then a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> = 3abc <br>∵ (0.2)<sup>3</sup> + (– 0.3)<sup>3</sup> + (0.1)<sup>3</sup> <br>= 3 (0.2) (–0.3) (0.1) <br>= –0.018",
          "code": "SATQ",
          "options": null,
          "val": 50,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If a + b + c = 9 and ab + bc + ca = 26, find a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup>.",
          "ans": "(a + b + c)<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> +c<sup>2</sup> + 2(ab + bc + ca) <br>⇒ (9)<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> +c<sup>2</sup> + 2 × 26 <br>⇒ a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> = 81 – 52 = 29.",
          "code": "SATQ",
          "options": null,
          "val": 51,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If a + b + c = 7 and ab + bc + ca = 20, find the value of a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup>.",
          "ans": "(a + b + c)<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> + 2(ab + bc + ca) <br>∴ (7)<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> + 2(20) <br>∴ 49 = a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> + 40 <br>∴ a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> = 49 – 40 = 9",
          "code": "SATQ",
          "options": null,
          "val": 52,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 52,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s52.jpg",
            "width": "198",
            "height": "45"
          },
          "ansimg": {
            "image": "ch2s52a.jpg",
            "width": "263",
            "height": "407"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 53,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s53.jpg",
            "width": "230",
            "height": "50"
          },
          "ansimg": {
            "image": "ch2s53a.jpg",
            "width": "360",
            "height": "420"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify: (5a + 3b)<sup>3</sup> - (5a - 3b)<sup>3</sup>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 54,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2s54a.jpg",
            "width": "553",
            "height": "187"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Which of the following expressions are polynomials? Justify your answer:",
          "ans": "Polynomials: (i), (ii), (iv), (vii) because the exponent of the variable after simplification in each of these is a whole number.",
          "code": "SATQ",
          "options": null,
          "val": 55,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch2s55.jpg",
            "width": "440",
            "height": "220"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the co-efficients of <i>x</i><sup>2</sup> in the following: <br>5 - <i>x</i><sup>2</sup> + <i>x</i>",
          "ans": "The co-efficient of <i>x</i><sup>2</sup> is –1.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the co-efficients of <i>x</i><sup>2</sup> in the following: <br>3 + <i>x</i><sup>2</sup> + <i>x</i><sup>3</sup>",
          "ans": "The co-efficient of <i>x</i><sup>2</sup> is 1.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the co-efficients of <i>x</i><sup>2</sup> in the following:",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch2vs3.jpg",
            "width": "60",
            "height": "35"
          },
          "ansimg": {
            "image": "ch2vs3a.jpg",
            "width": "170",
            "height": "40"
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the co-efficients of <i>x</i><sup>2</sup> in the following:",
          "ans": "The co-efficient of <i>x</i><sup>2</sup> is 0.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch2vs4.jpg",
            "width": "60",
            "height": "30"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Give one example each of binomial of degree 43 and of a monomial of degree 1003.",
          "ans": null,
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch2vs5.jpg",
            "width": "470",
            "height": "40"
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the degree of the following polynomial: 11",
          "ans": "The only term is 11 which can be written as 11 <i>x</i><sup>0</sup> and so the exponent is 0. Therefore, the degree is 0.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 6
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the degree of the following polynomial: 9<i>t</i> − √11",
          "ans": "Highest power term in <i>p</i>(<i>t</i>) is it and the exponent is 1. So, the degree is 1.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 7
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the degree of the following polynomial: 9 - y<sup>2</sup>",
          "ans": "Highest power term in <i>p</i>(y) is –y<sup>2</sup> and the exponent is 2. So, the degree is 2.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 8
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the degree of the following polynomial: 7<i>x</i><sup>3</sup> + 5<i>x</i><sup>2</sup> + 11<i>x</i> + 3",
          "ans": "Highest power term in <i>p</i>(<i>x</i>) is 7<i>x</i><sup>3</sup> and the exponent is 3. So, the degree is 3.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 9
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following as linear, quadratic and cubic polynomial: <br><i>x</i><sup>2</sup> + 5<i>x</i> + 3",
          "ans": "Quadratic",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 10
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following as linear, quadratic and cubic polynomial: <br>7<i>x</i> - 3<i>x</i><sup>3</sup>",
          "ans": "Cubic",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 11
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following as linear, quadratic and cubic polynomial: <br>5y + 13y<sup>2</sup> + 7",
          "ans": "Quadratic",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 12
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following as linear, quadratic and cubic polynomial: <br>7 + 3x",
          "ans": "Linear",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 13
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following as linear, quadratic and cubic polynomial: <br>9<i>t</i>",
          "ans": "Linear",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 14
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following as linear, quadratic and cubic polynomial: <br>3s<sup>2</sup>",
          "ans": "Quadratic",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 15
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Classify the following as linear, quadratic and cubic polynomial: <br>11<i>x</i><sup>3</sup>",
          "ans": "Cubic",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 16
        }
      ],
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      [],
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      [],
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      [],
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      [],
      [],
      [],
      []
    ],
    "pbq": "ch2_pbq",
    "gowf": "ch2_gowf",
    "afow": "ch2_afow",
    "cs": "ch2_cs",
    "afq": "ch2_afq",
    "fib": "ch2_fib",
    "grade": "Grade 9",
    "mcq": "ch2_mcq",
    "vsaq": "ch2_vsaq",
    "laq": "ch2_laq",
    "tf": "ch2_tf",
    "co": "ch2_co",
    "nf": "ch2_nf",
    "mtf": "ch2_mtf",
    "yn": "ch2_yn",
    "saq": "ch2_saq",
    "dtf": "ch2_dtf",
    "map": "ch2_map",
    "ctt": "ch2_ctt",
    "un": "ch2_un",
    "ctco": "ch2_ctco",
    "grf": "ch2_grf",
    "snc": "ch2_snc",
    "jtf": "ch2_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch3",
    "chapterName": "Chapter 3 - Coordinate Geometry",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Point (–3, 5) lies in the",
          "ans": "(b) second quadrant",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) first quadrant",
            "(b) second quadrant",
            "(c) third quadrant",
            "(d) fourth quadrant"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Signs of the abscissa and ordinate of a point in the second quadrant are respectively.",
          "ans": "(c) –, +",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) +, +",
            "(b) –, –",
            "(c) –, +",
            "(d) +, –"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Point (0, –7) lies ",
          "ans": "(c) on the y-axis",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) on the x-axis",
            "(b) in the second quadrant",
            "(c) on the y-axis",
            "(d) in the fourth quadrant"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Point (–10, 0) lies",
          "ans": "(a) on the negative direction of the x-axis.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) on the negative direction of the x-axis.",
            "(b) on the negative direction of the y-axis.",
            "(c) in the third quadrant",
            "(d) in the fourth quadrant"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Abscissa of all the points on the x-axis is",
          "ans": "(d) any number",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) 2",
            "(d) any number"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Ordinate of all points on the x-axis is",
          "ans": "(a) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) –1",
            "(d) any number"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point at which the two coordinate axes meet is called the",
          "ans": "(c) origin",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) abscissa",
            "(b) ordinate",
            "(c) origin",
            "(d) quadrant"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A point both of whose coordinates are negative will lie in",
          "ans": "(c) III quadrant",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) I quadrant",
            "(b) II quadrant",
            "(c) III quadrant",
            "(d) IV quadrant"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Points (1, –1), (2, –2), (4, –5), (–3, –4)",
          "ans": "(d) do not lie in the same quadrant",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) lie in II quadrant",
            "(b) lie in III quadrant",
            "(c) lie in IV quadrant",
            "(d) do not lie in the same quadrant"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If y-coordinate of a point is zero, then this point always lies",
          "ans": "(c) on x-axis",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) in I quadrant",
            "(b) in II quadrant",
            "(c) on x-axis",
            "(d) on y-axis"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point (–5, 2) and (2, –5) lie in the",
          "ans": "(c) II and IV quadrants, respectively",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) same quadrant",
            "(b) II and III quadrants, respectively",
            "(c) II and IV quadrants, respectively",
            "(d) IV and II quadrants, respectively"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has",
          "ans": "(d) y-coordinate = 5 or – 5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) x-coordinate = – 5",
            "(b) y-coordinate = 5 only",
            "(c) y-coordinate = – 5 only",
            "(d) y-coordinate = 5 or – 5"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Point (–3, 5) lies in the",
          "ans": "(b) second quadrant",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) first quadrant",
            "(b) second quadrant",
            "(c) third quadrant",
            "(d) fourth quadrant"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Signs of the abscissa and ordinate of a point in the second quadrant are respectively",
          "ans": "(c) –, +",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) +, +",
            "(b) –, –",
            "(c) –, +",
            "(d) +, –"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Point (0, –7) lies",
          "ans": "(c) on the y-axis",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) on the x-axis",
            "(b) in the second quadrant",
            "(c) on the y-axis",
            "(d) in the fourth quadrant"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Point (– 10, 0) lies",
          "ans": "(a) on the negative direction of the x-axis",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) on the negative direction of the x-axis",
            "(b) on the negative direction of the y-axis",
            "(c) in the third quadrant",
            "(d) in the fourth quadrant"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Abscissa of all the points on the x-axis is",
          "ans": "(d) any number",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) 2",
            "(d) any number"
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Ordinate of all points on the x-axis is",
          "ans": "(a) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) – 1",
            "(d) any number"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point at which the two coordinate axes meet is called the",
          "ans": "(c) origin",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) abscissa",
            "(b) ordinate",
            "(c) origin",
            "(d) quadrant"
          ],
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A point both of whose coordinates are negative will lie in",
          "ans": "(c) III quadrant",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) I quadrant",
            "(b) II quadrant",
            "(c) III quadrant",
            "(d) IV quadrant"
          ],
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Points (1, –1), (2, –2), (4, –5), (–3, –4)",
          "ans": "(d) do not lie in the same quadrant",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) lie in II quadrant",
            "(b) lie in III quadrant",
            "(c) lie in IV quadrant",
            "(d) do not lie in the same quadrant"
          ],
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If y coordinate of a point is zero, then this point always lies",
          "ans": "(c) on x-axis",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) in I quadrant",
            "(b) in II quadrant",
            "(c) on x-axis",
            "(d) on y-axis"
          ],
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The points (–5, 2) and (2, –5) lie in the",
          "ans": "(c) II and IV quadrants, respectively",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) same quadrant",
            "(b) II and III quadrants, respectively",
            "(c) II and IV quadrants, respectively",
            "(d) IV and II quadrants, respectively"
          ],
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has",
          "ans": "(d) y coordinate = 5 or –5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) x coordinate = –5",
            "(b) y coordinate = 5 only",
            "(c) y coordinate = –5 only",
            "(d) y coordinate = 5 or –5"
          ],
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO which of the following figures is obtained?",
          "ans": "(b) Rectangle",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Square",
            "(b) Rectangle",
            "(c) Trapezium",
            "(d) Rhombus"
          ],
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If P (–1, 1), Q (3, –4), R(1, –1), S(–2, –3) and T (–4, 4) are plotted on the graph paper, then the point(s) in the fourth quadrant are",
          "ans": "(b) Q and R",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) P and T",
            "(b) Q and R",
            "(c) Only S",
            "(d) P and R"
          ],
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the coordinates of the two points are P (–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is",
          "ans": "(b) 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) –5",
            "(b) 1",
            "(c) –1",
            "(d) –2"
          ],
          "val": 27
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If P (5, 1), Q (8, 0), R (0, 4), S (0, 5) and O (0, 0) are plotted on the graph paper, then the point(s) on the x-axis are",
          "ans": "(d) Q and O",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) P and R",
            "(b) R and S",
            "(c) Only Q",
            "(d) Q and O"
          ],
          "val": 28
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Abscissa of a point is positive in",
          "ans": "(b) I and IV quadrants",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) I and II quadrants",
            "(b) I and IV quadrants",
            "(c) I quadrant only",
            "(d) II quadrant only"
          ],
          "val": 29
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The points whose abscissa and ordinate have different signs will lie in",
          "ans": "(d) II and IV quadrants",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) I and II quadrants",
            "(b) II and III quadrants",
            "(c) I and III quadrants",
            "(d) II and IV quadrants"
          ],
          "val": 30
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In the figure, coordinates of P are",
          "ans": "(b) (–2, 4)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (–4, 2)",
            "(b) (–2, 4)",
            "(c) (4, –2)",
            "(d) (2, –4)"
          ],
          "pic": {
            "image": "ch3m31.jpg",
            "width": "230",
            "height": "230"
          },
          "val": 31
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In the figure, the point identified by the coordinates (–5, 3) is",
          "ans": "(c) L",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) T",
            "(b) R",
            "(c) L",
            "(d) S"
          ],
          "pic": {
            "image": "ch3m32.jpg",
            "width": "300",
            "height": "300"
          },
          "val": 32
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point whose ordinate is 4 and which lies on y-axis is",
          "ans": "(b) (0, 4)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (4, 0)",
            "(b) (0, 4)",
            "(c) (1, 4)",
            "(d) (4, 2)"
          ],
          "pic": {
            "image": "ch3m32.jpg",
            "width": "300",
            "height": "300"
          },
          "val": 33
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the points P(0, 3), Q(1, 0), R(0, – 1), S(–5, 0), T(1, 2) do not lie on the x-axis?",
          "ans": "(c) P, R and T",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) P and R only",
            "(b) Q and S only",
            "(c) P, R and T",
            "(d) Q, S and T"
          ],
          "pic": {
            "image": "ch3m32.jpg",
            "width": "300",
            "height": "300"
          },
          "val": 34
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point which lies on y-axis at a distance of 5 units in the negative direction of y-axis is",
          "ans": "(c) (0, – 5)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (0, 5)",
            "(b) (5, 0)",
            "(c) (0, – 5)",
            "(d) (– 5, 0)"
          ],
          "pic": {
            "image": "ch3m32.jpg",
            "width": "300",
            "height": "300"
          },
          "val": 35
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The perpendicular distance of the point P (3, 4) from the y-axis is",
          "ans": "(a) 3",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3",
            "(b) 4",
            "(C) 5",
            "(d) 7"
          ],
          "pic": {
            "image": "ch3m32.jpg",
            "width": "300",
            "height": "300"
          },
          "val": 36
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tPoint (3, 0) lies in the first quadrant.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tPoints (1, –1) and (–1, 1) lie in the same quadrant.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": " ",
          "ans": "False",
          "code": "TF",
          "pic": {
            "image": "ch3tf3.jpg",
            "width": "500",
            "height": "45"
          },
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0).\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t(–1, 7) is a point in the IInd quadrant.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 5
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "If x ≠ y, then (x, y) __________ (y, x).",
          "ans": "≠",
          "code": "FIB",
          "val": 1
        }
      ],
      [],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and (6, 1) in the Cartesian plane.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch3s1a.jpg",
            "width": "450",
            "height": "430"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Locate the following points on Cartesian plane taking the scale 1 cm = 1 unit on both the axes. A(3, 2), B(–3, –5), C(5, –7), D(–6, 3), E(4, 0), F(0, –3), G(0, 0), H(–7,0).",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch3s2a.jpg",
            "width": "450",
            "height": "420"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Write the coordinates of each of the points P, Q, R, S, T and O from the figure.",
          "ans": "The coordinates of various points are: <br>P (1, 1) &emsp;&emsp;&emsp; Q (–3, 0) &emsp;&emsp;&emsp; R (–2, –3) <br>S (2, 1) &emsp;&emsp;&emsp; T (4, –2) &emsp;&emsp;&emsp; O (0, 0)",
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch3s3.jpg",
            "width": "370",
            "height": "367"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Plot the points (x, y) given by the following table:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch3s4.jpg",
            "width": "389",
            "height": "80"
          },
          "ansimg": {
            "image": "ch3s4a.jpg",
            "width": "440",
            "height": "395"
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "Find the coordinates of the point which lies on x- and y-axis both.",
          "ans": "The origin O (0, 0) lies on both the coordinate axes.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Find the coordinates of the point whose ordinate is –4 and which lies on y-axis.",
          "ans": "Ordinate = –4 and point lies on y-axis. <br>∴ Required point which lies on the y-axis should be (0, –4).",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.",
          "ans": "Here, Abscissa = 5 and the point lies on the x-axis. <br>∴ y = 0 <br>Hence, required point is (5, 0).",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In which quadrant do points (–5, 2) and (2, –5) lie?",
          "ans": "(–5, 2) → IInd quadrant. <br>(2, –5) → IVth quadrant.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "If (<i>x</i>, 2) and (–2, <i>y</i>) are equal, then find <i>x</i> and <i>y</i>.",
          "ans": "<i>x</i> =–2, <i>y</i> = 2",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the equation of y-axis.",
          "ans": "<i>x</i> = 0",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 6
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Write the equation of x-axis.",
          "ans": "<i>y</i> = 0",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 7
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In which quadrant do the following points lie. <br>(a) abscissa is –1 and ordinate is 4. <br>(b) abscissa is 4 and ordinate is –2",
          "ans": "(a) (–1, 4) → IInd quadrant. <br>(b) (4, –2) → IVth quadrant.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 8
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
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      [],
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      [],
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      [],
      [],
      [],
      [],
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      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch3_pbq",
    "gowf": "ch3_gowf",
    "afow": "ch3_afow",
    "cs": "ch3_cs",
    "afq": "ch3_afq",
    "fib": "ch3_fib",
    "grade": "Grade 9",
    "mcq": "ch3_mcq",
    "vsaq": "ch3_vsaq",
    "laq": "ch3_laq",
    "tf": "ch3_tf",
    "co": "ch3_co",
    "nf": "ch3_nf",
    "mtf": "ch3_mtf",
    "yn": "ch3_yn",
    "saq": "ch3_saq",
    "dtf": "ch3_dtf",
    "map": "ch3_map",
    "ctt": "ch3_ctt",
    "un": "ch3_un",
    "ctco": "ch3_ctco",
    "grf": "ch3_grf",
    "snc": "ch3_snc",
    "jtf": "ch3_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch4",
    "chapterName": "Chapter 4 - Linear Equations in Two Variables",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "A linear equation in two variables is of the form ax + by + c = 0, where",
          "ans": "(a) a ≠ 0, b ≠ 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a ≠ 0, b ≠ 0",
            "(b) a = 0, b ≠ 0",
            "(c) a ≠ 0, b = 0",
            "(d) a = 0, c = 0"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Any point on the y-axis is of the form",
          "ans": "(c) (0, <i>y</i>)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (<i>x</i>, 0)",
            "(b) (<i>x</i>, <i>y</i>)",
            "(c) (0, <i>y</i>)",
            "(d) (<i>y</i>, <i>y</i>)"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The linear equation 3<i>x</i> – <i>y</i> = <i>x</i> – 1 has",
          "ans": "(c) infinitely many solutions",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a unique solution",
            "(b) two solutions",
            "(c) infinitely many solutions",
            "(d) no solution"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If (2, 0) is a solution of the linear equation 2<i>x</i> + 3<i>y</i> = <i>k</i>, then the value of <i>k</i> is",
          "ans": "(a) 4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4",
            "(b) 6",
            "(c) 5",
            "(d) 2"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Any solution of the linear equation 2<i>x</i> + 0<i>y</i> + 9 = 0 in two variables is of the form",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch4m5.jpg",
            "width": "360",
            "height": "100"
          },
          "ansimg": {
            "image": "ch4m5a.jpg",
            "width": "100",
            "height": "47"
          },
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "<i>x</i> = 5, <i>y</i> = 2 is a solution of the linear equation",
          "ans": "(c) <i>x</i> + <i>y</i> = 7",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i> + 2<i>y</i> = 7",
            "(b) 5<i>x</i> + 2<i>y</i> = 7",
            "(c) <i>x</i> + <i>y</i> = 7",
            "(d) 5<i>x</i> + <i>y</i> = 7"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form.",
          "ans": "(b) <i>x</i> + <i>y</i> = 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>y</i> – <i>x</i> = 0",
            "(b) <i>x</i> + <i>y</i> = 0",
            "(c) –2<i>x</i> + <i>y</i> = 0",
            "(d) –<i>x</i> + 2<i>y</i> = 0"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The graph of the linear equation 2<i>x</i> + 3<i>y</i> = 6 cuts the y-axis at the point",
          "ans": "(d) (0, 2)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (2, 0)",
            "(b) (0, 3)",
            "(c) (3, 0)",
            "(d) (0, 2)"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The equation <i>x</i> = 7, in two variables, can be written as",
          "ans": "(b) 1.<i>x</i> + 0.<i>y</i> = 7",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1.<i>x</i> + 1.<i>y</i> = 7",
            "(b) 1.<i>x</i> + 0.<i>y</i> = 7",
            "(c) 0.<i>x</i> + 1.<i>y</i> = 7",
            "(d) 0.<i>x</i> + 0.<i>y</i> = 7"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Any point on the x-axis is of the form",
          "ans": "(c) (<i>x</i>, 0)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (<i>x</i>, <i>y</i>)",
            "(b) (0, <i>y</i>)",
            "(c) (<i>x</i>, 0)",
            "(d) (<i>x</i>, <i>x</i>)"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The equation of x-axis is of the form",
          "ans": "(b) <i>y</i> = 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i> = 0",
            "(b) <i>y</i> = 0",
            "(c) <i>x</i> + <i>y</i> = 0",
            "(d) <i>x</i> = <i>y</i>"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The graph of <i>y</i> = 6 is a line",
          "ans": "(a) parallel to x-axis at a distance 6 units from the origin.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) parallel to x-axis at a distance 6 units from the origin.",
            "(b) parallel to y-axis at a distance 6 units from the origin.",
            "(c) making an intercept 6 on the x-axis.",
            "(d) making an intercept 6 on both the axis."
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The graph of the linear equation <i>y</i> = <i>x</i> passes through the point",
          "ans": "(c) (1, 1 )",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch4m13.jpg",
            "width": "370",
            "height": "110"
          },
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point of the form (<i>a</i>, <i>a</i>) always lies on",
          "ans": "(c) on the line <i>y</i> = <i>x</i>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) x-axis",
            "(b) y-axis",
            "(c) on the line <i>y</i> = <i>x</i>",
            "(d) on the line <i>x</i> + <i>y</i> = 0"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point of the form (<i>a</i>, –<i>a</i>) lies on the line",
          "ans": "(d) <i>x</i> + <i>y</i> = 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i> = <i>a</i>",
            "(b) <i>y</i> = –<i>a</i>",
            "(c) <i>y</i> = <i>x</i>",
            "(d) <i>x</i> + <i>y</i> = 0"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The linear equation 2<i>x</i> – 5<i>y</i> = 7 has",
          "ans": "(c) Infinitely many solutions",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) A unique solution",
            "(b) Two solutions",
            "(c) Infinitely many solutions",
            "(d) No solution"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The equation 2x + 5y = 7 has a unique solution, if x, y are:",
          "ans": "(a) Natural numbers",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Natural numbers",
            "(b) Positive real numbers",
            "(c) Real numbers",
            "(d) Rational numbers"
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If (2, 0) is a solution of the linear equation 2<i>x</i> + 3<i>y</i> = <i>k</i>, then the value of <i>k</i> is",
          "ans": "(a) 4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4",
            "(b) 6",
            "(c) 5",
            "(d) 2"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Any solution of the linear equation 2<i>x</i> + 0<i>y</i> + 9 = 0 in two variables is of the form",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch4m19.jpg",
            "width": "450",
            "height": "110"
          },
          "ansimg": {
            "image": "ch4m19a.jpg",
            "width": "107",
            "height": "57"
          },
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point",
          "ans": "(d) (0, 2)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (2, 0)",
            "(b) (0, 3)",
            "(c) (3, 0)",
            "(d) (0, 2)"
          ],
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The equation <i>x</i> = 7, in two variables, can be written as",
          "ans": "(b) 1. <i>x</i> + 0. <i>y</i> = 7",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1 . <i>x</i> + 1 . <i>y</i> = 7",
            "(b) 1. <i>x</i> + 0. <i>y</i> = 7",
            "(c) 0 . <i>x</i> + 1 . <i>y</i> = 7",
            "(d) 0 . <i>x</i> + 0 . <i>y</i> = 7"
          ],
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Any point on the x-axis is of the form",
          "ans": "(c) (<i>x</i>, 0)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (<i>x</i>, <i>y</i>)",
            "(b) (0, <i>y</i>)",
            "(c) (<i>x</i>, 0)",
            "(d) (<i>x</i>, <i>x</i>)"
          ],
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Any point on the line <i>y</i> = <i>x</i> is of the form",
          "ans": "(a) (a, a)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (a, a)",
            "(b) (0, a)",
            "(c) (a, 0)",
            "(d) (a, –a)"
          ],
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The equation of x-axis is of the form",
          "ans": "(b) <i>y</i> = 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i> = 0",
            "(b) <i>y</i> = 0",
            "(c) <i>x</i> + <i>y</i> = 0",
            "(d) <i>x</i> = <i>y</i>"
          ],
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The graph of <i>y</i> = 6 is a line",
          "ans": "(a) parallel to x-axis at a distance 6 units from the origin",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) parallel to x-axis at a distance 6 units from the origin",
            "(b) parallel to y-axis at a distance 6 units from the origin",
            "(c) making an intercept 6 on the x-axis.",
            "(d) making an intercept 6 on both the axes."
          ],
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "<i>x</i> = 5, <i>y</i> = 2 is a solution of the linear equation",
          "ans": "(c) <i>x</i> + <i>y</i> = 7",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i> + 2<i>y</i> = 7",
            "(b) 5<i>x</i> + 2<i>y</i> = 7",
            "(c) <i>x</i> + <i>y</i> = 7",
            "(d) 5<i>x</i> + <i>y</i> = 7"
          ],
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If a linear equation has solutions (–2, 2), (0, 0) and (2, – 2), then it is of the form",
          "ans": "(b) <i>x</i> + <i>y</i> = 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>y</i> – <i>x</i> = 0",
            "(b) <i>x</i> + <i>y</i> = 0",
            "(c) –2<i>x</i> + <i>x</i> = 0",
            "(d) –<i>x</i> + 2<i>y</i> = 0"
          ],
          "val": 27
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The positive solutions of the equation <i>ax</i> + <i>by</i> + <i>c</i> = 0 always lie in the",
          "ans": "(a) 1st quadrant",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1st quadrant",
            "(b) 2nd quadrant",
            "(c) 3rd quadrant",
            "(d) 4th quadrant"
          ],
          "val": 28
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The graph of the linear equation 2<i>x</i> + 3<i>y</i> = 6 is a line which meets the x-axis at the point",
          "ans": "(c) (3, 0)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (0, 2)",
            "(b) (2, 0)",
            "(c) (3, 0)",
            "(d) (0, 3)"
          ],
          "val": 29
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The graph of the linear equation <i>y</i> = <i>x</i> passes through the point",
          "ans": "(c) (1, 1)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch4m30.jpg",
            "width": "299",
            "height": "100"
          },
          "val": 30
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:",
          "ans": "(b) Remains the same",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Changes",
            "(b) Remains the same",
            "(c) Changes in case of multiplication only",
            "(d) Changes in case of division only"
          ],
          "val": 31
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "How many linear equations in <i>x</i> and <i>y</i> can be satisfied by <i>x</i> = 1 and <i>y</i> = 2?",
          "ans": "(c) Infinitely many",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Only one",
            "(b) Two",
            "(c) Infinitely many",
            "(d) Three"
          ],
          "val": 32
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point of the form (a, a) always lies on:",
          "ans": "(c) On the line <i>y</i> = <i>x</i>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) x-axis",
            "(b) y-axis",
            "(c) On the line <i>y</i> = <i>x</i>",
            "(d) On the line <i>x</i> + <i>y</i> = 0"
          ],
          "val": 33
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The point of the form (a, –a) always lies on the line",
          "ans": "(d) <i>x</i> + <i>y</i> = 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <i>x</i> = a",
            "(b) <i>y</i> = –a",
            "(c) <i>y</i> = <i>x</i>",
            "(d) <i>x</i> + <i>y</i> = 0"
          ],
          "val": 34
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe solution of a linear equation is not affected when the same number is added to (or subtracted from) both the sides of the equation.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe solution of a linear equation is not affected when you multiply or divide both the sides of the equation by the same non-zero number.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t<i>y</i><sup>2</sup> = <i>x</i> is a linear equation.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe point (0, 3) lies on the graph of the linear equation 3<i>x</i> + 4<i>y</i> = 12.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe graph of the linear equation <i>x</i> + 2<i>y</i> = 7 passes through the point (0, 7).\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe graph given below represents the linear equation <i>x</i> + <i>y</i> = 0.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "pic": {
            "image": "ch4tf6.jpg",
            "width": "190",
            "height": "190"
          },
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe graph given below represents the linear equation <i>x</i> = 3. See the figure.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "pic": {
            "image": "ch4tf7.jpg",
            "width": "190",
            "height": "190"
          },
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "",
          "ans": "False",
          "code": "TF",
          "pic": {
            "image": "ch4tf8.jpg",
            "width": "330",
            "height": "150"
          },
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery point on the graph of a linear equation in two variables does not represent a solution of the linear equation.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe graph of every linear equation in two variables need not be a line.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 10
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "An equation of the form <i>ax</i> + <i>by</i> + <i>c</i> = 0, where <i>a</i>, <i>b</i> and <i>c</i> are real numbers and a and b are not both zero, is called a ____________ in two variables.",
          "ans": "linear equation",
          "code": "FIB",
          "val": 1
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw the graphs of linear equations <i>y</i> = <i>x</i> and <i>y</i> = –<i>x</i> on the same Cartesian plane. What do you observe?",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4d1a.jpg",
            "width": "510",
            "height": "635"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw the graph of each of the following: <br><i>x</i> = –1",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4d2a.jpg",
            "width": "650",
            "height": "330"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw the graph of each of the following: <br>2<i>y</i> + 5 = 0",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4d3a.jpg",
            "width": "625",
            "height": "330"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw the graph of the line x – 2y = 3. From the graph, find the co-ordinates of the points when: <br>(i) x = 5 <br>(ii) y = 0.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4d4a.jpg",
            "width": "630",
            "height": "570"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Cost of 7 pens and 8 pencils is ₹87 and cost of 6 pens and 4 pencils is ₹66. Write linear equations representing the above data and draw its graph. Also, find the cost of 1 pen and 1 pencil from the graph.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4d5a.jpg",
            "width": "565",
            "height": "620"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is (i) 5 metre/second<sup>2</sup>, (ii) 6 metre/second<sup>2</sup>.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4d6a.jpg",
            "width": "660",
            "height": "590"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "If the points A(3, 5) and B(1, 4) lie on the graph of the linear equation <i>ax</i> + <i>by</i> = 7, find the value of <i>a</i> and <i>b</i>.",
          "ans": "Given linear equation is <i>ax</i> + <i>by</i> = 7 <br>The points A (3, 5) and B(1, 4) lie on the graph of above equation. <br>∴ 3<i>a</i> + 5<i>b</i> = 7  &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; . . . (i) <br>and <i>a</i> + 4<i>b</i> = 7 &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&nbsp;&nbsp; . . . (ii) <br>Multiply equation (ii) by 3, we get 3<i>a</i> + 12<i>b</i> = 21 . . . &emsp;&emsp;&nbsp; (iii) <br>Subtracting (iii) from (i), we get –7<i>b</i> = –14 ⇒ <i>b</i> = 2 <br>Substituting the value of <i>b</i> = 2 in (i), we get <br>3<i>a</i> + 5 × 2 = 7 <br>⇒ 3<i>a</i> = –3 <br>⇒ <i>a</i> = –1 <br>Hence, <i>a</i> = –1 and <i>b</i> = 2.",
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the value of a for which the equation 2<i>x</i> + <i>ay</i> = 5 has (1, –1) as a solution. Find two more solutions for the equation obtained.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4d8.jpg",
            "width": "480",
            "height": "480"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Let <i>y</i> varies directly as <i>x</i>. If <i>y</i> = 12 when <i>x</i> = 4, then write a linear equation. What is the value of <i>y</i> when <i>x</i> = 5?",
          "ans": "We have <i>y</i> a <i>x</i> ⇒ <i>y</i> = <i>kx</i> &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;. . . (i) <br>where <i>k</i> is constant of proportionality. <br>when <i>x</i> = 4, then <i>y</i> = 12. <br>⇒ 12 = <i>k</i>. 4 <br>⇒ <i>k</i> = 3 <br>∴ Required equation is <i>y</i> = 3<i>x</i>. <br>Now, putting <i>x</i> = 5 and <i>k</i> = 3 in equation (i), we get <br><i>y</i> = 3 × 5 =15",
          "code": "LATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Show that the points A(1, 2), B(–1, –16) and C(0, –7) lie on the graph of the linear equation <i>y</i> = 9<i>x</i> – 7.",
          "ans": "Consider <i>y</i> = 9<i>x</i> – 7 &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; . . . (i) <br>Put <i>x</i> = 1, y = 2 in equation (i), we get <br>2 = 9 × 1 – 7 <br>⇒ 2 = 2 (True) <br>Since the point A (1, 2) satisfies the equation (i), A (1, 2) lies on the graph of given equation (i). <br>Put <i>x</i> = –1, <i>y</i> = –16 in equation (i), we get <br>–16 = 9 × (–1) –7 <br>⇒ –16 = –16 (True) <br>For C(0, –7), put <i>x</i> = 0, <i>y</i> = –7 in equation (i), we get –7 = 9 × (0) –7 <br>⇒ –7 = –7 (True) <br>Hence, the points A (1, 2), B(–1, –16) and C (0, –7) lie on the graph of linear equation <i>y</i> = 9<i>x</i> – 7",
          "code": "LATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Solve for <i>x</i>:",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch4d10.jpg",
            "width": "190",
            "height": "50"
          },
          "ansimg": {
            "image": "ch4d10a.jpg",
            "width": "220",
            "height": "400"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Write two solution of the following equation: <br><i>x</i> - 4<i>y</i> = 0",
          "ans": "<i>x</i> – 4<i>y</i> = 0 <br>⇒ &emsp; <i>x</i> = 4<i>y</i> <br><i>y</i> = 0 &emsp; ⇒ &emsp; <i>x</i> = 0 <br><i>y</i> = 1 &emsp; ⇒ &emsp; <i>x</i> = 4 <br>Hence, two of the infinitely many solutions of <i>x</i> – 4<i>y</i> = 0 are (0, 0) and (4, 1).",
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Write two solution of the following equation: <br>π<i>x</i> + <i>y</i> = 9",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s2a.jpg",
            "width": "480",
            "height": "130"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Check which of the following are solutions of the equation <i>x</i> – 2<i>y</i> = 4 and which are not. <br>(√2, 4√2)",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s3.jpg",
            "width": "190",
            "height": "273"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Check which of the following are solutions of the equation <i>x</i> – 2<i>y</i> = 4 and which are not. <br>(1, 1)",
          "ans": "Put <i>x</i> = 1 and <i>y</i> = 1 in equation <i>x</i> – 2<i>y</i> = 4. <br>L.H.S. = 1 – 2(1) = 1 – 2 = –1 <br>R.H.S. = 4 <br>Clearly, L.H.S. ≠ R.H.S. <br>∴ (1, 1) is not the solution of <i>x</i> – 2<i>y</i> = 4.",
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Check which of the following are solutions of the equation <i>x</i> – 2<i>y</i> = 4 and which are not. <br>(2, 0)",
          "ans": "Put <i>x</i> = 2 and <i>y</i> = 0 in equation <i>x</i> – 2<i>y</i> = 4. <br>L.H.S. = 2 – 2(0) = 2 <br>R.H.S. = 4 <br>Clearly, L.H.S. ≠ R.H.S. <br>∴ (2, 0) is not the solution of <i>x</i> – 2<i>y</i> = 4",
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Check which of the following are solutions of the equation <i>x</i> – 2<i>y</i> = 4 and which are not. <br>(0, –2)",
          "ans": "Put <i>x</i> = 0 and <i>y</i> = –2 in equation <i>x</i> – 2<i>y</i> = 4. <br>L.H.S. = 0 – 2(–2) = 4 <br>R.H.S. = 4 <br>Clearly, L.H.S. = R.H.S. <br>∴ (0, –2) is the solution of equation <i>x</i> – 2<i>y</i> = 4.",
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If <i>x</i> = 2<i>p</i> – 1 and <i>y</i> = <i>p</i> is a solution of the equation 3<i>x</i> – 5<i>y</i> = 7, find the value of <i>p</i>.",
          "ans": "<i>x</i> = 2<i>p</i> – 1 and <i>y</i> = <i>p</i> is a solution of equation 3<i>x</i> – 5<i>y</i> = 7. <br>∴ 3(2<i>p</i> – 1) – 5<i>p</i> = 7 <br>∴ 6<i>p</i> – 3 – 5<i>p</i> = 7 <br>∴ <i>p</i> – 3 = 7 <br>∴ <i>p</i> = 10",
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If the point (3, 4) lies on the graph of 3<i>y</i> = <i>ax</i> + 7, then find the value of <i>a</i>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s8a.jpg",
            "width": "370",
            "height": "220"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "For what value of <i>c</i>, the linear equation 2<i>x</i> + <i>cy</i> = 8 has equal values of <i>x</i> and <i>y</i> for its solution.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s9a.jpg",
            "width": "350",
            "height": "190"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Solve the equation <i>x</i> + 6 = 4(3 – <i>x</i>) + 9.",
          "ans": "<i>x</i> + 6 = 4(3 – <i>x</i>) + 9 <br>⇒ <i>x</i> + 6 = 12 – 4<i>x</i> + 9 <br>⇒ 5<i>x</i> = 15 <br>⇒ <i>x</i> = 3 <br>Thus, <i>x</i> = 3 is a solution of given equation.",
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s10a.jpg",
            "width": "130",
            "height": "150"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Solve for <i>x</i>:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch4s11.jpg",
            "width": "150",
            "height": "50"
          },
          "ansimg": {
            "image": "ch4s11a.jpg",
            "width": "200",
            "height": "220"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A three-wheeler scooter charges ₹ 10 for the first kilometre and ₹ 4.50 each for every subsequent kilometre. For a distance of <i>x</i> km, an amount of ₹ <i>y</i> is paid. Write the linear equation representing the above information.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s12a.jpg",
            "width": "290",
            "height": "292"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch4s13.jpg",
            "width": "380",
            "height": "70"
          },
          "ansimg": {
            "image": "ch4s13a.jpg",
            "width": "170",
            "height": "210"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch4s14.jpg",
            "width": "407",
            "height": "70"
          },
          "ansimg": {
            "image": "ch4s14a.jpg",
            "width": "170",
            "height": "275"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch4s15.jpg",
            "width": "662",
            "height": "113"
          },
          "ansimg": {
            "image": "ch4s15a.jpg",
            "width": "160",
            "height": "400"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch4s16.jpg",
            "width": "500",
            "height": "85"
          },
          "ansimg": {
            "image": "ch4s16a.jpg",
            "width": "330",
            "height": "310"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Give the geometric representation of equation <i>x</i> = 3 on number line in one variable.",
          "ans": "When <i>x</i> = 3 is treated as a solution in one variable, it represents a point on the number line as shown below:",
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s17a.jpg",
            "width": "300",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Give the geometric representation of equation <i>x</i> = 3 in Cartesian plane, in two variables.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s18a.jpg",
            "width": "630",
            "height": "273"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Give geometric representation of 2<i>y</i> + 7 = 0 as an equation in one variable.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 19,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s19a.jpg",
            "width": "320",
            "height": "140"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Give geometric representation of 2<i>y</i> + 7 = 0 as an equation in two variables.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 20,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch4s20a.jpg",
            "width": "497",
            "height": "284"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
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      [],
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      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch4_pbq",
    "gowf": "ch4_gowf",
    "afow": "ch4_afow",
    "cs": "ch4_cs",
    "afq": "ch4_afq",
    "fib": "ch4_fib",
    "grade": "Grade 9",
    "mcq": "ch4_mcq",
    "vsaq": "ch4_vsaq",
    "laq": "ch4_laq",
    "tf": "ch4_tf",
    "co": "ch4_co",
    "nf": "ch4_nf",
    "mtf": "ch4_mtf",
    "yn": "ch4_yn",
    "saq": "ch4_saq",
    "dtf": "ch4_dtf",
    "map": "ch4_map",
    "ctt": "ch4_ctt",
    "un": "ch4_un",
    "ctco": "ch4_ctco",
    "grf": "ch4_grf",
    "snc": "ch4_snc",
    "jtf": "ch4_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch5",
    "chapterName": "Chapter 5 - Introduction to Euclid's Geometry",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "The three steps from solids to points are",
          "ans": "(a) solids - surfaces - lines - points",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) solids - surfaces - lines - points",
            "(b) solids - lines - surfaces - points",
            "(c) lines - points - surfaces - solids",
            "(d) lines - surfaces - points - solids"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Euclid divided his famous treatise “The Elements” into",
          "ans": "(a) 13 chapters",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 13 chapters",
            "(b) 12 chapters",
            "(c) 11 chapters",
            "(d) 9 chapters"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The total number of propositions in the elements are",
          "ans": "(a) 465",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 465",
            "(b) 460",
            "(c) 13",
            "(d) 55"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Boundaries of solids are",
          "ans": "(a) surfaces",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) surfaces",
            "(b) curves",
            "(c) lines",
            "(d) points"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The three steps from solids to points are:",
          "ans": "(a) Solids - surfaces - lines - points",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Solids - surfaces - lines - points",
            "(b) Solids - lines - surfaces - points",
            "(c) Lines - points - surfaces - solids",
            "(d) Lines - surfaces - points - solids"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The number of dimensions a solid has:",
          "ans": "(c) 3",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1",
            "(b) 2",
            "(c) 3",
            "(d) 0"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The number of dimensions a surface has:",
          "ans": "(b) 2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1",
            "(b) 2",
            "(c) 3",
            "(d) 0"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The number of dimension a point has:",
          "ans": "(a) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0",
            "(b) 1",
            "(c) 2",
            "(d) 3"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Euclid divided his famous treatise “The Elements” into:",
          "ans": "(a) 13 chapters",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 13 chapters",
            "(b) 12 chapters",
            "(c) 11 chapters",
            "(d) 9 chapters"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The total number of propositions in the Elements are:",
          "ans": "(a) 465",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 465",
            "(b) 460",
            "(c) 13",
            "(d) 55"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Boundaries of solids are:",
          "ans": "(a) surfaces",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) surfaces",
            "(b) curves",
            "(c) lines",
            "(d) points"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Boundaries of surfaces are:",
          "ans": "(b) curves",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) surfaces",
            "(b) curves",
            "(c) lines",
            "(d) points"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio.",
          "ans": "(b) 4 : 2 : 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1 : 3 : 4",
            "(b) 4 : 2 : 1",
            "(c) 4 : 4 : 1",
            "(d) 4 : 3 : 2"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio.",
          "ans": "(b) 4 : 2 : 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1 : 3 : 4",
            "(b) 4 : 2 : 1",
            "(c) 4 : 4 : 1",
            "(d) 4 : 3 : 2"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A pyramid is a solid figure, the base of which is",
          "ans": "(d) any polygon",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) only a triangle",
            "(b) only a square",
            "(c) only a rectangle",
            "(d) any polygon"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The side faces of a pyramid are:",
          "ans": "(a) Triangles",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Triangles",
            "(b) Squares",
            "(c) Polygons",
            "(d) Trapeziums"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "It is known that if <i>x</i> + <i>y</i> = 10 then <i>x</i> + <i>y</i> + <i>z</i> = 10 + <i>z</i>. The Euclid’s axiom that illustrates this statement is:",
          "ans": "(b) Second Axiom",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) First Axiom",
            "(b) Second Axiom",
            "(c) Third Axiom",
            "(d) Fourth Axiom"
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In ancient India, the shapes of altars used for household rituals were:",
          "ans": "(a) Squares and circles",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "options": [
            "(a) Squares and circles",
            "(b) Triangles and rectangles",
            "(c) Trapeziums and pyramids",
            "(d) Rectangles and squares"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:",
          "ans": "(c) Nine",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Seven",
            "(b) Eight",
            "(c) Nine",
            "(d) Eleven"
          ],
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Greeks emphasised on:",
          "ans": "(b) Deductive reasoning",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Inductive reasoning",
            "(b) Deductive reasoning",
            "(c) Both a and b",
            "(d) Practical use of geometry"
          ],
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In Ancient India, altars with combination of shapes like rectangles, triangles and trapeziums were used for:",
          "ans": "(a) Public worship",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Public worship",
            "(b) Household rituals",
            "(c) Both a and b",
            "(d) None of a, b, c"
          ],
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Euclid belongs to the country:",
          "ans": "(c) Greece",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Babylonia",
            "(b) Egypt",
            "(c) Greece",
            "(d) India"
          ],
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Thales belongs to the country:",
          "ans": "(c) Greece",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Babylonia",
            "(b) Egypt",
            "(c) Greece",
            "(d) Rome"
          ],
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Pythagoras was a student of:",
          "ans": "(a) Thales",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Thales",
            "(b) Euclid",
            "(c) Both a and b",
            "(d) Archimedes"
          ],
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following needs a proof?",
          "ans": "(a) Theorem",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Theorem",
            "(b) Axiom",
            "(c) Definition",
            "(d) Postulate"
          ],
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Euclid stated that all right angles are equal to each other in the form of",
          "ans": "(c) a postulate",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) an axiom",
            "(b) a definition",
            "(c) a postulate",
            "(d) a proof"
          ],
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "‘Lines are parallel if they do not intersect’ is stated in the form of",
          "ans": "(b) a definition",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) an axiom",
            "(b) a definition",
            "(c) a postulate",
            "(d) a proof"
          ],
          "val": 27
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEuclidean geometry is valid only for curved surfaces.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe boundaries of the solids are curves.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe edges of a surface are curves.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe things which are double of the same thing are equal to one another.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe statements that are proved are called axioms.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEuclidean geometry is valid only for curved surfaces.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe boundaries of the solids are curves.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe edges of a surface are curves.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe things which are double of the same thing are equal to one another.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe statements that are proved are called axioms.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l” is known as Playfair’s axiom.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo distinct intersecting lines cannot be parallel to the same line.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 14
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tAttempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 15
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l” is known as Playfair’s axiom.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 16
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo distinct intersecting lines cannot be parallel to the same line.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 17
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tAttempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 18
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "The boundaries of the surfaces are _____________ or _____________.",
          "ans": "curves, straight lines",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A solid has ____________ dimensions.",
          "ans": "three",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A surface has ____________ dimensions.",
          "ans": "two",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A line has ____________ dimension.",
          "ans": "one",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "A point has ____________ dimension.",
          "ans": "no",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A ____________ is that which has no part.",
          "ans": "point",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A ____________ is breadthless length.",
          "ans": "line",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The ends of a line segment are ____________.",
          "ans": "points",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A ____________ is a line which lies evenly with the points on itself.",
          "ans": "straight line",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A ____________ is that which has length and breadth only.",
          "ans": "surface",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The ____________ of a surface are lines.",
          "ans": "edges",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A ____________ is a surface which lies evenly with the straight lines on itself.",
          "ans": "plane surface",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A ____________ may be drawn from any one point to any other point.",
          "ans": "straight line",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Given two distinct points, there is a ____________ line that passes through them.",
          "ans": "unique",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A circle can be drawn with any ____________ and any radius.",
          "ans": "centre",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "All ____________ angles are equal to one another.",
          "ans": "right",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If A, B and C are three points on a line and B lies between A and C, then ___________ + ___________ = AC.",
          "ans": "AB, BC",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two distinct lines cannot have ____________ than one point in common.",
          "ans": "more",
          "code": "FIB",
          "val": 18
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Study the following statement. <br>“ Two intersecting lines cannot be perpendicular to the same line.” <br>Check whether it is an equivalent version to Euclid’s fifth postulate.",
          "ans": "Yes, above statement is equivalent version of 5th postulate. <br>Let <i>l</i> and <i>m</i> be two lines intersecting at <i>P</i>. <br>If possible suppose <i>l</i> ⊥ <i>n</i> and <i>m</i> ⊥ <i>n</i>. <br>∴ ∠ 1 = ∠ 2 = ∠ 3 = ∠ 4 = 90° <br>⇒ ∠ 1 + ∠ 2 = 180° and ∠ 3 + ∠ 4 = 180° <br>Then by Euclid’s 5th postulate l and m meet neither on the sides of ∠ 1 and ∠ 2 nor on side of ∠ 3 and ∠ 4 which contradicts our assumption. <br>Hence, our assumption that l ⊥ n and m ⊥ n is wrong. <br>So, two intersecting lines cannot be perpendicular to same line and it is equivalent version to Euclid’s fifth postulate.",
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch5d1.jpg",
            "width": "240",
            "height": "190"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, we have BX = 1/2 AB; BY = 1/2 BC and AB = BC. Show that BX = BY.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch5s1.jpg",
            "width": "270",
            "height": "240"
          },
          "ansimg": {
            "image": "ch5s1a.jpg",
            "width": "550",
            "height": "261"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C.",
          "ans": "∠ 1 = ∠ 3 &emsp;&emsp;&emsp;&emsp;&emsp; (Given) &emsp;&emsp;&emsp;&emsp;&emsp; . . . (1) <br>∠ 2 = ∠ 4 &emsp;&emsp;&emsp;&emsp;&emsp; (Given) &emsp;&emsp;&emsp;&emsp;&emsp; . . . (2) <br>Adding (1) and (2), we get ∠ 1 + ∠ 2 = ∠ 3 + ∠ 4 <br>[By Euclid’s axiom, “If equals are added to equals the wholes are equal.”] <br>⇒ ∠ A = ∠ C.",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch5s2.jpg",
            "width": "190",
            "height": "190"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch5s3.jpg",
            "width": "480",
            "height": "210"
          },
          "ansimg": {
            "image": "ch5s3a.jpg",
            "width": "553",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If in the figure, PQ = BD, then prove that PB = QD.",
          "ans": "PQ = BD &emsp;&emsp;&emsp;&emsp;&emsp; (Given) <br>⇒ PB + BQ = BQ + QD <br>⇒ PB = QD",
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch5s4.jpg",
            "width": "119",
            "height": "100"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null,
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Read the following axioms: <br>(i) Things which are equal to the same thing are equal to one another. <br>(ii) If equals are added to equals, the wholes are equal. <br>(iii) Things which are double of the same thing are equal to one another. <br>Check whether the given system of axioms is consistent or inconsistent.",
          "ans": "Let AB = CD . . . (1) <br>⇒ AB + AB = CD + CD <br>[Using (ii) above if equals are added to equals, the wholes are equal.] <br>⇒ 2 AB = 2CD <br>⇒ AB = CD <br>[Using (iii) above things which are double of the same thing are equal to one another.] <br>Thus, all three given axioms are all in complete agreement with each other, i.e., it is impossible to deduce from these axioms a statement that contradicts any axiom or previously proven statement.",
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null,
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null,
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
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      [],
      [],
      [],
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      [],
      [],
      [],
      [],
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      [],
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      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch5_pbq",
    "gowf": "ch5_gowf",
    "afow": "ch5_afow",
    "cs": "ch5_cs",
    "afq": "ch5_afq",
    "fib": "ch5_fib",
    "grade": "Grade 9",
    "mcq": "ch5_mcq",
    "vsaq": "ch5_vsaq",
    "laq": "ch5_laq",
    "tf": "ch5_tf",
    "co": "ch5_co",
    "nf": "ch5_nf",
    "mtf": "ch5_mtf",
    "yn": "ch5_yn",
    "saq": "ch5_saq",
    "dtf": "ch5_dtf",
    "map": "ch5_map",
    "ctt": "ch5_ctt",
    "un": "ch5_un",
    "ctco": "ch5_ctco",
    "grf": "ch5_grf",
    "snc": "ch5_snc",
    "jtf": "ch5_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch6",
    "chapterName": "Chapter 6 - Introduction to Euclid's Geometry",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "If one angle of a triangle is equal to the sum of the other two angles, then the triangle is",
          "ans": "(d) a right triangle",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) an isosceles triangle",
            "(b) an obtuse triangle",
            "(c) an equilateral triangle",
            "(d) a right triangle"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch6m2.jpg",
            "width": "360",
            "height": "100"
          },
          "ansimg": {
            "image": "ch6m2a.jpg",
            "width": "76",
            "height": "40"
          },
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is",
          "ans": "(a) an acute angled triangle",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) an acute angled triangle",
            "(b) an obtuse angled triangle",
            "(c) a right triangle",
            "(d) an isosceles triangle"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In the figure, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to",
          "ans": "(c) 145°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 85°",
            "(b) 135°",
            "(c) 145°",
            "(d) 110°"
          ],
          "pic": {
            "image": "ch6m4.jpg",
            "width": "240",
            "height": "210"
          },
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If one angle of a triangle is equal to the sum of the other two angles, then the triangle is",
          "ans": "(d) a right triangle",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) an isosceles triangle",
            "(b) an obtuse triangle",
            "(c) an equilateral triangle",
            "(d) a right triangle"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch6m6.jpg",
            "width": "380",
            "height": "100"
          },
          "ansimg": {
            "image": "ch6m6a.jpg",
            "width": "70",
            "height": "48"
          },
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is",
          "ans": "(a) an acute angled triangle",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) an acute angled triangle",
            "(b) an obtuse angled triangle",
            "(c) a right triangle",
            "(d) an isosceles triangle"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be",
          "ans": "(d) 155°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 50°",
            "(b) 65°",
            "(c) 145°",
            "(d) 155°"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In the figure, POQ is a line. The value of x is",
          "ans": "(a) 20°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 20°",
            "(b) 25°",
            "(c) 30°",
            "(d) 35°"
          ],
          "pic": {
            "image": "ch6m9.jpg",
            "width": "230",
            "height": "90"
          },
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In the figure, if OP||RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to",
          "ans": "(c) 60°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 40°",
            "(b) 50°",
            "(c) 60°",
            "(d) 70°"
          ],
          "pic": {
            "image": "ch6m10.jpg",
            "width": "230",
            "height": "100"
          },
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is",
          "ans": "(b) 40°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 60°",
            "(b) 40°",
            "(c) 80°",
            "(d) 20°"
          ],
          "val": 11
        }
      ],
      [],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "A part (or portion) of a line with two end points is called a ____________.",
          "ans": "line segment",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A part of a line with one end point is called a ____________.",
          "ans": "ray",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If three or more points lie on the same line, these points are called ____________ points.",
          "ans": "collinear",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The rays making an angle are called the ____________ of the angle and the end point is called the ____________ of the angle.",
          "ans": "arms, vertex",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "If three or more points do not lie on the same line, these points are called ____________ points.",
          "ans": "non-collinear",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "An ____________ angle measures between 0° and 90°, whereas a ____________ angle is exactly equal to 90°.",
          "ans": "acute, right",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "An angle greater than 90° but less than 180° is called an ____________ angle.",
          "ans": "obtuse",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A ____________ angle is equal to 180°.",
          "ans": "straight",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "An angle which is greater than 180° but less than 360° is called a ____________ angle.",
          "ans": "reflex",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two angles whose sum is 90° are called ____________ angles.",
          "ans": "complementary",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two angles whose sum is 180° are called ____________ angles.",
          "ans": "supplementary",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When the sum of two adjacent angles is 180°, then they are called a ____________ pair of angles.",
          "ans": "linear pair",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a ____________.",
          "ans": "line",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If two lines intersect each other, then the vertically opposite angles are ____________.",
          "ans": "equal",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a transversal intersects two parallel lines, then each pair of corresponding angles is ____________.",
          "ans": "equal",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are ____________.",
          "ans": "parallel",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a transversal intersects two parallel lines, then each pair of alternate interior angles is ____________.",
          "ans": "equal",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a transversal intersects two lines such that a pair of alternate interior angles are equal, then the two lines are ____________.",
          "ans": "parallel",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is ____________.",
          "ans": "supplementary",
          "code": "FIB",
          "val": 19
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are ____________.",
          "ans": "parallel",
          "code": "FIB",
          "val": 20
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Lines which are parallel to the same line are ____________ to each other.",
          "ans": "parallel",
          "code": "FIB",
          "val": 21
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The sum of the angles of a triangle is ____________.",
          "ans": "180°",
          "code": "FIB",
          "val": 22
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two ____________ angles.",
          "ans": "interior opposite",
          "code": "FIB",
          "val": 23
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "An exterior angle of a triangle is greater than either of its ____________ angles.",
          "ans": "interior opposite",
          "code": "FIB",
          "val": 24
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6d1.jpg",
            "width": "655",
            "height": "215"
          },
          "ansimg": {
            "image": "ch6d1a.jpg",
            "width": "450",
            "height": "330"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": " ",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6d2.jpg",
            "width": "650",
            "height": "45"
          },
          "ansimg": {
            "image": "ch6d2a.jpg",
            "width": "460",
            "height": "576"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "   ",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6d3.jpg",
            "width": "650",
            "height": "30"
          },
          "ansimg": {
            "image": "ch6d3a.jpg",
            "width": "660",
            "height": "420"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Prove that a triangle must have at least two acute angles.",
          "ans": "We know that sum of all angles in a triangle is 180º. <br>If possible suppose that the two angles say ∠A and ∠B of a DABC are obtuse or right angle, then ∠A + ∠B <br>+ ∠C = 180º <br>But ∠A + ∠B > 180º [in case both are obtuse] &emsp;&emsp;&emsp;&emsp;&emsp; (1) <br>But ∠A + ∠B = 180º [in case both are right angles.] <br>⇒ ∠C = 0º &emsp;&emsp;&emsp;&emsp;&emsp; (2) <br>Which is impossible. <br>Both (1) and (2) contradict the property of triangle. <br>∴ Our assumption is wrong. <br>Thus, at least two angles of a triangle are acute angles.",
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "    ",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6d5.jpg",
            "width": "660",
            "height": "180"
          },
          "ansimg": {
            "image": "ch6d5a.jpg",
            "width": "620",
            "height": "510"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "    ",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6d6.jpg",
            "width": "660",
            "height": "230"
          },
          "ansimg": {
            "image": "ch6d6a.jpg",
            "width": "490",
            "height": "386"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Prove that sum of the angles of a hexagon is 720°.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6d7.jpg",
            "width": "330",
            "height": "160"
          },
          "ansimg": {
            "image": "ch6d7a.jpg",
            "width": "530",
            "height": "500"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s1.jpg",
            "width": "660",
            "height": "240"
          },
          "ansimg": {
            "image": "ch6s1a.jpg",
            "width": "470",
            "height": "390"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "What value of x would make XOY a line if ∠XOZ = 7x + 20° and ∠YOZ = 3x in the figure.",
          "ans": "&emsp;&emsp; ∠XOZ + ∠YOZ = 180º (Linear pair) <br>⇒ 7x + 20º + 3x = 180º <br>⇒ 10x = 160º <br>⇒ x = 16º",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s2.jpg",
            "width": "330",
            "height": "160"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, if ∠POR and ∠QOR form a linear pair and a – b = 80°, then find the value of a and b.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s3.jpg",
            "width": "330",
            "height": "160"
          },
          "ansimg": {
            "image": "ch6s3a.jpg",
            "width": "500",
            "height": "180"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If the complement of an angle is one-third of its supplement, find the angle.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null,
          },
          "ansimg": {
            "image": "ch6s4a.jpg",
            "width": "230",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s5.jpg",
            "width": "568",
            "height": "272"
          },
          "ansimg": {
            "image": "ch6s5a.jpg",
            "width": "614",
            "height": "279"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "  ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s6.jpg",
            "width": "660",
            "height": "239"
          },
          "ansimg": {
            "image": "ch6s6a.jpg",
            "width": "636",
            "height": "273"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "   ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s7.jpg",
            "width": "650",
            "height": "240"
          },
          "ansimg": {
            "image": "ch6s7a.jpg",
            "width": "500",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch6s8a.jpg",
            "width": "500",
            "height": "410"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, <i>l</i> || m. ∠1 and ∠2 are in the ratio 5 : 4. Find ∠3 and ∠4.",
          "ans": "∠1 : ∠2 = 5 : 4 <br>Let ∠1 = 5x, ∠2 = 4x <br>∠1 + ∠2 = 180º (Linear pair) <br>⇒ 5x + 4x = 180º <br>⇒ 9x = 180º <br>⇒ x = 20º <br>So, ∠1= 100º and ∠2 = 80º <br>∠2 = ∠3 (Corresponding angles) <br>⇒ ∠3 = 80º <br>∠3 + ∠4 = 180º [Linear pair] <br>80º + ∠4 = 180º <br>∠4 = 100º",
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s9.jpg",
            "width": "300",
            "height": "200"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, find <i>x</i>.",
          "ans": "In △ABC, <br>∠A + ∠B + ∠C = 180º <br>⇒ 40º + ∠B + 90º = 180º <br>⇒ ∠B = 50º <br>In △BDE, <br>∠B + ∠D + ∠E = 180º <br>⇒ 50º + x + 100º = 180º [∵ ∠B = 50º] <br>⇒ &emsp; x = 180º – 150º <br>⇒ &emsp; x = 30º",
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s10.jpg",
            "width": "230",
            "height": "150"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "   ",
          "ans": "In △QTR, <br>∠TQR + ∠QTR + ∠TRQ = 180º [Angle sum property of triangle] <br>⇒ 40º + 90º + x = 180º <br>⇒ &emsp; x = 180º – 130º <br>⇒ &emsp; x = 50º <br>For △PRS, ∠PSQ = ∠SPR + ∠PRS [∵ Exterior angle is equal to sum of interior angles.] <br>⇒ &emsp; y = 30º + x <br>⇒ &emsp; y = 30º + 50º <br>⇒ &emsp; y = 80º <br>So, x = 50º and y = 80º",
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s11.jpg",
            "width": "510",
            "height": "180"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Prove that sum of the exterior angles of a triangle is 360°.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s12.jpg",
            "width": "200",
            "height": "200"
          },
          "ansimg": {
            "image": "ch6s12a.jpg",
            "width": "560",
            "height": "240"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, find the value of <i>x</i>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch6s13.jpg",
            "width": "160",
            "height": "140"
          },
          "ansimg": {
            "image": "ch6s13a.jpg",
            "width": "660",
            "height": "330"
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "For what value of <i>x</i> + <i>y</i> in the figure will ABC be a line? Justify your answer.",
          "ans": "<i>x</i> + <i>y</i> must be equal to 180°. For ABC to be a line, the sum of the two adjacent angles must be 180°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch6vs1.jpg",
            "width": "230",
            "height": "100"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Can a triangle have all angles less than 60°? Give reason for your answer.",
          "ans": "No, angle sum will be less than 180°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Can a triangle have two obtuse angles? Give reason for your answer.",
          "ans": "No, angle sum cannot be more than 180°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "How many triangles can be drawn having its angles as 45°, 64° and 72°? Give reason for your answer.",
          "ans": "None, angle sum cannot be 181°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "How many triangles can be drawn having its angles as 53°, 64° and 63°? Give reason for your answer.",
          "ans": "Infinitely many triangles, sum of the angles of every triangle is 180°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In the figure, find the value of x for which the lines l and m are parallel.",
          "ans": "136°",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch6vs6.jpg",
            "width": "250",
            "height": "150"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 6
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.",
          "ans": "No, each of these will be a right angle only when they form a linear pair.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 7
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer.",
          "ans": "Each will be a right angle. Linear pair axiom.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 8
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In the figure, which of the two lines are parallel and why?",
          "ans": "<i>l</i> || m because 132° + 48° = 180°, <i>p</i> is not parallel to <i>q</i>, because 73° + 106° ≠ 180°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch6vs9.jpg",
            "width": "470",
            "height": "170"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 9
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Two lines <i>l</i> and <i>m</i> are perpendicular to the same line <i>n</i>. Are <i>l</i> and <i>m</i> perpendicular to each other? Give reason for your answer.",
          "ans": "No, they are parallel",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 10
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch6_pbq",
    "gowf": "ch6_gowf",
    "afow": "ch6_afow",
    "cs": "ch6_cs",
    "afq": "ch6_afq",
    "fib": "ch6_fib",
    "grade": "Grade 9",
    "mcq": "ch6_mcq",
    "vsaq": "ch6_vsaq",
    "laq": "ch6_laq",
    "tf": "ch6_tf",
    "co": "ch6_co",
    "nf": "ch6_nf",
    "mtf": "ch6_mtf",
    "yn": "ch6_yn",
    "saq": "ch6_saq",
    "dtf": "ch6_dtf",
    "map": "ch6_map",
    "ctt": "ch6_ctt",
    "un": "ch6_un",
    "ctco": "ch6_ctco",
    "grf": "ch6_grf",
    "snc": "ch6_snc",
    "jtf": "ch6_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch7",
    "chapterName": "Chapter 7 - Triangles",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is not a criterion for congruence of triangles?",
          "ans": "(c) SSA",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) SAS",
            "(b) ASA",
            "(c) SSA",
            "(d) SSS"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If AB = QR, BC = PR and CA = PQ, then",
          "ans": "(b) ΔCBA ≅ ΔPRQ",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) ΔABC ≅ ΔPQR",
            "(b) ΔCBA ≅ ΔPRQ",
            "(c) ΔBAC ≅ ΔRPQ",
            "(d) ΔBCA ≅ ΔPQR"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In ΔABC, AB = AC and ∠B = 50°. Then ∠C is equal to",
          "ans": "(b) 50°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 40°",
            "(b) 50°",
            "(c) 80°",
            "(d) 130°"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In ΔABC, BC = AB and ∠B = 80°. Then ∠A is equal to",
          "ans": "(c) 50°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 80°",
            "(b) 40°",
            "(c) 50°",
            "(d) 100°"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(a) 4 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4 cm",
            "(b) 5 cm",
            "(c) 2 cm",
            "(d) 2.5 cm"
          ],
          "pic": {
            "image": "ch7m5.jpg",
            "width": "490",
            "height": "30"
          },
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is not a criterion for congruence of triangles?",
          "ans": "(c) SSA",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) SAS",
            "(b) ASA",
            "(c) SSA",
            "(d) SSS"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If AB = QR, BC = PR and CA = PQ, then",
          "ans": "(b) ΔCBA ≅ ΔPRQ",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) ΔABC ≅ ΔPQR",
            "(b) ΔCBA ≅ ΔPRQ",
            "(c) ΔBAC ≅ ΔRPQ",
            "(d) ΔPQR ≅ ΔBCA"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In ΔABC, AB = AC and ∠B = 50°. Then ∠C is equal to",
          "ans": "(b) 50°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 40°",
            "(b) 50°",
            "(c) 80°",
            "(d) 130°"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In ΔABC, BC = AB and ∠B = 80°. Then ∠A is equal to",
          "ans": "(c) 50°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 80°",
            "(b) 40°",
            "(c) 50°",
            "(d) 100°"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In ΔPQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is",
          "ans": "(a) 4 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4 cm",
            "(b) 5 cm",
            "(c) 2 cm",
            "(d) 2.5 cm"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "D is a point on the side BC of a ΔABC such that AD bisects ∠BAC. Then",
          "ans": "(b) BA &gt; BD",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) BD = CD",
            "(b) BA &gt; BD",
            "(c) BD &gt; BA",
            "(d) CD &gt; CA"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "It is given that ΔABC ≅ ΔFDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?",
          "ans": "(b) DF = 5 cm, ∠E = 60°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) DF = 5 cm, ∠F = 60°",
            "(b) DF = 5 cm, ∠E = 60°",
            "(c) DE = 5 cm, ∠E = 60°",
            "(d) DE = 5 cm, ∠D = 40°"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be",
          "ans": "(d) 3.4 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3.6 cm",
            "(b) 4.1 cm",
            "(c) 3.8 cm",
            "(d) 3.4 cm"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In ΔPQR, if ∠R &gt; ∠Q, then",
          "ans": "(b) PQ &gt; PR",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) QR &gt; PR",
            "(b) PQ &gt; PR",
            "(c) PQ &lt; PR",
            "(d) QR &lt; PR"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are",
          "ans": "(a) isosceles but not congruent",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) isosceles but not congruent",
            "(b) isosceles and congruent",
            "(c) congruent but not isosceles",
            "(d) neither congruent nor isosceles"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if",
          "ans": "(b) AC = DE",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) BC = EF",
            "(b) AC = DE",
            "(c) AC = EF",
            "(d) BC = DE"
          ],
          "val": 16
        }
      ],
      [],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. This rule is called _____________ rule.",
          "ans": "SAS Congruence",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. This rule is called _____________ rule.",
          "ans": "ASA Congruence",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal. This rule is called _____________ rule.",
          "ans": "AAS Congruence",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A triangles in which two sides are equal is called an _____________ triangle.",
          "ans": "isosceles",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "Angles opposite to equal sides of an isosceles triangle are _____________.",
          "ans": "equal",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The sides opposite to equal angles of a triangle are _____________.",
          "ans": "equal",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent. This rule is called _____________ rule.",
          "ans": "SSS Congruence",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then two triangles are congruent. This rule is called _____________ rule.",
          "ans": "RHS Congruence",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If two sides of a triangle are unequal, the angle opposite to the _____________ side is larger (or greater).",
          "ans": "longer",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "In any triangle, the side opposite to the _____________ angle is longer.",
          "ans": "larger (greater)",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The sum of any two sides of a triangle is _____________ than the third side.",
          "ans": "greater",
          "code": "FIB",
          "val": 11
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7d1.jpg",
            "width": "660",
            "height": "59"
          },
          "ansimg": {
            "image": "ch7d1a.jpg",
            "width": "670",
            "height": "570"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": " ",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7d2.jpg",
            "width": "660",
            "height": "269"
          },
          "ansimg": {
            "image": "ch7d2a.jpg",
            "width": "660",
            "height": "630"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Bisectors of the angles ∠B and ∠C of an isosceles triangle Δ ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null,
          },
          "ansimg": {
            "image": "ch7d3a.jpg",
            "width": "660",
            "height": "600"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7d4.jpg",
            "width": "585",
            "height": "30"
          },
          "ansimg": {
            "image": "ch7d4a.jpg",
            "width": "662",
            "height": "658"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7d5.jpg",
            "width": "660",
            "height": "40"
          },
          "ansimg": {
            "image": "ch7d5a.jpg",
            "width": "660",
            "height": "444"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Show that in a right angled triangle, the hypotenuse is the longest side.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch7d6a.jpg",
            "width": "660",
            "height": "570"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s1.jpg",
            "width": "660",
            "height": "210"
          },
          "ansimg": {
            "image": "ch7s1a.jpg",
            "width": "330",
            "height": "290"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": "In ΔABY and ΔACX, <br>AB = AC &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; (Given) <br>AY = AX &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; (Given) <br>∠A = ∠A &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;(Common) <br>∴ ΔABY ≅ ΔACX (SAS Rule)",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s2.jpg",
            "width": "660",
            "height": "270"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "  ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s3.jpg",
            "width": "660",
            "height": "299"
          },
          "ansimg": {
            "image": "ch7s3a.jpg",
            "width": "650",
            "height": "332"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "    ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s4.jpg",
            "width": "660",
            "height": "59"
          },
          "ansimg": {
            "image": "ch7s4a.jpg",
            "width": "660",
            "height": "480"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "     ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s5.jpg",
            "width": "660",
            "height": "59"
          },
          "ansimg": {
            "image": "ch7s5a.jpg",
            "width": "660",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "   ",
          "ans": "In ΔAXC and ΔAYB, <br>AX = AY &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; (Given) <br>∠A = ∠A &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; (Common) <br>AC = AB  &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; (Given) <br>∴ ΔAXC ≅ ΔAYB (SAS Congruence) <br>⇒ XC = YB",
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s6.jpg",
            "width": "660",
            "height": "270"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null,
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, ∠BCD = ∠ADC and ∠ACB = ∠BDA. Prove that AD = BC and ∠A= ∠B.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s7.jpg",
            "width": "250",
            "height": "200"
          },
          "ansimg": {
            "image": "ch7s7a.jpg",
            "width": "660",
            "height": "475"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "   ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s8.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch7s8a.jpg",
            "width": "660",
            "height": "510"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "   ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s9.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch7s9a.jpg",
            "width": "663",
            "height": "385"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "    ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s10.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch7s10a.jpg",
            "width": "660",
            "height": "430"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "     ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s11.jpg",
            "width": "467",
            "height": "33"
          },
          "ansimg": {
            "image": "ch7s11a.jpg",
            "width": "660",
            "height": "325"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": "MBD",
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s12.jpg",
            "width": "640",
            "height": "30"
          },
          "ansimg": {
            "image": "ch7s12a.jpg",
            "width": "660",
            "height": "476"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "   ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s13.jpg",
            "width": "590",
            "height": "260"
          },
          "ansimg": {
            "image": "ch7s13a.jpg",
            "width": "660",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s14.jpg",
            "width": "661",
            "height": "290"
          },
          "ansimg": {
            "image": "ch7s14a.jpg",
            "width": "660",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s15.jpg",
            "width": "620",
            "height": "200"
          },
          "ansimg": {
            "image": "ch7s15a.jpg",
            "width": "660",
            "height": "296"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s16.jpg",
            "width": "604",
            "height": "305"
          },
          "ansimg": {
            "image": "ch7s16a.jpg",
            "width": "660",
            "height": "260"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Show that in a quadrilateral □ABCD, AB + BC + CD + DA &lt; 2(BD + AC)",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch7s17a.jpg",
            "width": "660",
            "height": "321"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Two lines <i>l</i> and <i>m</i> intersect at the point O and P is a point on a line <i>n</i> passing through the point O such that P is equidistant from <i>l</i> and <i>m</i>. Prove that <i>n</i> is the bisector of the angle formed by <i>l</i> and <i>m</i>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch7s18a.jpg",
            "width": "660",
            "height": "420"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 19,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s19.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch7s19a.jpg",
            "width": "660",
            "height": "371"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 20,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s20.jpg",
            "width": "550",
            "height": "270"
          },
          "ansimg": {
            "image": "ch7s20a.jpg",
            "width": "660",
            "height": "240"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 21,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch7s21.jpg",
            "width": "555",
            "height": "30"
          },
          "ansimg": {
            "image": "ch7s21a.jpg",
            "width": "660",
            "height": "450"
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of Δ PQR should be equal to side AB of ΔABC so that the two triangles are congruent? Give reason for your answer.",
          "ans": "QR; They will be congruent by ASA.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ΔPQR should be equal to side BC of ΔABC so that the two triangles are congruent? Give reason for your answer.",
          "ans": "RP; They will be congruent by AAS.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?",
          "ans": "No; Angles must be included angles.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?",
          "ans": "No; Sides must be corresponding sides.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.",
          "ans": "No; Sum of the two sides = the third side.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "It is given that ΔABC ≅ ΔRPQ. Is it true to say that BC = QR? Why?",
          "ans": "No; BC = PQ.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 6
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "If ΔPQR ≅ ΔEDF, then is it true to say that PR = EF? Give reason for your answer.",
          "ans": "Yes; They are corresponding sides.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 7
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In ΔPQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? Give reason for your answer.",
          "ans": "PR; Side opposite the greater angle is longer.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 8
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "AD is a median of the triangle ABC. Is it true that AB + BC + CA &gt; 2 AD? Give reason for your answer.",
          "ans": "Yes; AB + BD &gt; AD and AC + CD &gt; AD.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 9
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.",
          "ans": "Yes; AB + BM &gt; AM and AC + CM &gt; AM.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 10
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.",
          "ans": "No; Sum of two sides is less than the third side.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 11
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.",
          "ans": "Yes, because in each case the sum of two sides is greater than the third side.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 12
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch7_pbq",
    "gowf": "ch7_gowf",
    "afow": "ch7_afow",
    "cs": "ch7_cs",
    "afq": "ch7_afq",
    "fib": "ch7_fib",
    "grade": "Grade 9",
    "mcq": "ch7_mcq",
    "vsaq": "ch7_vsaq",
    "laq": "ch7_laq",
    "tf": "ch7_tf",
    "co": "ch7_co",
    "nf": "ch7_nf",
    "mtf": "ch7_mtf",
    "yn": "ch7_yn",
    "saq": "ch7_saq",
    "dtf": "ch7_dtf",
    "map": "ch7_map",
    "ctt": "ch7_ctt",
    "un": "ch7_un",
    "ctco": "ch7_ctco",
    "grf": "ch7_grf",
    "snc": "ch7_snc",
    "jtf": "ch7_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch8",
    "chapterName": "Chapter 8 - Quadrilaterals",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Three angles of a quadrilateral are 75°, 90° and 75°. The fourth angle is:",
          "ans": "(d) 120°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 90°",
            "(b) 95°",
            "(c) 105°",
            "(d) 120°"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is",
          "ans": "(b) 50°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 55°",
            "(b) 50°",
            "(c) 40°",
            "(d) 25°"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "ABCD is a rhombus such that ∠ACB = 40°. Then ∠ADB is",
          "ans": "(c) 50°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 40°",
            "(b) 45°",
            "(c) 50°",
            "(d) 60°"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If angles ∠A, ∠B, ∠C and ∠D of the quadrilateral ☐ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ☐ABCD is a",
          "ans": "(c) trapezium",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) rhombus",
            "(b) parallelogram",
            "(c) trapezium",
            "(d) kite"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ☐PQRS, taken in order, is a rectangle, if",
          "ans": "(c) diagonals of ☐PQRS are perpendicular",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) ☐PQRS is a rectangle.",
            "(b) ☐PQRS is a parallelogram.",
            "(c) diagonals of ☐PQRS are perpendicular.",
            "(d) diagonals of ☐PQRS are equal."
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ☐PQRS, taken in order, is a rhombus, if",
          "ans": "(d) diagonals of ☐PQRS are equal",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) ☐PQRS is a rhombus",
            "(b) ☐PQRS is a parallelogram",
            "(c) diagonals of ☐PQRS are perpendicular",
            "(d) diagonals of ☐PQRS are equal"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Three angles of a quadrilateral are 75º, 90º and 75º. The fourth angle is",
          "ans": "(d) 120º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 90º",
            "(b) 95º",
            "(c) 105º",
            "(d) 120º"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is",
          "ans": "(b) 50º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 55º",
            "(b) 50º",
            "(c) 40º",
            "(d) 25º"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is",
          "ans": "(c) 50º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 40º",
            "(b) 45º",
            "(c) 50º",
            "(d) 60º"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if",
          "ans": "(c) diagonals of PQRS are perpendicular.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) PQRS is a rectangle.",
            "(b) PQRS is a parallelogram.",
            "(c) diagonals of PQRS are perpendicular.",
            "(d) diagonals of PQRS are equal."
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if",
          "ans": "(d) diagonals of PQRS are equal.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) PQRS is a rhombus.",
            "(b) PQRS is a parallelogram.",
            "(c) diagonals of PQRS are perpendicular.",
            "(d) diagonals of PQRS are equal."
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a",
          "ans": "(c) trapezium",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) rhombus",
            "(b) parallelogram",
            "(c) trapezium",
            "(d) kite"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a",
          "ans": "(d) quadrilateral whose opposite angles are supplementary",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) rectangle",
            "(b) rhombus",
            "(c) parallelogram",
            "(d) quadrilateral whose opposite angles are supplementary"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form",
          "ans": "(c) a rectangle",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a square",
            "(b) a rhombus",
            "(c) a rectangle",
            "(d) any other parallelogram"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is",
          "ans": "(b) a rectangle",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a rhombus",
            "(b) a rectangle",
            "(c) a square",
            "(d) any parallelogram"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "D and E are the mid-points of the sides AB and AC of D ABC and O is any point on side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively, then DEQP is",
          "ans": "(d) a parallelogram",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a square",
            "(b) a rectangle",
            "(c) a rhombus",
            "(d) a parallelogram"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if,",
          "ans": "(c) diagonals of ABCD are equal and perpendicular",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) ABCD is a rhombus.",
            "(b) diagonals of ABCD are equal.",
            "(c) diagonals of ABCD are equal and perpendicular.",
            "(d) diagonals of ABCD are perpendicular."
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to",
          "ans": "(c) 38º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "options": [
            "(a) 24º",
            "(b) 86º",
            "(c) 38º",
            "(d) 32º"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following is not true for a parallelogram?",
          "ans": "(c) opposite angles are bisected by the diagonals",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) opposite sides are equal",
            "(b) opposite angles are equal",
            "(c) opposite angles are bisected by the diagonals",
            "(d) diagonals bisect each other."
          ],
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "D and E are the mid-points of the sides AB and AC respectively of ΔABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is",
          "ans": "(c) DE = EF.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) ∠DAE = ∠EFC.",
            "(b) AE = EF.",
            "(c) DE = EF.",
            "(d) ∠ADE = ∠ECF."
          ],
          "val": 20
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA parallelogram is not a trapezium.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA kite is a parallelogram.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA trapezium is a parallelogram.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIn a parallelogram, adjacent sides are equal.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIn a parallelogram, adjacent angles are equal.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEach angle of a rectangle is an acute angle.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 6
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "The sum of the angles of a quadrilateral is _____________.",
          "ans": "360°",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If both pairs of opposite sides of quadrilaterals are parallel, then such quadrilaterals are called _____________.",
          "ans": "parallelograms",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If one pair of opposite sides of quadrilateral is parallel, then such quadrilateral is called a _____________.",
          "ans": "trapezium",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A parallelogram having all its angles right angles is called _____________.",
          "ans": "rectangle",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "A parallelogram having all sides equal is called a _____________.",
          "ans": "rhombus",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A parallelogram having all sides equal and all angles right angles is called a _____________.",
          "ans": "square",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If in quadrilateral, two pairs of adjacent sides are equal, then that quadrilateral is called a _____________.",
          "ans": "kite",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A square is _____________, _____________ and _____________.",
          "ans": "parallelogram, rectangle, rhombus",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A parallelogram is a _____________.",
          "ans": "trapezium",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A kite is not a _____________.",
          "ans": "parallelogram",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A trapezium is not a _____________.",
          "ans": "parallelogram",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A _____________ or a _____________ is not a square.",
          "ans": "rectangle, rhombus",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A diagonal of a parallelogram divides it into two _____________ triangles.",
          "ans": "congruent",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "In a parallelogram, _____________ sides are equal.",
          "ans": "opposite",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If each pair of opposite sides of a quadrilateral is equal, then that quadrilateral is a _____________.",
          "ans": "parallelogram",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "In a parallelogram, _____________ angles are equal.",
          "ans": "opposite",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If in a quadrilateral, each pair of opposite angles is equal, then it is a _____________.",
          "ans": "parallelogram",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The diagonals of a parallelogram _____________ each other.",
          "ans": "bisect",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the diagonals of a quadrilateral bisect each other, then that quadrilateral is a _____________.",
          "ans": "parallelogram",
          "code": "FIB",
          "val": 19
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Each angle of a rectangle is a _____________ angle.",
          "ans": "right",
          "code": "FIB",
          "val": 20
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The diagonals of a rhombus are _____________ to each other.",
          "ans": "perpendicular",
          "code": "FIB",
          "val": 21
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The quadrilateral formed by the bisectors of interior angles is a _____________.",
          "ans": "rectangle",
          "code": "FIB",
          "val": 22
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The bisectors of angles of a parallelogram form a _____________.",
          "ans": "rectangle",
          "code": "FIB",
          "val": 23
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A quadrilateral is a parallelogram if a pair of _____________ sides is equal and parallel.",
          "ans": "opposite",
          "code": "FIB",
          "val": 24
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The line segment joining the mid-points of two sides of a triangle is _____________ to the third side.",
          "ans": "parallel",
          "code": "FIB",
          "val": 25
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The line drawn through the mid-point of one side of a triangle, parallel to another side _____________ the third side.",
          "ans": "bisects",
          "code": "FIB",
          "val": 26
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d1.jpg",
            "width": "660",
            "height": "55"
          },
          "ansimg": {
            "image": "ch8d1a.jpg",
            "width": "672",
            "height": "653"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d2.jpg",
            "width": "608",
            "height": "30"
          },
          "ansimg": {
            "image": "ch8d2a.jpg",
            "width": "659",
            "height": "534"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "  ",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d3.jpg",
            "width": "630",
            "height": "150"
          },
          "ansimg": {
            "image": "ch8d3a.jpg",
            "width": "660",
            "height": "628"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch8d4a.jpg",
            "width": "660",
            "height": "594"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d5.jpg",
            "width": "570",
            "height": "30"
          },
          "ansimg": {
            "image": "ch8d5a.jpg",
            "width": "665",
            "height": "651"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Two parallel lines <i>l</i> and m are intersected by a transversal <i>p</i> (see figure). Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d6.jpg",
            "width": "300",
            "height": "220"
          },
          "ansimg": {
            "image": "ch8d6a.jpg",
            "width": "657",
            "height": "570"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d7.jpg",
            "width": "660",
            "height": "200"
          },
          "ansimg": {
            "image": "ch8d7a.jpg",
            "width": "662",
            "height": "539"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d8.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch8d8a.jpg",
            "width": "660",
            "height": "660"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8d9.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch8d9a.jpg",
            "width": "660",
            "height": "480"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s1.jpg",
            "width": "660",
            "height": "30"
          },
          "ansimg": {
            "image": "ch8s1a.jpg",
            "width": "660",
            "height": "152"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": " ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s2.jpg",
            "width": "660",
            "height": "204"
          },
          "ansimg": {
            "image": "ch8s2a.jpg",
            "width": "270",
            "height": "300"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "  ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s3.jpg",
            "width": "660",
            "height": "58"
          },
          "ansimg": {
            "image": "ch8s3a.jpg",
            "width": "660",
            "height": "380"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the figure, ☐ABCD is a parallelogram. Find the values of <i>x</i> and <i>y</i>.",
          "ans": "x + 110° = 180° <br>⇒ x = 180° – 110° = 70° <br>Also, ∠ADC = ∠BCE = 110° &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; <br>[Corresponding angles] <br>⇒ y = 110°",
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s4.jpg",
            "width": "265",
            "height": "130"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If opposite angles of a parallelogram are (3<i>x</i> – 5)° and (51 – <i>x</i>)°. Find the measure of each angle.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null,
          },
          "ansimg": {
            "image": "ch8s5a.jpg",
            "width": "400",
            "height": "476"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s6.jpg",
            "width": "450",
            "height": "30"
          },
          "ansimg": {
            "image": "ch8s6a.jpg",
            "width": "418",
            "height": "385"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s7.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch8s7a.jpg",
            "width": "660",
            "height": "396"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s8.jpg",
            "width": "540",
            "height": "210"
          },
          "ansimg": {
            "image": "ch8s8a.jpg",
            "width": "660",
            "height": "310"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch8s9.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch8s9a.jpg",
            "width": "660",
            "height": "535"
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the lengths of AC and BD.",
          "ans": "6 cm, 4 cm; Diagonals of a parallelogram bisect each other.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.",
          "ans": "No; Diagonals of a parallelogram bisect each other.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Can the angles 110º, 80º, 70º and 95º be the angles of a quadrilateral? Why or why not?",
          "ans": "No; Angle sum must be 360°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In quadrilateral ABCD, ∠A + ∠D = 180º. What special name can be given to this quadrilateral?",
          "ans": "Trapezium.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?",
          "ans": "Rectangle.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.",
          "ans": "No; Diagonals of a rectangle need not be perpendicular.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 6
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.",
          "ans": "No; sum of the angles of a quadrilateral is 360°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 7
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In D ABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.",
          "ans": "MBD",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch8vs8a.jpg",
            "width": "150",
            "height": "45"
          },
          "val": 8
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In the figure, it is given that BDEF and FDCE are parallelograms. Can you say that BD = CD? Why or why not?",
          "ans": "Yes; because BD = EF and CD = EF.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch8vs9.jpg",
            "width": "180",
            "height": "140"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 9
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "In the figure, ABCD and AEFG are two parallelograms. If ∠C = 55º, determine ∠F.",
          "ans": "55°, ∠F = ∠A and ∠A = ∠C.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch8vs10.jpg",
            "width": "180",
            "height": "110"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 10
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Can all the angles of a quadrilateral be acute angles? Give reason for your answer.",
          "ans": "No; Angle sum of a quadrilateral is 360°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 11
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Can all the angles of a quadrilateral be right angles? Give reason for your answer.",
          "ans": "Yes, Angle sum of a quadrilateral is 360°.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 12
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Diagonals of a quadrilateral ABCD bisect each other. If ∠A = 35º, determine ∠B.",
          "ans": "145°",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 13
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Opposite angles of a quadrilateral ABCD are equal. If AB = 4 cm, determine CD.",
          "ans": "4 cm",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 14
        }
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    "gowf": "ch8_gowf",
    "afow": "ch8_afow",
    "cs": "ch8_cs",
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    "fib": "ch8_fib",
    "grade": "Grade 9",
    "mcq": "ch8_mcq",
    "vsaq": "ch8_vsaq",
    "laq": "ch8_laq",
    "tf": "ch8_tf",
    "co": "ch8_co",
    "nf": "ch8_nf",
    "mtf": "ch8_mtf",
    "yn": "ch8_yn",
    "saq": "ch8_saq",
    "dtf": "ch8_dtf",
    "map": "ch8_map",
    "ctt": "ch8_ctt",
    "un": "ch8_un",
    "ctco": "ch8_ctco",
    "grf": "ch8_grf",
    "snc": "ch8_snc",
    "jtf": "ch8_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch9",
    "chapterName": "Chapter 9 - Areas of Parallelograms and Triangles",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is",
          "ans": "(d) a rhombus of area 24 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a rectangle of area 24 cm<sup>2</sup>",
            "(b) a square of area 25 cm<sup>2</sup>",
            "(c) a trapezium of area 24 cm<sup>2</sup>",
            "(d) a rhombus of area 24 cm<sup>2</sup>"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The median of a triangle divides it into two",
          "ans": "(a) triangles of equal area.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) triangles of equal area.",
            "(b) congruent triangles.",
            "(c) right triangles.",
            "(d) isosceles triangles."
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The median of a triangle divides it into two",
          "ans": "(a) triangles of equal area",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) triangles of equal area",
            "(b) congruent triangles",
            "(c) right triangles",
            "(d) isosceles triangles"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In which of the following figures, you find two polygons on the same base and between the same parallels?",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch9m4.jpg",
            "width": "625",
            "height": "266"
          },
          "ansimg": {
            "image": "ch9m4a.jpg",
            "width": "275",
            "height": "129"
          },
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is:",
          "ans": "(d) a rhombus of area 24 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a rectangle of area 24 cm<sup>2</sup>",
            "(b) a square of area 25 cm<sup>2</sup>",
            "(c) a trapezium of area 24 cm<sup>2</sup>",
            "(d) a rhombus of area 24 cm<sup>2</sup>"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, the area of parallelogram ABCD is:",
          "ans": "(c) DC × DL",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) AB × BM",
            "(b) BC × BN",
            "(c) DC × DL",
            "(d) AD × DL"
          ],
          "pic": {
            "image": "ch9m6.jpg",
            "width": "250",
            "height": "140"
          },
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, if parallelogram ABCD and rectangle ABEM are of equal area, then:",
          "ans": "(c) Perimeter of ABCD 7gt; Perimeter of ABEM",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch9m7.jpg",
            "width": "589",
            "height": "133"
          },
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch9m8.jpg",
            "width": "329",
            "height": "104"
          },
          "ansimg": {
            "image": "ch9m8a.jpg",
            "width": "117",
            "height": "47"
          },
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is",
          "ans": "(b) 1 : 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1 : 2",
            "(b) 1 : 1",
            "(c) 2 : 1",
            "(d) 3 : 1"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD",
          "ans": "(d) need not be any of (a), (b) or (c)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) is a rectangle",
            "(b) is always a rhombus",
            "(c) is a parallelogram",
            "(d) need not be any of (a), (b) or (c)"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is",
          "ans": "(b) 1 : 2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1 : 3",
            "(b) 1 : 2",
            "(c) 3 : 1",
            "(d) 1 : 4"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "ABCD is a trapezium with parallel sides AB = a cm and DC = b cm in the figure. E and F are the mid-points of the non-parallel sides. The ratio of ar (☐ABFE) and ar (☐EFCD) is",
          "ans": "(b) (3a + b) : (a + 3b)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a : b",
            "(b) (3a + b) : (a + 3b)",
            "(c) (a + 3b) : (3a + b)",
            "(d) (2a + b) : (3a + b)"
          ],
          "pic": {
            "image": "ch9m12.jpg",
            "width": "230",
            "height": "125"
          },
          "val": 12
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo figures are said to be on the same base and between the same parallels if they have a common base (side) and the vertices (or the vertex) opposite to the common base of each figure lie on a line parallel to the base.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tABCD is a parallelogram and X is the mid-point of AB. If ar (☐AXCD) = 24 cm<sup>2</sup>, then ar (ꕔABC) = 24 cm<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tPQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then ar (ꕔPAS) = 30 cm<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tPQRS is a parallelogram whose area is 180 cm<sup>2</sup> and A is any point on the diagonal QS. The area of ∆ASR = 90 cm<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tABC and BDE are two equilateral triangles such that D is the mid-point of BC.\n\t",
          "ans": "True",
          "code": "TF",
          "pic": {
            "image": "ch9tf5.jpg",
            "width": "304",
            "height": "40"
          },
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIn figure, ABCD and EFGD are two parallelograms and G is the mid-point of CD.\n\t",
          "ans": "False",
          "code": "TF",
          "pic": {
            "image": "ch9tf6.jpg",
            "width": "315",
            "height": "42"
          },
          "val": 6
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "Two figures are called _____________ if they have the same shape and same size.",
          "ans": "congruent",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If two figures are congruent, then they must have _____________ area.",
          "ans": "equal",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Parallelograms on the same base and between the same parallels are _____________ in area.",
          "ans": "equal",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Area of a parallelogram is the _____________ of its any side and the corresponding altitude.",
          "ans": "product",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "Parallelograms on the same (or equal bases) and having equal areas lie between the same _____________.",
          "ans": "parallels",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two triangles on the same base (or equal bases) and between the same parallels are _____________ in area.",
          "ans": "equal",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two triangles having the same base (or equal bases) and equal area lie between the same _____________.",
          "ans": "parallels",
          "code": "FIB",
          "val": 7
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d1.jpg",
            "width": "660",
            "height": "327"
          },
          "ansimg": {
            "image": "ch9d1a.jpg",
            "width": "320",
            "height": "569"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d2.jpg",
            "width": "660",
            "height": "260"
          },
          "ansimg": {
            "image": "ch9d2a.jpg",
            "width": "646",
            "height": "387"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d3.jpg",
            "width": "660",
            "height": "70"
          },
          "ansimg": {
            "image": "ch9d3a.jpg",
            "width": "655",
            "height": "747"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d4.jpg",
            "width": "660",
            "height": "331"
          },
          "ansimg": {
            "image": "ch9d4a.jpg",
            "width": "664",
            "height": "746"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d5.jpg",
            "width": "660",
            "height": "268"
          },
          "ansimg": {
            "image": "ch9d5a.jpg",
            "width": "628",
            "height": "416"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d6.jpg",
            "width": "445",
            "height": "40"
          },
          "ansimg": {
            "image": "ch9d6a.jpg",
            "width": "645",
            "height": "755"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d7.jpg",
            "width": "550",
            "height": "270"
          },
          "ansimg": {
            "image": "ch9d7a.jpg",
            "width": "596",
            "height": "472"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9d8.jpg",
            "width": "595",
            "height": "270"
          },
          "ansimg": {
            "image": "ch9d8a.jpg",
            "width": "423",
            "height": "701"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the given figure,",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s1.jpg",
            "width": "519",
            "height": "222"
          },
          "ansimg": {
            "image": "ch9s1a.jpg",
            "width": "620",
            "height": "60"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the given figure, ☐PQRS is a parallelogram. Find the value of y.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s2.jpg",
            "width": "300",
            "height": "300"
          },
          "ansimg": {
            "image": "ch9s2a.jpg",
            "width": "420",
            "height": "130"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": "Area of parallelogram ☐ABCD = Base × Height <br> &emsp; ⇒ 30 = AD × AQ<br> &emsp; ⇒ 30 = 6 × AQ<br> &emsp; ⇒ AQ = 5 cm",
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s3.jpg",
            "width": "520",
            "height": "330"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s4.jpg",
            "width": "460",
            "height": "240"
          },
          "ansimg": {
            "image": "ch9s4a.jpg",
            "width": "300",
            "height": "190"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s5.jpg",
            "width": "660",
            "height": "280"
          },
          "ansimg": {
            "image": "ch9s5a.jpg",
            "width": "270",
            "height": "190"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s6.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch9s6a.jpg",
            "width": "288",
            "height": "577"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s7.jpg",
            "width": "660",
            "height": "268"
          },
          "ansimg": {
            "image": "ch9s7a.jpg",
            "width": "500",
            "height": "236"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The area of the parallelogram ☐ABCD is 90 cm2. Find (i) ar (☐ABEF) (ii) ar (ꕔABD) (iii) ar (DBEF). See the figure.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s8.jpg",
            "width": "360",
            "height": "240"
          },
          "ansimg": {
            "image": "ch9s8a.jpg",
            "width": "650",
            "height": "330"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s9.jpg",
            "width": "660",
            "height": "70"
          },
          "ansimg": {
            "image": "ch9s9a.jpg",
            "width": "590",
            "height": "360"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s10.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch9s10a.jpg",
            "width": "600",
            "height": "389"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s11.jpg",
            "width": "640",
            "height": "35"
          },
          "ansimg": {
            "image": "ch9s11a.jpg",
            "width": "450",
            "height": "444"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s12.jpg",
            "width": "600",
            "height": "295"
          },
          "ansimg": {
            "image": "ch9s12a.jpg",
            "width": "150",
            "height": "213"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s13.jpg",
            "width": "415",
            "height": "45"
          },
          "ansimg": {
            "image": "ch9s13a.jpg",
            "width": "380",
            "height": "340"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s14.jpg",
            "width": "660",
            "height": "320"
          },
          "ansimg": {
            "image": "ch9s14a.jpg",
            "width": "535",
            "height": "331"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s15.jpg",
            "width": "660",
            "height": "70"
          },
          "ansimg": {
            "image": "ch9s15a.jpg",
            "width": "660",
            "height": "450"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A circle is inscribed in an equilateral triangle of side 12 cm touching the sides of the triangle. Find the radius of the circle.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch9s16a.jpg",
            "width": "385",
            "height": "385"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Show that median of a triangle divides it into two triangles of equal area.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch9s17a.jpg",
            "width": "400",
            "height": "380"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch9s18.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch9s18a.jpg",
            "width": "390",
            "height": "450"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch9_pbq",
    "gowf": "ch9_gowf",
    "afow": "ch9_afow",
    "cs": "ch9_cs",
    "afq": "ch9_afq",
    "fib": "ch9_fib",
    "grade": "Grade 9",
    "mcq": "ch9_mcq",
    "vsaq": "ch9_vsaq",
    "laq": "ch9_laq",
    "tf": "ch9_tf",
    "co": "ch9_co",
    "nf": "ch9_nf",
    "mtf": "ch9_mtf",
    "yn": "ch9_yn",
    "saq": "ch9_saq",
    "dtf": "ch9_dtf",
    "map": "ch9_map",
    "ctt": "ch9_ctt",
    "un": "ch9_un",
    "ctco": "ch9_ctco",
    "grf": "ch9_grf",
    "snc": "ch9_snc",
    "jtf": "ch9_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch10",
    "chapterName": "Chapter 10 - Circles",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(d) 8 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 17 cm",
            "(b) 15 cm",
            "(c) 4 cm",
            "(d) 8 cm"
          ],
          "pic": {
            "image": "ch10m1.jpg",
            "width": "660",
            "height": "60"
          },
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(a) 2 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2 cm",
            "(b) 3 cm",
            "(c) 4 cm",
            "(d) 5 cm"
          ],
          "pic": {
            "image": "ch10m2.jpg",
            "width": "565",
            "height": "203"
          },
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is:",
          "ans": "(d) 8 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 17 cm",
            "(b) 15 cm",
            "(c) 4 cm",
            "(d) 8 cm"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:",
          "ans": "(a) 2 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2 cm",
            "(b) 3 cm",
            "(c) 4 cm",
            "(d) 5 cm"
          ],
          "pic": {
            "image": "ch10m4.jpg",
            "width": "140",
            "height": "150"
          },
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is:",
          "ans": "(c) 10 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 6 cm",
            "(b) 8 cm",
            "(c) 10 cm",
            "(d) 12 cm"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, if ABC = 20º, then AOC is equal to:",
          "ans": "(b) 40º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 20º",
            "(b) 40º",
            "(c) 60º",
            "(d) 10º"
          ],
          "pic": {
            "image": "ch10m6.jpg",
            "width": "160",
            "height": "150"
          },
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to:",
          "ans": "(d) 45º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 30º",
            "(b) 60º",
            "(c) 90º",
            "(d) 45º"
          ],
          "pic": {
            "image": "ch10m7.jpg",
            "width": "170",
            "height": "170"
          },
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, if ∠OAB = 40º, then ∠ACB is equal to:",
          "ans": "(a) 50º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 50º",
            "(b) 40º",
            "(c) 60º",
            "(d) 70°"
          ],
          "pic": {
            "image": "ch10m8.jpg",
            "width": "210",
            "height": "200"
          },
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to:",
          "ans": "(c) 70º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 60º",
            "(b) 50º",
            "(c) 70º",
            "(d) 80º"
          ],
          "pic": {
            "image": "ch10m9.jpg",
            "width": "210",
            "height": "200"
          },
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to:",
          "ans": "(b) 50º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 80º",
            "(b) 50º",
            "(c) 40º",
            "(d) 30º"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to:",
          "ans": "(c) 60º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 30º",
            "(b) 45º",
            "(c) 60º",
            "(d) 120º"
          ],
          "pic": {
            "image": "ch10m11.jpg",
            "width": "210",
            "height": "200"
          },
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In figure, ∠AOB = 90º and ∠ABC = 30º, then ∠CAO is equal to:",
          "ans": "(d) 60º",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 30º",
            "(b) 45º",
            "(c) 90º",
            "(d) 60º"
          ],
          "pic": {
            "image": "ch10m12.jpg",
            "width": "210",
            "height": "200"
          },
          "val": 12
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe degree measure of semicircle is 180°.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tWe can draw as many tangents from an exterior point to a given circle.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "",
          "ans": "False",
          "code": "TF",
          "pic": {
            "image": "ch10tf3.jpg",
            "width": "460",
            "height": "35"
          },
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "",
          "ans": "True",
          "code": "TF",
          "pic": {
            "image": "ch10tf4.jpg",
            "width": "470",
            "height": "40"
          },
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf a circle is divided into four equal arcs, then each arc is a major arc.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tLength of a chord can never exceed the radius.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe degree measure of quadrant of a circle is 90°.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tChord and secant are same with respect to a circle.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo congruent circles with centre O and O′ intersect at two points A and B. Then ∠AOB = ∠AO′B.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tCongruent arcs (or equal arcs) of a circle subtend equal angles at the centre.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\t☐ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf A, B, C and D are four points such that ∠BAC = 45° and ∠ BDC = 45°, then A, B, C, D are concyclic.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 14
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 15
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tTwo congruent circles with centres O and O' intersect at two points A and B. Then ∠AOB = ∠AO'B.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 16
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThrough three collinear points a circle can be drawn.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 17
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 18
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf AOB is a diameter of a circle and C is a point on the circle, then AC<sup>2</sup> + BC<sup>2</sup> = AB<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 19
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 20
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 21
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 22
        }
        
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a _____________.",
          "ans": "circle",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The line segment joining the centre and any point on the circle is also called a _____________ of the circle.",
          "ans": "radius",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The part of circle inside the circle is called the _____________ of the circle.",
          "ans": "interior",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The part of circle outside the circle is called the _____________ of the circle.",
          "ans": "exterior",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "The circle and its interior make up the _____________ region.",
          "ans": "circular",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The line segment joining two points of a circle is called a _____________ of the circle.",
          "ans": "chord",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The chord passing through the centre of the circle is called a _____________ of the circle.",
          "ans": "diameter",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A diameter is the _____________ chord and all diameters have the same _____________.",
          "ans": "longest, length",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The length of diameter is _____________ times the radius.",
          "ans": "two",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A piece of a circle between two points is called an _____________.",
          "ans": "arc",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The arc having ends as ends of a diameter is called a _____________.",
          "ans": "semicircle",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The length of the circle is called its _____________.",
          "ans": "circumference",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The region between a chord and either of its arcs is called a _____________ of the circle.",
          "ans": "segment",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The region between an arc and the two radii, joining the centre to the end points of the arc, is called a _____________.",
          "ans": "sector",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When two arcs are equal, that is, each is a semicircle, then both segments and both sectors become the same and each is known as a _____________ region.",
          "ans": "semicircular",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A _____________ is the largest chord of the circle.",
          "ans": "diameter",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Concentric circles have _____________ centre but different radii.",
          "ans": "same",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A point whose distance from centre is less than its radius lies in _____________ of the circle.",
          "ans": "interior",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "C1 (O, S) and C2 (O′, S′) are two congruent circles with S = 6 cm and S′ = _____________.",
          "ans": "6 cm",
          "code": "FIB",
          "val": 19
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A line which intersects the circle in two different points is called _____________.",
          "ans": "secant",
          "code": "FIB",
          "val": 20
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Equal _____________ of a circle subtend equal angles at the centre.",
          "ans": "chords",
          "code": "FIB",
          "val": 21
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the angles subtended by the chords of a circle at the centre are equal, then the _____________ are equal.",
          "ans": "chords",
          "code": "FIB",
          "val": 22
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The _____________ from the centre of a circle to a chord bisects the chord.",
          "ans": "perpendicular",
          "code": "FIB",
          "val": 23
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The line drawn through the centre of a circle to bisect a chord is _____________ to the chord.",
          "ans": "perpendicular",
          "code": "FIB",
          "val": 24
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "There is one and only one circle passing through _____________ given non-collinear points.",
          "ans": "three",
          "code": "FIB",
          "val": 25
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The length of the perpendicular from a point to a line is the _____________ of the line from the point.",
          "ans": "distance",
          "code": "FIB",
          "val": 26
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Equal _____________ of a circle (or of congruent circles) are equidistant from the centre (or centres).",
          "ans": "chords",
          "code": "FIB",
          "val": 27
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Chords equidistant from the centre of a circle are _____________ in length.",
          "ans": "equal",
          "code": "FIB",
          "val": 28
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If two chords of a circle are equal, then their corresponding _____________ are congruent.",
          "ans": "arcs",
          "code": "FIB",
          "val": 29
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If two arcs are congruent, then their corresponding _____________ are equal.",
          "ans": "chords",
          "code": "FIB",
          "val": 30
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The angle subtended by an arc at the centre is _____________ the angle subtended by it at any point on the remaining part of the circle.",
          "ans": "double",
          "code": "FIB",
          "val": 31
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Angles in the same _____________ of a circle are equal.",
          "ans": "segment",
          "code": "FIB",
          "val": 32
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A quadrilateral is called _____________ if all the four vertices of it lie on a circle.",
          "ans": "cyclic",
          "code": "FIB",
          "val": 33
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The sum of either pair of opposite angles of a cyclic quadrilateral is _____________.",
          "ans": "180°",
          "code": "FIB",
          "val": 34
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the sum of a pair of opposite angles of a quadrilateral is 180°, the quadrilateral is _____________.",
          "ans": "cyclic",
          "code": "FIB",
          "val": 35
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10d1.jpg",
            "width": "490",
            "height": "40"
          },
          "ansimg": {
            "image": "ch10d1a.jpg",
            "width": "660",
            "height": "720"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch10d2a.jpg",
            "width": "660",
            "height": "666"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "If non-parallel sides of a trapezium are equal, prove that it is cyclic.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch10d3a.jpg",
            "width": "574",
            "height": "654"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch10d4a.jpg",
            "width": "644",
            "height": "615"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10d5.jpg",
            "width": "660",
            "height": "270"
          },
          "ansimg": {
            "image": "ch10d5a.jpg",
            "width": "660",
            "height": "478"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "In figure, find out the values of x and y if ∠A = 2x + 10°, ∠B = x + 20°, ∠C = y – 50° and ∠D = y – 10°. Also, find measure of each of its angles.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10d6.jpg",
            "width": "660",
            "height": "270"
          },
          "ansimg": {
            "image": "ch10d6a.jpg",
            "width": "660",
            "height": "478"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": "MBD",
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s1.jpg",
            "width": "630",
            "height": "60"
          },
          "ansimg": {
            "image": "ch10s1a.jpg",
            "width": "640",
            "height": "548"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In figure, AC = BD. Prove that ∠OAB = ∠OCD.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s2.jpg",
            "width": "230",
            "height": "220"
          },
          "ansimg": {
            "image": "ch10s2a.jpg",
            "width": "537",
            "height": "356"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": "∠AOB + ∠AOC = 180º <br>⇒ 2∠AOC = 180º &emsp;&emsp;&emsp; (∵ ∠AOB = ∠AOC) <br>⇒ ∠AOC = 90º <br>⇒ ∠AOC = ∠BOE = 90º &emsp;&emsp;&emsp; (Vertically opposite angles) <br>Now, in DBOE, x + 20º + 90º = 180º <br>⇒ x = 70º",
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s3.jpg",
            "width": "660",
            "height": "266"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s4.jpg",
            "width": "650",
            "height": "235"
          },
          "ansimg": {
            "image": "ch10s4a.jpg",
            "width": "520",
            "height": "240"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": "In △ABC, ∠C = 90º &emsp;&emsp;&emsp;&emsp;&emsp; [Angle in a semicircle is a right angle.] <br>We have AC = 12 cm <br>AB = 2 × 6.5 = 13 cm <br>In △ABC, BC<sup>2</sup> = AB<sup>2</sup> – AC<sup>2</sup> <br>⇒ BC<sup>2</sup> = 169 – 144 <br>⇒ BC<sup>2</sup> = 25 <br>⇒ BC = 5 cm",
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s5.jpg",
            "width": "35",
            "height": "40"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s6.jpg",
            "width": "440",
            "height": "240"
          },
          "ansimg": {
            "image": "ch10s6a.jpg",
            "width": "430",
            "height": "180"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Diameter of a circle is 26 cm and length of one of its chord is 10 cm. Find the distance of the chord from the centre of the circle.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch10s7a.jpg",
            "width": "610",
            "height": "498"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s8.jpg",
            "width": "610",
            "height": "30"
          },
          "ansimg": {
            "image": "ch10s8a.jpg",
            "width": "612",
            "height": "424"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s9.jpg",
            "width": "630",
            "height": "270"
          },
          "ansimg": {
            "image": "ch10s9a.jpg",
            "width": "540",
            "height": "270"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s10.jpg",
            "width": "470",
            "height": "35"
          },
          "ansimg": {
            "image": "ch10s10a.jpg",
            "width": "540",
            "height": "155"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s11.jpg",
            "width": "630",
            "height": "60"
          },
          "ansimg": {
            "image": "ch10s11a.jpg",
            "width": "635",
            "height": "415"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s12.jpg",
            "width": "650",
            "height": "30"
          },
          "ansimg": {
            "image": "ch10s12a.jpg",
            "width": "650",
            "height": "470"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral formed is cyclic.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch10s13a.jpg",
            "width": "546",
            "height": "446"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The circumcentre of the triangle ∆ABC is O. Prove that ∠OBC + ∠BAC = 90°.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch10s14a.jpg",
            "width": "605",
            "height": "475"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In the given figure, ∠ACB = 40°. Find ∠OAB.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s15.jpg",
            "width": "230",
            "height": "220"
          },
          "ansimg": {
            "image": "ch10s15a.jpg",
            "width": "560",
            "height": "210"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In figure, ∠BCP = 110° and ∠ADQ = 95°, then find sum of ∠DAB and ∠CBA.",
          "ans": "Here, ☐ABCD is a cyclic quadrilateral and the exterior angle of a cyclic quadrilateral is equal to its opposite interior angle. <br>Therefore, ∠DAB = ∠BCP <br>⇒ ∠DAB = 110º (1) <br>Similarly, ∠CBA = ∠ADQ <br>⇒ ∠CBA = 95º (2) <br>Adding (1) and (2), we get <br>∠DAB + ∠CBA = 110º + 95º = 205º",
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s16.jpg",
            "width": "300",
            "height": "230"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": "☐ABCD is a cyclic quadrilateral. <br>⇒ ∠BCD + ∠BAD = 180º <br>⇒ ∠BCD + 70º = 180º <br>⇒ ∠BCD = 110º <br>In DBCD, we have ∠CBD + ∠BCD + ∠BDC = 180º <br>⇒ 30º + 110º + ∠BDC = 180º <br>⇒ ∠BDC = 40º <br>Hence, ∠BCD = 110º and ∠BDC = 40º",
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s17.jpg",
            "width": "660",
            "height": "270"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch10s18.jpg",
            "width": "460",
            "height": "270"
          },
          "ansimg": {
            "image": "ch10s18a.jpg",
            "width": "516",
            "height": "420"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch10_pbq",
    "gowf": "ch10_gowf",
    "afow": "ch10_afow",
    "cs": "ch10_cs",
    "afq": "ch10_afq",
    "fib": "ch10_fib",
    "grade": "Grade 9",
    "mcq": "ch10_mcq",
    "vsaq": "ch10_vsaq",
    "laq": "ch10_laq",
    "tf": "ch10_tf",
    "co": "ch10_co",
    "nf": "ch10_nf",
    "mtf": "ch10_mtf",
    "yn": "ch10_yn",
    "saq": "ch10_saq",
    "dtf": "ch10_dtf",
    "map": "ch10_map",
    "ctt": "ch10_ctt",
    "un": "ch10_un",
    "ctco": "ch10_ctco",
    "grf": "ch10_grf",
    "snc": "ch10_snc",
    "jtf": "ch10_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch11",
    "chapterName": "Chapter 11 - Constructions",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "With the help of a ruler and a compass it is not possible to construct an angle of:",
          "ans": "(b) 40°",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 37.5°",
            "(b) 40°",
            "(c) 22.5°",
            "(d) 67.5°"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The construction of a triangle ABC, given that BC = 6 cm, B = 45° is not possible when difference of AB and AC is equal to:",
          "ans": "(a) 6.9 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 6.9 cm",
            "(b) 5.2 cm",
            "(c) 5.0 cm",
            "(d) 4.0 cm"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to:",
          "ans": "(d) 2.8 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3.2 cm",
            "(b) 3.1 cm",
            "(c) 3 cm",
            "(d) 2.8 cm"
          ],
          "val": 3
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tAn angle of 52.5° can be constructed.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tAn angle of 42.5° can be constructed.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA triangle ABC can be constructed in which BC = 6 cm, ∠C = 30° and AC – AB = 4 cm.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA triangle ABC can be constructed in which ∠B = 105°, ∠C = 90° and AB + BC + AC = 10 cm.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA triangle ABC can be constructed in which ∠B = 60°, ∠C = 45° and AB + BC + AC = 12 cm.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 6
        }
      ],
      [],
      [],
      [],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct an angle of measure 195°.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s1a.jpg",
            "width": "640",
            "height": "510"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct an angle of 120°.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s2a.jpg",
            "width": "660",
            "height": "420"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct an angle of 90°. Draw its bisector.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s3a.jpg",
            "width": "659",
            "height": "700"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct an equilateral triangle with side 3.5 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s4a.jpg",
            "width": "659",
            "height": "377"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct an angle of measure 37.5°.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s5a.jpg",
            "width": "437",
            "height": "485"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct a DABC in which BC = 5 cm, ∠B = 60° and AC + AB = 7.5 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s6a.jpg",
            "width": "518",
            "height": "604"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct a DPQR in which QR = 3 cm, ∠PQR = 45° and PQ – PR = 2 cm.",
          "ans":null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s7a.jpg",
            "width": "564",
            "height": "780"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct a right triangle whose base is 3.5 cm and sum of its hypotenuse and other side is 5.5 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s8a.jpg",
            "width": "660",
            "height": "784"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct a triangle DPQR in which QR = 8 cm, ∠Q = 60° and PR – PQ = 3 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s9a.jpg",
            "width": "452",
            "height": "725"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct a triangle DABC such that ∠B = 45°, ∠C = 60° and AB + BC + CA = 10 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s10a.jpg",
            "width": "633",
            "height": "567"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct a triangle having its perimeter 12.5 cm and the ratio of the angles as 3 : 4 : 5.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s11a.jpg",
            "width": "572",
            "height": "668"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s12a.jpg",
            "width": "649",
            "height": "466"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct an equilateral triangle if its altitude is 3.2 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s13a.jpg",
            "width": "658",
            "height": "527"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Construct an equilateral triangle with perimeter 14.5 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch11s14a.jpg",
            "width": "560",
            "height": "537"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch11_pbq",
    "gowf": "ch11_gowf",
    "afow": "ch11_afow",
    "cs": "ch11_cs",
    "afq": "ch11_afq",
    "fib": "ch11_fib",
    "grade": "Grade 9",
    "mcq": "ch11_mcq",
    "vsaq": "ch11_vsaq",
    "laq": "ch11_laq",
    "tf": "ch11_tf",
    "co": "ch11_co",
    "nf": "ch11_nf",
    "mtf": "ch11_mtf",
    "yn": "ch11_yn",
    "saq": "ch11_saq",
    "dtf": "ch11_dtf",
    "map": "ch11_map",
    "ctt": "ch11_ctt",
    "un": "ch11_un",
    "ctco": "ch11_ctco",
    "grf": "ch11_grf",
    "snc": "ch11_snc",
    "jtf": "ch11_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch12",
    "chapterName": "Chapter 12 - Heron’s Formula",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "An isosceles right triangle has area 8 cm<sup>2</sup>. The length of its hypotenuse is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch12m1.jpg",
            "width": "224",
            "height": "60"
          },
          "ansimg": {
            "image": "ch12m1a.jpg",
            "width": "88",
            "height": "32"
          },
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The perimeter of an equilateral triangle is 60 m. The area is",
          "ans": "(d) 100√3 m<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 10√3 m<sup>2</sup>",
            "(b) 15√3 m<sup>2</sup>",
            "(c) 20√3 m<sup>2</sup>",
            "(d) 100√3 m<sup>2</sup>"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is",
          "ans": "(c) 1344 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1322 cm<sup>2</sup>",
            "(b) 1311 cm<sup>2</sup>",
            "(c) 1344 cm<sup>2</sup>",
            "(d) 1392 cm<sup>2</sup>"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The area of an equilateral triangle with side 2√3 cm is",
          "ans": "(a) 5.196 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 5.196 cm<sup>2</sup>",
            "(b) 0.866 cm<sup>2</sup>",
            "(c) 3.496 cm<sup>2</sup>",
            "(d) 1.732 cm<sup>2</sup>"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The length of each side of an equilateral triangle having an area of 9√3 cm<sup>2</sup> is",
          "ans": "(d) 6 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 8 cm",
            "(b) 36 cm",
            "(c) 4 cm",
            "(d) 6 cm"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the area of an equilateral triangle is 16√3 cm<sup>2</sup>, then the perimeter of the triangle is",
          "ans": "(b) 24 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 48 cm",
            "(b) 24 cm",
            "(c) 12 cm",
            "(d) 36 cm"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude",
          "ans": "(c) 24√5 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 16√5 cm",
            "(b) 10√5 cm",
            "(c) 24√5 cm",
            "(d) 28 cm"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The area of an isosceles triangle, having base 2 cm and the length of one of the equal sides 4 cm, is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch12m8.jpg",
            "width": "305",
            "height": "99"
          },
          "ansimg": {
            "image": "ch12m8a.jpg",
            "width": "95",
            "height": "33"
          },
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per cm<sup>2</sup> is",
          "ans": "(b) ₹ 2.16",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) ₹ 2.00",
            "(b) ₹ 2.16",
            "(c) ₹ 2.48",
            "(d) ₹ 3.00"
          ],
          "val": 9
        }
      ],
      [
        { 
          "heading": "State True or False.",
          "qus": "\n\t\tThe area of a triangle with base 4 cm and height 6 cm is 24 cm<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe area of DABC is 8 cm<sup>2</sup> in which AB = AC = 4 cm and ∠A = 90°.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe area of the equilateral triangle is 20√3 cm<sup>2</sup> whose each side is 8 cm.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe cost of levelling the ground is the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹3 per m<sup>2</sup> is ₹918. \n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIn a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe area of a triangle with base 4 cm and height 6 cm is 24 cm<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe area of ∆ABC is 8 cm<sup>2</sup> in which AB = AC = 4 cm and ∠A = 90º.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "",
          "ans": "True",
          "code": "TF",
          "pic": {
            "image": "ch12tf8.jpg",
            "width": "690",
            "height": "50"
          },
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe area of the equilateral triangle is 20√3 cm<sup>2</sup> whose each side is 8 cm.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe base and the corresponding altitude of a parallelogram are 10 cm and 3.5 cm, respectively. The area of the parallelogram is 30 cm<sup>2</sup>.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe area of a regular hexagon of side ‘<i>a</i>’ is the sum of the areas of the five equilateral triangles with side <i>a</i>.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹3 per m<sup>2</sup> is ₹918.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIn a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 14
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "",
          "ans": "base",
          "code": "FIB",
          "pic": {
            "image": "ch12f1.jpg",
            "width": "315",
            "height": "40"
          },
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "",
          "ans": "Heron’s",
          "code": "FIB",
          "pic": {
            "image": "ch12f2.jpg",
            "width": "660",
            "height": "60"
          },
          "val": 2
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of ₹2000 per m<sup>2</sup> a year. A company hired one of its walls for 6 months. How much rent did it pay?",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12d1a.jpg",
            "width": "407",
            "height": "565"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Sides of a triangle are in the ratio 12 : 17 : 25 and its perimeter is 540 cm. Find its area.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12d2a.jpg",
            "width": "495",
            "height": "660"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12d3a.jpg",
            "width": "410",
            "height": "560"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "The unequal side of an isosceles triangle is 6 cm and its perimeter is 24 cm. Find its area.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12d4a.jpg",
            "width": "390",
            "height": "590"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "The sides of a quadrilateral ☐ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively and the angle between the first two sides is a right angle. Find its area.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12d5a.jpg",
            "width": "480",
            "height": "722"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A rhombus-shaped sheet with perimeter 40 cm and one diagonal 12 cm is painted on both sides at the rate of ₹5 per cm<sup>2</sup>. Find the cost of painting.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12d6a.jpg",
            "width": "409",
            "height": "779"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of parallelogram.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12d7a.jpg",
            "width": "628",
            "height": "567"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12d8.jpg",
            "width": "660",
            "height": "270"
          },
          "ansimg": {
            "image": "ch12d8a.jpg",
            "width": "400",
            "height": "504"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Two sides of a triangle are 8 cm and 11 cm and its perimeter is 32 cm. Find the area of the triangle.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12s1a.jpg",
            "width": "400",
            "height": "294"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side of its base is 3 : 2. Find the area of the triangle.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12s2a.jpg",
            "width": "400",
            "height": "390"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of ₹7 per m<sup>2</sup>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12s3a.jpg",
            "width": "475",
            "height": "506"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A triangular park has sides 120 m, 80 m and 50 m. A gardener has to put a fence all around it and also plant grass inside. How much area does he need to plant? Find the cost of fencing it with barbed wire at the rate of ₹20 per metre leaving a space 3 m wide for a gate on one side.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12s4a.jpg",
            "width": "444",
            "height": "473"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A garden is in the shape of a quadrilateral. The sides of the garden are 9 m, 40 m, 28 m and 15 m respectively in consecutive order and the angle between first two sides is a right angle. Find the area of the garden.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12s5a.jpg",
            "width": "410",
            "height": "540"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. It costs ₹4 to plough 1 m<sup>2</sup> of the field, find the total cost of ploughing the field.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12s6a.jpg",
            "width": "659",
            "height": "520"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12s7.jpg",
            "width": "660",
            "height": "201"
          },
          "ansimg": {
            "image": "ch12s7a.jpg",
            "width": "400",
            "height": "450"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the area of the trapezium ☐PQRS with height PQ given in figure.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12s8.jpg",
            "width": "230",
            "height": "190"
          },
          "ansimg": {
            "image": "ch12s8a.jpg",
            "width": "439",
            "height": "593"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12s9.jpg",
            "width": "660",
            "height": "60"
          },
          "ansimg": {
            "image": "ch12s9a.jpg",
            "width": "430",
            "height": "497"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, at minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12s10a.jpg",
            "width": "600",
            "height": "445"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch12_pbq",
    "gowf": "ch12_gowf",
    "afow": "ch12_afow",
    "cs": "ch12_cs",
    "afq": "ch12_afq",
    "fib": "ch12_fib",
    "grade": "Grade 9",
    "mcq": "ch12_mcq",
    "vsaq": "ch12_vsaq",
    "laq": "ch12_laq",
    "tf": "ch12_tf",
    "co": "ch12_co",
    "nf": "ch12_nf",
    "mtf": "ch12_mtf",
    "yn": "ch12_yn",
    "saq": "ch12_saq",
    "dtf": "ch12_dtf",
    "map": "ch12_map",
    "ctt": "ch12_ctt",
    "un": "ch12_un",
    "ctco": "ch12_ctco",
    "grf": "ch12_grf",
    "snc": "ch12_snc",
    "jtf": "ch12_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch13",
    "chapterName": "Chapter 13 - Surface Areas and Volumes",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "If length, breadth and height of a cuboid are 10 cm, 15 cm and 20 cm respectively, then surface area of cuboid will be",
          "ans": "(c) 1300 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 650 cm<sup>2</sup>",
            "(b) 1350 cm<sup>2</sup>",
            "(c) 1300 cm<sup>2</sup>",
            "(d) 1325 cm<sup>2</sup>"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If each edge of the cube is 5 cm, then surface area of this cube will be",
          "ans": "(d) 150 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 25 cm<sup>2</sup>",
            "(b) 100 cm<sup>2</sup>",
            "(c) 125 cm<sup>2</sup>",
            "(d) 150 cm<sup>2</sup>"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If length, breadth and height of a cuboid are 5 cm, 7 cm and 10 cm respectively, then lateral surface area will be",
          "ans": "(a) 240 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 240 cm<sup>2</sup>",
            "(b) 220 cm<sup>2</sup>",
            "(c) 200 cm<sup>2</sup>",
            "(d) 260 cm<sup>2</sup>"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Lateral surface area of a cube of side 5 cm will be",
          "ans": "(b) 100 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 25 cm<sup>2</sup>",
            "(b) 100 cm<sup>2</sup>",
            "(c) 50 cm<sup>2</sup>",
            "(d) 75 cm<sup>2</sup>"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a cylinder, radius is doubled and height is halved, curved surface area will be",
          "ans": "(c) same",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) halved",
            "(b) doubled",
            "(c) same",
            "(d) four times"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the radius of the base of the cylinder is 14 cm and height of the cylinder is 3 cm, then curved surface area of cylinder = ___________.",
          "ans": "(d) 264 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 260 cm<sup>2</sup>",
            "(b) 246 cm<sup>2</sup>",
            "(c) 270 cm<sup>2</sup>",
            "(d) 264 cm<sup>2</sup>"
          ],
          "pic": {
            "image": "ch13m6.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If radius of the base of the cylinder is 21 cm and height of the cylinder is 2 cm, then total surface area of cylinder = __________.",
          "ans": "(c) 3036 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3000 cm<sup>2</sup>",
            "(b) 3840 cm<sup>2</sup>",
            "(c) 3036 cm<sup>2</sup>",
            "(d) 3048 cm<sup>2</sup>"
          ],
          "pic": {
            "image": "ch13m6.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The total surface area of a cone whose radius is s/2 and slant height 2l is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2πs(l + s)",
            "ch13m8b.jpg",
            "(c) πs(l + s)",
            "(d) 2πsl"
          ],
          "ansimg": {
            "image": "ch13m8b.jpg",
            "width": "99",
            "height": "45"
          },
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The curved surface area of a right circular cone whose slant height is 15 cm and base radius is 14 cm = ___________.",
          "ans": "(d) 660 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 650 cm<sup>2</sup>",
            "(b) 600 cm<sup>2</sup>",
            "(c) 670 cm<sup>2</sup>",
            "(d) 660 cm<sup>2</sup>"
          ],
          "pic": {
            "image": "ch13m9.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The height of cone is 12 cm and base radius of cone is 21 cm. Then total surface area of cone = ___________.",
          "ans": "(c) 2982.33 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2981.33 cm<sup>2</sup>",
            "(b) 2983.33 cm<sup>2</sup>",
            "(c) 2982.33 cm<sup>2</sup>",
            "(d) 2980 cm<sup>2</sup>"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Surface area of sphere of radius 14 cm = ___________.",
          "ans": "(c) 2464 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2460 cm<sup>2</sup>",
            "(b) 2446 cm<sup>2</sup>",
            "(c) 2464 cm<sup>2</sup>",
            "(d) 2500 cm<sup>2</sup>"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Curved surface area of a hemisphere of radius 21 cm = ___________.",
          "ans": "(d) 2772 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2770 cm<sup>2</sup>",
            "(b) 2700 cm<sup>2</sup>",
            "(c) 2774 cm<sup>2</sup>",
            "(d) 2772 cm<sup>2</sup>"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Total surface area of a hemisphere of radius 7 cm = ___________.",
          "ans": "(b) 462 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 460 cm<sup>2</sup>",
            "(b) 462 cm<sup>2</sup>",
            "(c) 464 cm<sup>2</sup>",
            "(d) 463 cm<sup>2</sup>"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The total surface area of a cube is 96 cm<sup>2</sup>. The volume of the cube is",
          "ans": "(c) 64 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 8 cm<sup>3</sup>",
            "(b) 512 cm<sup>3</sup>",
            "(c) 64 cm<sup>3</sup>",
            "(d) 27 cm<sup>3</sup>"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Volume of a cuboid having length 10 cm, breadth 5 cm and height 2 cm = ___________.",
          "ans": "(d) 100 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 50 cm<sup>3</sup>",
            "(b) 110 cm<sup>3</sup>",
            "(c) 90 cm<sup>3</sup>",
            "(d) 100 cm<sup>3</sup>"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Volume of a cube having edge 5 cm = ___________.",
          "ans": "(b) 125 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 25 cm<sup>3</sup>",
            "(b) 125 cm<sup>3</sup>",
            "(c) 100 cm<sup>3</sup>",
            "(d) 120 cm<sup>3</sup>"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Volume of cylinder having radius 7 cm and height 2 cm = ___________.",
          "ans": "(d) 308 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 300 cm<sup>3</sup>",
            "(b) 310 cm<sup>3</sup>",
            "(c) 306 cm<sup>3</sup>",
            "(d) 308 cm<sup>3</sup>"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If volume of cylinder is 110 cm<sup>2</sup> and its height is 5 cm, then base area of cylinder = __________.",
          "ans": "(b) 22 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 20 cm<sup>2</sup>",
            "(b) 22 cm<sup>2</sup>",
            "(c) 24 cm<sup>2</sup>",
            "(d) 21 cm<sup>2</sup>"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Volume of cone having base radius 14 cm and height 9 cm = ___________.",
          "ans": "(d) 1848 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1840 cm<sup>3</sup>",
            "(b) 1845 cm<sup>3</sup>",
            "(c) 1850 cm<sup>3</sup>",
            "(d) 1848 cm<sup>3</sup>"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The volume of cone is 308 cm3 and radius of cone is 7 cm. Then height of cone = __________.",
          "ans": "(c) 6 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4 cm",
            "(b) 5 cm",
            "(c) 6 cm",
            "(d) 8 cm"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The radius of a sphere is 2s, then its volume will be",
          "ans": "(d) <sup>32</sup>/<sup>3</sup>πs<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) <sup>4</sup>/<sub>3</sub>πs<sup>3</sup>",
            "(b) 4πs<sup>3</sup>",
            "(c) <sup>8</sup>/<sub>3</sub>πs<sup>3</sup>",
            "(d) <sup>32</sup>/<sub>3</sub>πs<sup>3</sup>"
          ],
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is",
          "ans": "(b) 2.1 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4.2 cm",
            "(b) 2.1 cm",
            "(c) 2.4 cm",
            "(d) 1.6 cm"
          ],
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Volume of hemisphere having radius 21 cm = ___________.",
          "ans": "(b) 19404 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 19400 cm<sup>3</sup>",
            "(b) 19404 cm<sup>3</sup>",
            "(c) 19405 cm<sup>3</sup>",
            "(d) 19403 cm<sup>3</sup>"
          ],
          "pic": {
            "image": "ch13m10.jpg",
            "width": "103",
            "height": "47"
          },
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The radius of a sphere is 2r, then its volume will be",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch13m24.jpg",
            "width": "250",
            "height": "99"
          },
          "ansimg": {
            "image": "ch13m24a.jpg",
            "width": "80",
            "height": "47"
          },
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The total surface area of a cube is 96 cm<sup>2</sup>. The volume of the cube is:",
          "ans": "(c) 64 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 8 cm<sup>3</sup>",
            "(b) 512 cm<sup>3</sup>",
            "(c) 64 cm<sup>3</sup>",
            "(d) 27 cm<sup>3</sup>"
          ],
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is:",
          "ans": "(b) 2.1 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4.2 cm",
            "(b) 2.1 cm",
            "(c) 2.4 cm",
            "(d) 1.6 cm"
          ],
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a cylinder, radius is doubled and height is halved, curved surface area will be",
          "ans": "(c) same",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) halved",
            "(b) doubled",
            "(c) same",
            "(d) four times"
          ],
          "val": 27
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The total surface area of a cone whose radius is r/2 and slant height 2l is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2πr (l + r)",
            "ch13m28b.jpg",
            "(c) πr(l + r)",
            "(d) 2πrl"
          ],
          "ansimg": {
            "image": "ch13m28b.jpg",
            "width": "102",
            "height": "37"
          },
          "val": 28
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is:",
          "ans": "(b) 20 : 27",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 10 : 17",
            "(b) 20 : 27",
            "(c) 17 : 27",
            "(d) 20 : 37"
          ],
          "val": 29
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The lateral surface area of a cube is 256 m<sup>2</sup>. The volume of the cube is",
          "ans": "(a) 512 m<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 512 m<sup>3</sup>",
            "(b) 64 m<sup>3</sup>",
            "(c) 216 m<sup>3</sup>",
            "(d) 256 m<sup>3</sup>"
          ],
          "val": 30
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit which is 16 m long, 12m wide and 4 m deep is",
          "ans": "(b) 1920",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1900",
            "(b) 1920",
            "(c) 1800",
            "(d) 1840"
          ],
          "val": 31
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5 m) is",
          "ans": "(a) 15 m",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 15 m",
            "(b) 16 m",
            "(c) 10 m",
            "(d) 12 m"
          ],
          "val": 32
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is",
          "ans": "(a) 1 : 4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1 : 4",
            "(b) 1 : 3",
            "(c) 2 : 3",
            "(d) 2 : 1"
          ],
          "val": 33
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the radius of a cylinder is doubled and its curved surface is not changed, the height must be halved.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the radius of a cylinder is doubled and height is halved, the volume will be doubled.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the radius of a right circular cone is halved and height is doubled, the volume remains unchanged.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is 3 times the volume of the cone.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe volume of largest right circular cone that can be fitted in a cube whose edge is 2s equals to the volume of a hemisphere of radius s.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of sphere will be 6 : π.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIn a right circular cone, height, radius and slant height do not always be sides of a right triangle.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tThe volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tA cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the length of the diagonal of a cube is 6√3cm, then the length of the edge of the cube is 3 cm.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 14
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6: p.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 15
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the radius of a cylinder is doubled and height is halved, the volume will be doubled.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 16
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "Outer surface of a cuboid is made up of _____________ rectangles.",
          "ans": "six",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If <i>l</i>, <i>b</i> and <i>h</i> are length, breadth and height of a cuboid, then surface area of cuboid = ________________.",
          "ans": "2(<i>lb</i> + <i>bh</i> + <i>hl</i>)",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Cuboid, whose length, breadth and height are all equal, is called a _____________.",
          "ans": "cube",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If each edge of the cube is a, then surface area of this cube = _____________.",
          "ans": "6a<sup>2</sup>",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "If <i>l</i>, <i>b</i> and <i>h</i> are length,breadth and height of a cuboid, then lateral surface area of this cuboid = _____________.",
          "ans": "2<i>h</i> (<i>l</i> + <i>b</i>)",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Lateral surface area of a cube of side a = _____________.",
          "ans": "4a<sup>2</sup>",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the radius of the base of the cylinder and h is height of the cylinder, then curved surface area of a cylinder = _____________.",
          "ans": "2πrh",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the radius of the base of the cylinder and h is height of the cylinder, then total surface area of cylinder = _____________.",
          "ans": "2πr(<i>r</i> + <i>h</i>)",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is radius of base of right circular cone and l is slant height of right circular cone, then curved surface area of cone = ___________.",
          "ans": "πrl",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is radius of base of right circular cone and l and h are slant height and height of right circular cone respectively, then <i>l</i><sup>2</sup> = ___________.",
          "ans": "r<sup>2</sup> + h<sup>2</sup>",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is radius of base of right circular cone and l is slant height of right circular cone, then total surface area of a cone. = ___________.",
          "ans": "πr(l + r)",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A three dimensional figure (solid figure) which is made up of all points in the space, which lie at a constant distance from a fixed point is called a ___________.",
          "ans": "sphere",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the radius of the sphere, then surface area of a sphere = ___________.",
          "ans": "4πr<sup>2</sup>",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The curved surface area of hemisphere is ___________ the surface area of the sphere.",
          "ans": "half",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the radius of the sphere, then curved surface area of a hemisphere = ___________.",
          "ans": "2πr<sup>2</sup>",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the radius of the sphere, then total surface area of a hemisphere = ___________.",
          "ans": "3πr<sup>2</sup>",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If an object is solid, then the measure of the space occupied by such an object is called ___________ of the object.",
          "ans": "volume",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If <i>l</i>, b and h are length,breadth and height of a cuboid respectively, then volume of cuboid = ___________.",
          "ans": "<i>lbh</i>",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If a is the edge of the cube, then volume of cube = ___________.",
          "ans": "a<sup>3</sup>",
          "code": "FIB",
          "val": 19
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the base radius of cylinder and h is the height of the cylinder, then volume of a cylinder = ___________.",
          "ans": "πr<sup>2</sup>h",
          "code": "FIB",
          "val": 20
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Volume of cylinder = ___________ × height.",
          "ans": "base area",
          "code": "FIB",
          "val": 21
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the base radius of cone and h is the height of the cone, then volume of cone = ___________",
          "ans": "⅓πr<sup>2</sup>h",
          "code": "FIB",
          "val": 22
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is radius of the sphere, then volume of a sphere = ___________.",
          "ans": "¾πr<sup>3</sup>",
          "code": "FIB",
          "val": 23
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r is the radius of the hemisphere, then volume of a hemisphere =___________.",
          "ans": "⅔πr<sup>3</sup>",
          "code": "FIB",
          "val": 24
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Three metal cubes whose edges measure 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find its edge. Also, find the surface area of the new cube.",
          "ans": "Let the edge of a new cube be a cm. <br>Now, volume of the new cube = sum of the volumes of three cubes<br>⇒ a<sup>3</sup> = 3<sup>3</sup> + 4<sup>3</sup> + 5<sup>3</sup><br>⇒ a<sup>3</sup> = 27 + 64 + 125 <br>⇒ a<sup>3</sup> = 216<br>⇒ a<sup>3</sup> = 6<sup>3</sup> <br>⇒ a = 6 cm <br>Thus, edge of new cube = 6 cm <br>∴ Surface area of the new cube = 6a<sup>2</sup> = 6 × (6)<sup>2</sup> = 216 cm<sup>2</sup>",
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Shahid has built a cubical water tank with lid for his house with each edge 2 m. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles if one dozen of tiles costs him ₹480.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13d2a.jpg",
            "width": "436",
            "height": "457"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Length of mathematics lab is 1⅓ times its breadth and its height is ½ times its length. The cost of whitewashing the walls at the rate of ₹2.60 per m2 is ₹291.20. Find the cost of tiling the floor at the rate of ₹6.75 per m<sup>2</sup>.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13d3a.jpg",
            "width": "415",
            "height": "774"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "The total surface area of the cuboidal box is 63200 cm<sup>2</sup> and its length, breadth and height are in the ratio 8 : 5 : 3. Find the dimensions of the cuboidal box.",
          "ans": "Let length, breadth and height of cuboidal box be 8x, 5x and 3x respectively. <br>Total surface area of cubiodal box = 63200 cm<sup>2</sup> <br>⇒ 2(lb + bh + hl) = 63200 <br>⇒ 2[(8x × 5x) + (5x × 3x) + (3x × 8x)] = 63200 <br>⇒ 2(40x<sup>2</sup> + 15x<sup>2</sup> + 24x<sup>2</sup>) = 63200 <br>⇒ 2(79x<sup>2</sup>) = 63200 <br>⇒ 158 x<sup>2</sup> = 63200 <br>⇒ x<sup>2</sup> = 400 <br>⇒ x = 20 <br>So, length of cuboidal box = 8x <br>= 8 × 20 <br>= 160 cm <br>Breadth of cubiodal box = 5x <br>= 5 × 20 <br>= 100 cm <br>Height of cubiodal box = 3x <br>= 3 × 20 = 60 cm.",
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13d5.jpg",
            "width": "699",
            "height": "81"
          },
          "ansimg": {
            "image": "ch13d5a.jpg",
            "width": "501",
            "height": "727"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A cone of height 24 cm has a curved surface area 550 cm<sup>2</sup>. Find its volume.",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13d6.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13d6a.jpg",
            "width": "457",
            "height": "675"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A right circular cone of height 4 cm has a curved surface area of 47.1 cm2. Find the volume. (Take p = 3.14)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13d7a.jpg",
            "width": "395",
            "height": "720"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "The lateral surface area of a cube is 64 m<sup>2</sup>. Find its total surface area.",
          "ans": "Lateral surface area of cube = 64 m<sup>2</sup><br>⇒ 4a<sup>2</sup> = 64 <br>⇒ a<sup>2</sup> = 64/4 <br>⇒ a<sup>2</sup> = 16 <br>⇒ a = 4 m <br>Now, total surface area of cube = 6a<sup>2</sup> <br>= 6 × (4)<sup>2</sup> <br>= 6 × 16 <br>= 96 m<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The edge of a cube is 10.5 mm. Find its total surface area in cm<sup>2</sup>.",
          "ans": "The edge of a cube a = 10.5 mm <br>= 1.05 cm <br>Total surface area of cube <br>= 6a<sup>2</sup> <br>= 6 × (1.05)<sup>2</sup> <br>= 6 × 1.1025 <br>= 6.615 cm<sup>2</sup> <br>= 6.62 cm<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m<sup>2</sup>. How many revolutions did it make?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s3.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s3a.jpg",
            "width": "473",
            "height": "593"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A rectangle strip 5 cm × 25 cm is rotated completely about the 25 cm side. Find the total surface area of the solid thus generated.",
          "ans": "Clearly, the solid thus generated will be a right circular cylinder having its radius as 5 cm and height 25 cm.<br>∴ Radius, r = 5 cm and height, h = 25 cm",
          "code": "SATQ",	
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s3.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s4a.jpg",
            "width": "602",
            "height": "207"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The difference between the outside and inside surface of a cylindrical pipe 14 cm in length is 44 cm2. Find the thickness of the pipe.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s3.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s5a.jpg",
            "width": "408",
            "height": "442"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A roller 1.5 m long has a diameter of 70 cm. How many revolutions will it make to level a playground measuring 50 m × 33 m?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s3.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s6a.jpg",
            "width": "418",
            "height": "411"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The diameter of a road roller 1 m 40 cm long is 80 cm. If it takes 60 revolutions to level the surface, find the cost of levelling the surface at ₹10 per square metre.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s3.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s7a.jpg",
            "width": "378",
            "height": "381"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Twenty cylindrical pillars of the Rajya Sabha are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of ₹2.50 per square metre",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s3.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s8a.jpg",
            "width": "453",
            "height": "346"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The ratio of the curved surface area to the total surface area of right circular cylinder is 1 : 2. Find the ratio of height and radius of cylinder.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s9a.jpg",
            "width": "303",
            "height": "432"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s10a.jpg",
            "width": "428",
            "height": "384"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If slant height of a cone is 21 m and diameter of base is 24 m, then find its total surface area.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s11a.jpg",
            "width": "351",
            "height": "230"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The radius of a cone is 3 cm and vertical height is 4 cm. Find the area of the curved surface.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s12.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s12a.jpg",
            "width": "309",
            "height": "468"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A bus stop is barricaded from the remaining part of the road by using 40 hollow cones made of recycled cardboard. Each cone has a base radius of 20 cm and height 80 cm. If the outer side of each of the cones is to be painted and the cost of painting is ₹15 per square metre. Find the cost of painting all these 40 cones.<br>(Take π = 3.14 and √0.68 = 0.82).",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s13a.jpg",
            "width": "371",
            "height": "349"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the curved surface area of a right circular cone whose slant height is 8 cm and base radius is 7 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s14.jpg",
            "width": "47",
            "height": "103"
          },
          "ansimg": {
            "image": "ch13s14a.jpg",
            "width": "285",
            "height": "153"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A conical military tent is 5 m high and the diameter of the base is 24 m. Find the cost of canvas used in making this tent at the rate of π14 per square metre.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s15.jpg",
            "width": "47",
            "height": "103"
          },
          "ansimg": {
            "image": "ch13s15a.jpg",
            "width": "324",
            "height": "344"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The curved surface area of a right circular cone of radius 6 cm is 188.4 cm<sup>2</sup>. Find its height. (Take p = 3.14)",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s16a.jpg",
            "width": "289",
            "height": "378"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the total surface area of a hemisphere of radius 10 cm. [Use p = 3.14]",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s17a.jpg",
            "width": "357",
            "height": "256"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s18.jpg",
            "width": "47",
            "height": "103"
          },
          "ansimg": {
            "image": "ch13s18a.jpg",
            "width": "540",
            "height": "187"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the curved surface area and total surface area of a hemisphere of radius 35 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 19,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s19.jpg",
            "width": "47",
            "height": "103"
          },
          "ansimg": {
            "image": "ch13s19a.jpg",
            "width": "380",
            "height": "321"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The diameter of a sphere is decreased by 25%. By what per cent its surface area will decrease?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 20,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s20a.jpg",
            "width": "345",
            "height": "566"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The surface area of a sphere is 5544 cm<sup>2</sup>, find the radius of the sphere.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 21,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s21.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s21a.jpg",
            "width": "241",
            "height": "216"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The radii of two hemispheres are in the ratio 1 : 4. Compare their lateral surface area.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 22,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s22a.jpg",
            "width": "365",
            "height": "381"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the total surface area of hemisphere of radius 21 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 23,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s23.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s23a.jpg",
            "width": "273",
            "height": "192"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m3. If the present depth of water is 1.3 m, find the volume of water already used from the tank.",
          "ans": "Here, volume of cubical tank = 15.625 m<sup>3</sup><br>Depth = 1.3 m <br>Let edge of the cube be x cm. <br>Volume of cubical tank = 15.625 m<sup>3</sup> <br>∴ x<sup>3</sup> = 15.625 <br>∴ x<sup>3</sup> = (2.5)<sup>3</sup> <br>∴ x = 2.5 cm <br>Now, height of water = 1.3 m <br>Height of water used = 2.5 – 1.3 = 1.2 m <br>Volume of water used = 1.2 × 2.5 × 2.5 = 7.5 m<sup>3</sup>.",
          "code": "SATQ",
          "options": null,
          "val": 24,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A small village having a population of 5000 requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m × 25 m × 15 m. For how many days will the water of this tank last?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 25,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s25a.jpg",
            "width": "419",
            "height": "438"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The side of a cube is 8 cm. If it is cut into smaller cubes of side 2 cm, then find the number of such cubes.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 26,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s26a.jpg",
            "width": "386",
            "height": "321"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The weight of a metallic cuboid is 112 kg. Its width is 28 cm and length is 32 cm. If 1 cm3 of the metal weighs 25 grams, find the height of the cuboid.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 27,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s27a.jpg",
            "width": "308",
            "height": "161"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A teak wood log is cut first in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is 1.104 m<sup>3</sup>. How many rectangular planks of size 2.3 m × 0.75 m × 0.04 m can be cut from the cuboid?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 28,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s28a.jpg",
            "width": "490",
            "height": "380"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 29,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s29a.jpg",
            "width": "309",
            "height": "192"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A rectangular reservoir is 90 m long and 75 m wide. At what speed per hour must water flow into it through a square pipe of 10 cm wide so that the water rises by 2.4 m in 18 hours?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 30,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s30a.jpg",
            "width": "587",
            "height": "423"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A school provides milk to the students daily in cylindrical glasses of diameter 7 cm. If the glass is filled with milk up to a height of 12 cm, find how many litres of milk is needed to serve 1600 students.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 31,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s31.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s31a.jpg",
            "width": "375",
            "height": "218"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimetres of iron has been used in making the tube?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 32,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s32.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s32a.jpg",
            "width": "511",
            "height": "470"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "30 circular plates, each of radius 14 cm and thickness 3 cm, are placed one above the another to form a cylindrical solid. Find <br>(i) the total surface area <br>(ii) volume of the cylinder so formed.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 33,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s33.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s33a.jpg",
            "width": "439",
            "height": "311"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Rainwater falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if the rainfall is 1 cm? (Take p = 3.14).",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 34,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s34a.jpg",
            "width": "323",
            "height": "315"	
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The radius and height of a cylinder are in the ratio 2 : 3. If the volume of the cylinder is 1617 cm3, then find its radius and height.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 35,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s35.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s35a.jpg",
            "width": "283",
            "height": "449"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "1.1 cm<sup>3</sup> of gold is drawn into a wire of 0.1 mm in diameter. Find the length of the wire in metre.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 36,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s36.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s36a.jpg",
            "width": "371",
            "height": "287"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the weight of a lead pipe 3.5 m long. The external diameter of pipe is 2.4 cm and thickness of the pipe is 2 mm and 1 c.c. of lead weighs 10 grams.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 37,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s37.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s37a.jpg",
            "width": "611",
            "height": "557"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A patient in a hospital is given soup daily in cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height 4 cm, find the quantity of soup needs to be prepared daily to serve 250 patients.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 38,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s38.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s38a.jpg",
            "width": "467",
            "height": "320"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The volume of metallic cylindrical pipe is 748 cm<sup>3</sup>. Its length is 14 cm and its external radius is 9 cm. Find its thickness.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 39,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s39.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s39a.jpg",
            "width": "266",
            "height": "472"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface area of the solid so formed.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 40,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s40.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s40a.jpg",
            "width": "486",
            "height": "257"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 41,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s41.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s41a.jpg",
            "width": "539",
            "height": "747"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the volume of a right circular cone with radius 6 cm and height 14 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 42,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s42.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s42a.jpg",
            "width": "352",
            "height": "139"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Volume of a right circular cone is 9856 cm3. If diameter of the cone is 28 cm, find the curved surface area of the cone.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 43,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s43.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s43a.jpg",
            "width": "430",
            "height": "384"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The surface area of a sphere of radius 5 cm is five times the curved surface area of a cone of radius 4 cm. Find the height and volume of the cone.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 44,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s44.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s44a.jpg",
            "width": "563",
            "height": "604"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the quantity of water that a conical vessel of radius 7 cm and slant height 25 cm can hold.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 45,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s45a.jpg",
            "width": "309",
            "height": "192"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm when it is completely immersed in water.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 46,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s46.jpg",
            "width": "103",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s46a.jpg",
            "width": "357",
            "height": "347"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A shopkeeper has one spherical laddoo of radius 5 cm. With the same amount of material, how many laddoos of radius 2.5 cm can be made?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 47,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s47a.jpg",
            "width": "420",
            "height": "559"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The volumes of the two spheres are in the ratio 64:27. Find the ratio of their surface areas.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 48,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s48a.jpg",
            "width": "496",
            "height": "388"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 49,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s49.jpg",
            "width": "107",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s49a.jpg",
            "width": "264",
            "height": "281"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 50,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s50a.jpg",
            "width": "472",
            "height": "375"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 51,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s51a.jpg",
            "width": "686",
            "height": "384"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the volume and surface area of the largest sphere carved out a cube of edge 7 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 52,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s52.jpg",
            "width": "107",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s52a.jpg",
            "width": "580",
            "height": "233"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the amount of water displaced by a solid spherical ball whose diameter is 28 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 53,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s53.jpg",
            "width": "107",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s53a.jpg",
            "width": "701",
            "height": "313"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "How many spherical bullet can be made out a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 54,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13s54.jpg",
            "width": "107",
            "height": "47"
          },
          "ansimg": {
            "image": "ch13s54a.jpg",
            "width": "388",
            "height": "281"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Twenty-seven solid iron spheres, each of radius r and surface area s, are melted to form a sphere with surface area s′. Find <br>(i) the radius r′ of the new sphere. <br>(ii) the ratio of s and s′.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 55,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s55a.jpg",
            "width": "309",
            "height": "192"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Two solid spheres made of the same metal have weights 5920 grams and 740 grams respectively. Determine the radius of the larger sphere if the diameter of the smaller one is 5 cm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 56,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13s56a.jpg",
            "width": "360",
            "height": "671"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
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      [],
      [],
      [],
      [],
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      [],
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      [],
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      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch13_pbq",
    "gowf": "ch13_gowf",
    "afow": "ch13_afow",
    "cs": "ch13_cs",
    "afq": "ch13_afq",
    "fib": "ch13_fib",
    "grade": "Grade 9",
    "mcq": "ch13_mcq",
    "vsaq": "ch13_vsaq",
    "laq": "ch13_laq",
    "tf": "ch13_tf",
    "co": "ch13_co",
    "nf": "ch13_nf",
    "mtf": "ch13_mtf",
    "yn": "ch13_yn",
    "saq": "ch13_saq",
    "dtf": "ch13_dtf",
    "map": "ch13_map",
    "ctt": "ch13_ctt",
    "un": "ch13_un",
    "ctco": "ch13_ctco",
    "grf": "ch13_grf",
    "snc": "ch13_snc",
    "jtf": "ch13_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch14",
    "chapterName": "Chapter 14 - Statistics",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "The range of the data: <br>25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is",
          "ans": "(d) 26",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 10",
            "(b) 15",
            "(c) 18",
            "(d) 26"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is",
          "ans": "(b) 7",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 6",
            "(b) 7",
            "(c) 8",
            "(d) 12"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is",
          "ans": "(c) 35",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 15",
            "(b) 25",
            "(c) 35",
            "(d) 40"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Let <i>m</i> be the mid-point and <i>l</i> be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is",
          "ans": "(b) 2<i>m</i> – <i>l</i>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2<i>m</i> + <i>l</i>",
            "(b) 2<i>m</i> – <i>l</i>",
            "(c) <i>m</i> – <i>l</i>",
            "(d) <i>m</i> – 2<i>l</i>"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The class marks of a frequency distribution are given as follows: 15, 20, 25, …<br>The class corresponding to the class mark 20 is",
          "ans": "(b) 17.5 – 22.5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 12.5 – 17.5",
            "(b) 17.5 – 22.5",
            "(c) 18.5 – 21.5",
            "(d) 19.5 – 20.5"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In the class intervals 10 – 20, 20 – 30, the number 20 is included in",
          "ans": "(b) 20 – 30",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 10 – 20",
            "(b) 20 – 30",
            "(c) both the intervals",
            "(d) none of these intervals."
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Mode of the data <br>15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is",
          "ans": "(b) 15",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 14",
            "(b) 15",
            "(c) 16",
            "(d) 17"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The class mark of the class 90 – 120 is",
          "ans": "(b) 105",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 90",
            "(b) 105",
            "(c) 115",
            "(d) 120"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is",
          "ans": "(d) 38",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 28",
            "(b) 30",
            "(c) 35",
            "(d) 38"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The class mark of the class 90–120 is:",
          "ans": "(b) 105",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 90",
            "(b) 105",
            "(c) 115",
            "(d) 120"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The range of the data: <br>25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is",
          "ans": "(d) 26",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 10",
            "(b) 15",
            "(c) 18",
            "(d) 26",
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is:",
          "ans": "(b) 7",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 6",
            "(b) 7",
            "(c) 8",
            "(d) 12"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is:",
          "ans": "(c) 35",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 15",
            "(b) 25",
            "(c) 35",
            "(d) 40"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Let m be the mid-point and l be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is:",
          "ans": "(b) 2<i>m</i> – <i>l</i>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2<i>m</i> + <i>l</i>",
            "(b) 2<i>m</i> – <i>l</i>",
            "(c) <i>m</i> – <i>l</i>",
            "(d) <i>m</i> – 2<i>l</i>"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The class marks of a frequency distribution are given as follows: <br>15, 20, 25, ... <br>The class corresponding to the class mark 20 is:",
          "ans": "(b) 17.5 – 22.5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 12.5 – 17.5",
            "(b) 17.5 – 22.5",
            "(c) 18.5 – 21.5",
            "(d) 19.5 – 20.5"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In the class intervals 10–20, 20–30, the number 20 is included in:",
          "ans": "(b) 20–30",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 10–20",
            "(b) 20–30",
            "(c) both the intervals",
            "(d) none of these intervals"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A grouped frequency table with class intervals of equal sizes using 250–270 (270 not included in this interval) as one of the class interval is constructed for the following data: <br>268, 220, 368, 258, 242, 310, 272, 342, <br>310, 290, 300, 320, 319, 304, 402, 318, <br>406, 292, 354, 278, 210, 240, 330, 316, <br>406, 215, 258, 236. <br>The frequency of the class 310–330 is:",
          "ans": "(c) 6",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4",
            "(b) 5",
            "(c) 6",
            "(d) 7"
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A grouped frequency distribution table with classes of equal sizes using 63–72 (72 included) as one of the class is constructed for the following data: <br>30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, <br>40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96, <br>102, 110, 88, 74, 112, 14, 34, 44.<br>The number of classes in the distribution will be:",
          "ans": "(b) 10",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 9",
            "(b) 10",
            "(c) 11",
            "(d) 12"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "To draw a histogram to represent the following frequency distribution:",
          "ans": "(d) 2",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 6",
            "(b) 5",
            "(c) 3",
            "(d) 2"
          ],
          "pic": {
            "image": "ch14m19.jpg",
            "width": "580",
            "height": "96"
          },
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is:",
          "ans": "(d) 38",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 28",
            "(b) 30",
            "(c) 35",
            "(d) 38"
          ],
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the mean of the observations:<br>x, x + 3, x + 5, x + 7, x + 10 <br>is 9, the mean of the last three observations is",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch14m21.jpg",
            "width": "224",
            "height": "90"
          },
          "ansimg": {
            "image": "ch14m21a.jpg",
            "width": "70",
            "height": "45"
          },
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(b) 0",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) –1",
            "(b) 0",
            "(c) 1",
            "(d) n – 1"
          ],
          "pic": {
            "image": "ch14m22.jpg",
            "width": "542",
            "height": "54"
          },
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If each observation of the data is increased by 5, then their mean",
          "ans": "(d) is increased by 5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) remains the same",
            "(b) becomes 5 times the original mean",
            "(c) is decreased by 5",
            "(d) is increased by 5"
          ],
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch14m24.jpg",
            "width": "699",
            "height": "144"
          },
          "ansimg": {
            "image": "ch14m24a.jpg",
            "width": "88",
            "height": "45"
          },
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": " ",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch14m25.jpg",
            "width": "610",
            "height": "193"
          },
          "ansimg": {
            "image": "ch14m25a.jpg",
            "width": "114",
            "height": "62"
          },
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "  ",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "options": null,
          "pic": {
            "image": "ch14m26.jpg",
            "width": "705",
            "height": "256"
          },
          "ansimg": {
            "image": "ch14m26a.jpg",
            "width": "104",
            "height": "101"
          },
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be:",
          "ans": "(b) 51",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 50.5",
            "(b) 51",
            "(c) 51.5",
            "(d) 52"
          ],
          "val": 27
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be –3.5. The mean of the given numbers is:",
          "ans": "(d) 56.5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 46.5",
            "(b) 49.5",
            "(c) 53.5",
            "(d) 56.5"
          ],
          "val": 28
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is:",
          "ans": "(b) 36",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 23",
            "(b) 36",
            "(c) 38",
            "(d) 40"
          ],
          "val": 29
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The median of the data <br>78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is",
          "ans": "(c) 54",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 45",
            "(b) 49.5",
            "(c) 54",
            "(d) 56"
          ],
          "val": 30
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "For drawing a frequency polygon of a continous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abcissae are respectively:",
          "ans": "(c) class marks of the classes",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) upper limits of the classes",
            "(b) lower limits of the classes",
            "(c) class marks of the classes",
            "(d) upper limits of perceeding classes"
          ],
          "val": 31
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Median of the following numbers: <br>4, 4, 5, 7, 6, 7, 7, 12, 3 is",
          "ans": "(b) 5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 4",
            "(b) 5",
            "(c) 6",
            "(d) 7"
          ],
          "val": 32
        }
      ],
      [],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "Facts or figures which are numerical or otherwise, collected with a definite purpose are called ___________.",
          "ans": "data",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When the information was collected by the investigator herself or himself with a definite objective in her or his mind, the data obtained is called ___________ data.",
          "ans": "primary",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When the information was gathered from a source which already had the information stored, the data obtained is called ___________ data.",
          "ans": "secondary",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The difference between the highest and the lowest values of the observations in given data is called the ___________.",
          "ans": "range",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks",
          "qus": "The range of data 27, 18, 19, 21, 25, 35, 38 is ___________.",
          "ans": "20",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If class marks of a distribution are 17, 25, 33, 41, 49, 57, then the width of each class interval is ___________.",
          "ans": "8",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If marks of students of a class are arranged in ascending order, then it is called an ___________.",
          "ans": "array",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Groupings of a large amount of data are called ___________ or ___________ intervals .",
          "ans": "classes, class intervals",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The size of class or class interval is called ___________ or ___________.",
          "ans": "class size, class width",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The least number in the class is called ___________.",
          "ans": "lower class limit",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The greatest number in the class is called ___________.",
          "ans": "upper class limit",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A __________ graph is a pictorial representation of data in which usually bars of uniform width are drawn with equal spacing between them on one axis, depicting the variable.",
          "ans": "bar",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A graphical representation of a grouped frequency distribution with continuous classes is called ___________.",
          "ans": "histogram",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The mid-points of the class intervals are called ___________.",
          "ans": "class marks",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The ___________ of a number of observations is the sum of the values of all the observations divided by the total number of observations.",
          "ans": "mean (or average)",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The ___________ is that value of the given number of observations which divides it into exactly two parts.",
          "ans": "median",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The __________ is that value of the observation which occurs most frequently.",
          "ans": "mode",
          "code": "FIB",
          "val": 17
        }
      ],
      [],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "The monthly pocket money of six children is as follows: <br>₹ 105, ₹ 130, ₹ 140, ₹ 50, ₹ 25, ₹ 45<br>(i) What is the highest pocket money? <br>(ii) What is the lowest pocket money? <br>(iii) What is the range? <br>(iv) Arrange the amounts of pocket money in ascending order.",
          "ans": "(i) The highest pocket money is ₹ 140. <br>(ii) The lowest pocket money is ₹ 25. <br>(iii) The highest value of observation = ₹ 140 <br>The lowest value of observation = ₹ 25 <br>∴ Range = ₹140 – ₹25 = ₹115 <br>(iv) Amounts of pocket money in ascending order: <br>₹25, ₹45, ₹50, ₹105, ₹130, ₹140",
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The blood groups of 30 students are recorded as follows: <br>A, B, O, A, AB, O, A, O, B, A, O, B, A, AB, B, A, AB, B, A, A, O, A, AB, B, A, O, B, A, B, A. <br>Prepare a frequency distribution table for the data.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s2a.jpg",
            "width": "297",
            "height": "151"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The value of p up to 35 decimal places given below: <br>3.14159265358979323846264338327950288 <br>Make a frequency distribution of the digit 0 to 9 after the decimal point.",
          "ans": "3.14159265358979323846264338327950288",
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s3a.jpg",
            "width": "331",
            "height": "289"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Prepare a continuous grouped frequency distribution from the following data:",
          "ans": null,
          "code": "SATQ",	
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s4.jpg",
            "width": "322",
            "height": "191"
          },
          "ansimg": {
            "image": "ch14s4a.jpg",
            "width": "484",
            "height": "200"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Convert the given frequency distribution into a continuous grouped frequency distribution:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s5.jpg",
            "width": "363",
            "height": "196"
          },
          "ansimg": {
            "image": "ch14s5a.jpg",
            "width": "697",
            "height": "291"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The marks obtained by 40 students of a class in science (out of 100) are as follows:<br>50, 42, 48, 78, 83, 9, 70, 52, 43, 38, 5, 16, 20, 65, 41, 18, 24, 37, 60, 25, 18, 23, 47, 95, 17, 93, 3, 94, 6, 74, 66, 29, 13, 19, 27, 94, 80, 35, 48, 62.<br>Form a frequency table and a cumulative frequency table with equal intervals, one of them being (0 – 10) for the data.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s6a.jpg",
            "width": "699",
            "height": "513"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The expenditure of a family on different heads in a month is given below:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s7.jpg",
            "width": "432",
            "height": "273"
          },
          "ansimg": {
            "image": "ch14s7a.jpg",
            "width": "381",
            "height": "318"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Expenditure on Education of a country during a five year period (2002 – 2006), in crores of rupees, is given below:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s8.jpg",
            "width": "427",
            "height": "334"
          },
          "ansimg": {
            "image": "ch14s8a.jpg",
            "width": "423",
            "height": "413"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The following table gives the frequencies of most commonly used letters a, e, i, o, r, t, u from a page of a book:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s9.jpg",
            "width": "637",
            "height": "108"
          },
          "ansimg": {
            "image": "ch14s9a.jpg",
            "width": "393",
            "height": "424"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Draw a histogram of the following distribution:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s10.jpg",
            "width": "308",
            "height": "215"
          },
          "ansimg": {
            "image": "ch14s10a.jpg",
            "width": "290",
            "height": "280"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Draw a histogram to represent the following grouped frequency distribution:",
          "ans": "First of all we convert the class intervals into continuous form.",
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s11.jpg",
            "width": "318",
            "height": "233"
          },
          "ansimg": {
            "image": "ch14s11a.jpg",
            "width": "597",
            "height": "231"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The marks obtained (out of 100) by a class of 80 students are given below:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s12.jpg",
            "width": "361",
            "height": "240"
          },
          "ansimg": {
            "image": "ch14s12a.jpg",
            "width": "694",
            "height": "585"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s13.jpg",
            "width": "467",
            "height": "290"
          },
          "ansimg": {
            "image": "ch14s13a.jpg",
            "width": "390",
            "height": "317"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s14.jpg",
            "width": "657",
            "height": "359"
          },
          "ansimg": {
            "image": "ch14s14a.jpg",
            "width": "699",
            "height": "810"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Represent the following distribution by a frequency polygon:",
          "ans": "Here, we are given inclusive classes. First of all we will convert them into exclusive classes. Also, we introduce two more class intervals 9.5 – 19.5 and 99.5 – 109.5 each with frequency 0.",
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s15.jpg",
            "width": "403",
            "height": "276"
          },
          "ansimg": {
            "image": "ch14s15a.jpg",
            "width": "698",
            "height": "714"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find median of 12, 11, 6, 7, 10, 17, 9, 15, 13.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s16a.jpg",
            "width": "501",
            "height": "189"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The mean of x<sub>1</sub> and x<sub>2</sub> is 8 and the mean of x<sub>1</sub>, x<sub>2</sub> and x<sub>3</sub> is 9. Find x<sub>3</sub>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s17a.jpg",
            "width": "170",
            "height": "196"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The mean of 20 observations is 50. If the observation 50 is replaced by 140, what will be the resulting mean?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s18a.jpg",
            "width": "439",
            "height": "171"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 (out of 100) and that of boys is 71. Determine the mean score of the whole class.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 19,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s19a.jpg",
            "width": "340",
            "height": "454"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the median of 40, 42, 120, 99, 61, 92, 71, 58 and 56. If 58 is replaced by 85, then find the new median.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 20,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s20a.jpg",
            "width": "391",
            "height": "315"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The mean of first eight observations is 18 and mean of last eight observations is 20. If the mean of all fifteen observations is 19, find the 8th observation.",
          "ans": "Mean of first eight observations = 18 <br>∴ Sum of first eight observation = 8 × 18 = 144 <br>Similarly, sum of last eight observations = 8 × 20 = 160 <br>Sum of all fifteen observations = 15 × 19 = 285 <br>∴ 8th observation = (144 + 160) – 285 = 19.",
          "code": "SATQ",
          "options": null,
          "val": 21,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "For what value of x the mode of data is 12. Data: 12, 11, 10, 12, x, 10, 10, 9, 12, 10, 12.",
          "ans": "Frequency of 10 = 4 <br>Frequency of 12 = 4 <br>Now, the mode of the given data is 12. <br>So, it must have the maximum frequency. <br>Hence, the value of x must be 12. <br>Therefore, x = 12",
          "code": "SATQ",
          "options": null,
          "val": 22,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If a football team scored following number of goals in 10 matches, then find mean and median of data given: <br>2, 3, 4, 5, 0, 1, 3, 5, 4, 3.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 23,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14s23a.jpg",
            "width": "402",
            "height": "274"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the mean for the data:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 24,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s24.jpg",
            "width": "304",
            "height": "73"
          },
          "ansimg": {
            "image": "ch14s24a.jpg",
            "width": "448",
            "height": "247"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If the mean of the following data is 20.2, find the value of p:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 25,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14s25.jpg",
            "width": "305",
            "height": "73"
          },
          "ansimg": {
            "image": "ch14s25a.jpg",
            "width": "454",
            "height": "542"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In a diagnostic test in mathematics given to students, the following marks (out of 100) are recorded:<br>46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44 <br>Which ‘average’ will be a good representative of the above data and why?",
          "ans": "Median will be a good representative of the data, because <br>(i) each value occcurs once, <br>(ii) the data is influenced by extreme values.",
          "code": "SATQ",
          "options": null,
          "val": 26,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "The frequency distribution:",
          "ans": "Not correct. The classes are of varying widths, not of uniform widths.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch14vs1.jpg",
            "width": "563",
            "height": "481"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "A child says that the median of 3, 14, 18, 20, 5 is 18. What doesn’t the child understand about finding the median?",
          "ans": "Data has to be arranged in ascending (or descending ) order before finding the median.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "A football player scored the following number of goals in the 10 matches:",
          "ans": "No, the data have first to be arranged in ascending (or descending) order before finding the median.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch14vs3.jpg",
            "width": "501",
            "height": "187"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement.",
          "ans": "It is not correct. In a histogram, the area of each rectangle is propotional to the frequency of its class.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "The class marks of a continuous distribution are: <br>1.04, 1.14, 1.24, 1.34, 1.44, 1.54 and 1.64 <br>Is it correct to say that the last interval will be 1.55–1.73? Justify your answer.",
          "ans": "It is not correct. Reason is that difference between two consecutive marks should be equal to the class size.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "30 children were asked about the number of hours they watched TV programmes last week. The results are recorded as under:",
          "ans": "No. In fact the number of children who watch TV for 10 or more hours a week is 4 + 2, i.e. 6.",
          "code": "VSAQ",
          "option1": null,
          "option2": null,
          "option3": null,
          "aoption1": null,
          "aoption2": null,
          "aoption3": null,
          "pic": {
            "image": "ch14vs6.jpg",
            "width": "700",
            "height": "131"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          },
          "val": 6
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch14_pbq",
    "gowf": "ch14_gowf",
    "afow": "ch14_afow",
    "cs": "ch14_cs",
    "afq": "ch14_afq",
    "fib": "ch14_fib",
    "grade": "Grade 9",
    "mcq": "ch14_mcq",
    "vsaq": "ch14_vsaq",
    "laq": "ch14_laq",
    "tf": "ch14_tf",
    "co": "ch14_co",
    "nf": "ch14_nf",
    "mtf": "ch14_mtf",
    "yn": "ch14_yn",
    "saq": "ch14_saq",
    "dtf": "ch14_dtf",
    "map": "ch14_map",
    "ctt": "ch14_ctt",
    "un": "ch14_un",
    "ctco": "ch14_ctco",
    "grf": "ch14_grf",
    "snc": "ch14_snc",
    "jtf": "ch14_jtf"
  },
  {
    "subject": "Mathematics",
    "chapter": "ch15",
    "chapterName": "Chapter 15 - Probability",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following can’t be the probability of an event?",
          "ans": "(a) 1.5",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1.5",
            "(b) ⅗",
            "(c) 25%",
            "(d) 0.3"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will not be an ace is:",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch15m2.jpg",
            "width": "231",
            "height": "105"
          },
          "ansimg": {
            "image": "ch15m2a.jpg",
            "width": "65",
            "height": "45"
          },
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is:",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch15m3.jpg",
            "width": "231",
            "height": "105"
          },
          "ansimg": {
            "image": "ch15m3a.jpg",
            "width": "58",
            "height": "45"
          },
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is:",
          "ans": "(d) 0.8",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0.5",
            "(b) 0.6",
            "(c) 0.7",
            "(d) 0.8"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a survey of 364 children aged 19–36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is:",
          "ans": "(c) 0.75",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0.25",
            "(b) 0.50",
            "(c) 0.75",
            "(d) 0.80"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a medical examination of students of a class, the following blood groups are recorded:",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch15m6.jpg",
            "width": "659",
            "height": "182"
          },
          "ansimg": {
            "image": "ch15m6a.jpg",
            "width": "60",
            "height": "45"
          },
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Two coins are tossed 1000 times and the outcomes are recorded as below:",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch15m7.jpg",
            "width": "514",
            "height": "193"
          },
          "ansimg": {
            "image": "ch15m7a.jpg",
            "width": "60",
            "height": "50"
          },
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "80 bulbs are selected at random from a lot and their life time (in hrs) is recorded in the form of a frequency table given below:",
          "ans": "(d) 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "pic": {
            "image": "ch15m8.jpg",
            "width": "581",
            "height": "184"
          },
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Refer to Q. 5 above: <br>The probability that bulbs selected randomly from the lot has life less than 900 hours is:",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": null,
          "pic": {
            "image": "ch15m9.jpg",
            "width": "291",
            "height": "102"
          },
          "ansimg": {
            "image": "ch15m9a.jpg",
            "width": "60",
            "height": "50"
          },
          "val": 9
        }
      ],
      [],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "A ___________ is an action which results in one or several outcomes.",
          "ans": "trial",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "An __________ for an experiment is the collection of some outcomes of the experiment.",
          "ans": "event",
          "code": "FIB",
          "val": 2
        }
      ],
      [],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "A die was rolled 100 times and the number of times 6 came up was noted. If the experimental probability calculated from this information is ⅖, then how many times 6 came up? Justify your answer.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s1a.jpg",
            "width": "396",
            "height": "177"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "If theoretical probability of an event ‘E’ is 0.37. What is theoretical probability of event ‘not E’?",
          "ans": "P (not E) = 1 – P (E) <br>P (not E) = 1 – 0.37 = 0.63",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Marks obtained by 2500 students are shown in the following table:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15s3.jpg",
            "width": "408",
            "height": "304"
          },
          "ansimg": {
            "image": "ch15s3a.jpg",
            "width": "400",
            "height": "190"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "    ",
          "ans": null,
          "code": "SATQ",	
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15s4.jpg",
            "width": "700",
            "height": "75"
          },
          "ansimg": {
            "image": "ch15s4a.jpg",
            "width": "275",
            "height": "365"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A bag contains 3 red marbles and 4 blue marbles. A marble is drawn at random, find the probability that the marble drawn is (i) red in colour (ii) blue in colour.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s5a.jpg",
            "width": "376",
            "height": "268"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A survey found that ages of 250 workers in a factory is distributed as follows:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15s6.jpg",
            "width": "446",
            "height": "338"
          },
          "ansimg": {
            "image": "ch15s6a.jpg",
            "width": "391",
            "height": "340"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "What is the probability of getting a sum of 9 from two throws of a dice?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s7a.jpg",
            "width": "442",
            "height": "102"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Three unbiased coins are tossed. What is the probability of getting at most two heads?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s8a.jpg",
            "width": "548",
            "height": "167"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s9a.jpg",
            "width": "665",
            "height": "265"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a black card?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s10a.jpg",
            "width": "423",
            "height": "142"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A card is drawn at random from a pack of 52 cards. What is the probability of that the card drawn is a king?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s11a.jpg",
            "width": "383",
            "height": "141"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Four coins are tossed simultaneously 150 times with the following frequencies of different outcomes:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15s12.jpg",
            "width": "372",
            "height": "303"
          },
          "ansimg": {
            "image": "ch15s12a.jpg",
            "width": "510",
            "height": "296"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A card is drawn from a pack of 52 cards. What is the probability of getting a queen of club or a king of heart?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s13a.jpg",
            "width": "544",
            "height": "113"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15s14a.jpg",
            "width": "509",
            "height": "142"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A purse contains a number of ₹ 1, ₹ 2 and ₹ 5 coins as given below:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15s15.jpg",
            "width": "702",
            "height": "146"
          },
          "ansimg": {
            "image": "ch15s15a.jpg",
            "width": "382",
            "height": "112"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Can the experimental probability of an event be a negative number? If not, why?",
          "ans": "No, since the number of trials in which the event can happen cannot be negative, and the total number of trials is always positive.",
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Can the experimental probability of an event be greater than 1? Justify your answer.",
          "ans": "No, since the number of trials in which the event can happen cannot be greater than the total number of trials.",
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "As the number of tosses of a coin increases, the ratio of the number of heads to the total number of tosses will be ½. Is it correct? If not, write the correct one.",
          "ans": "No. As the number of tosses of a coin increases, the ratio of the number of heads to the total number of tosses will be nearer to ½, not exactly ½.",
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch15_pbq",
    "gowf": "ch15_gowf",
    "afow": "ch15_afow",
    "cs": "ch15_cs",
    "afq": "ch15_afq",
    "fib": "ch15_fib",
    "grade": "Grade 9",
    "mcq": "ch15_mcq",
    "vsaq": "ch15_vsaq",
    "laq": "ch15_laq",
    "tf": "ch15_tf",
    "co": "ch15_co",
    "nf": "ch15_nf",
    "mtf": "ch15_mtf",
    "yn": "ch15_yn",
    "saq": "ch15_saq",
    "dtf": "ch15_dtf",
    "map": "ch15_map",
    "ctt": "ch15_ctt",
    "un": "ch15_un",
    "ctco": "ch15_ctco",
    "grf": "ch15_grf",
    "snc": "ch15_snc",
    "jtf": "ch15_jtf"
  }
]

Youez - 2016 - github.com/yon3zu
LinuXploit