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var chpdata=[
{
  "subject": "Mathematics",
  "chapter": "ch1",
  "chapterName": "Chapter 1 - Real Numbers",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following will have a terminating decimal expansion?",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch1a3.jpg",
				"width": "64",
				"height": "40"
				},
				"options": [
					"ch1a1.jpg",
					"ch1a2.jpg",
					"ch1a3.jpg",
					"ch1a4.jpg"
				],
				"val": 1
			},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "On applying Euclid’s division lemma to a positive integer ‘a’ and b = 4, there exist integers q and s such that a = 4q + s, where s must satisfy:",
				"ans": "(b) 0 ≤ s < 4",
				"code": "MCQ",
				"options": [
					"(a) 0 < s ≤ 4",
					"(b) 0 ≤ s < 4",
					"(c) 0 < s < a",
					"(d) 4 ≤ s < a"
				],
				"val": 2
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "The largest number which divides 224 and 118 leaving remainders 4 and 3, respectively, is:",
				"ans": "(c) 5",
				"code": "MCQ",
				"options": [
					"(a) 15",
					"(b) 21",
					"(c) 5",
					"(d) 10"
				],
				"val": 3
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "For some integer q, every odd integer is of the form:",
				"ans": "(d) 2q + 1",
				"code": "MCQ",
				"options": [
					"(a) q",
					"(b) q + 2",
					"(c) 2q",
					"(d) 2q + 1"
				],
				"val": 4
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "If the HCF of 65 and 117 is expressible in the form 65 m – 117, then value of m is",
				"ans": "(b) 2",
				"code": "MCQ",
				"options": [
					"(a) 4",
					"(b) 2",
					"(c) 1",
					"(d) 3"
				],
				"val": 5
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "HCF (a, b) × LCM (a, b) = ______________",
				"ans": "(c) a × b",
				"code": "MCQ",
				"options": [
					"(a) a + b",
					"(b) a ÷ b",
					"(c) a × b",
					"(d) a – b"
				],
				"val": 6
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "If HCF (a, b) = 12 and a × b = 1500, then LCM (a, b)",
				"ans": "(a) 125",
				"code": "MCQ",
				"options": [
					"(a) 125",
					"(b) 800",
					"(c) 90",
					"(d) 3600"
				],
				"val": 7
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "LCM of smallest prime number and smallest composite number is:",
				"ans": "(b) 4",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) 4",
					"(c) 1",
					"(d) 8"
				],
				"val": 8
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "If x and y are both odd positive integers, then x<sup>2</sup> + y<sup>2</sup> is not divisible by _______________.",
				"ans": "(d) 4",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) 10",
					"(c) 18",
					"(d) 4"
				],
				"val": 9
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "∠3 + ∠5 is ___________ number.",
				"ans": "(c) irrational",
				"code": "MCQ",
				"options": [
					"(a) rational",
					"(b) natural",
					"(c) irrational",
					"(d) whole"
				],
				"val": 10
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "Two integers p and q are expressed in powers of primes as p = a<sup>15</sup>b<sup>3</sup>ef<sup>7</sup> and q = a<sup>4</sup>b<sup>15</sup>g<sup>2</sup>. Then LCM (p, q)",
				"ans": "a<sup>15</sup>b<sup>15</sup>ef<sup>7</sup>g<sup>2</sup>",
				"code": "MCQ",
				"options": [
					"(a) a<sup>15</sup>b<sup>15</sup>ef<sup>7</sup>g<sup>2</sup>",
					"(b) a<sup>4</sup>b<sup>3</sup>",
					"(c) a<sup>15</sup>b<sup>15</sup>g<sup>2</sup>",
					"(d) ef<sup>7</sup>g<sup>2</sup>"
				],
				"val": 11
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "The smallest number which when divided by 35 and 126 leaves the remainder 7 in each case.",
				"ans": "(c) 637",
				"code": "MCQ",
				"options": [
					"(a) 280",
					"(b) 273",
					"(c) 637",
					"(d) 421"
				],
				"val": 12
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is",
				"ans": "(d) 2520",
				"code": "MCQ",
				"options": [
					"(a) 10",
					"(b) 100",
					"(c) 504",
					"(d) 2520"
				],
				"val": 13
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) irrational",
				"code": "MCQ",
				"pic": {
				"image": "ch1a13.jpg",
				"width": "318",
				"height": "29"
				},
				"options": [
					"(a) prime",
					"(b) rational",
					"(c) irrational",
					"(d) whole"
				],
				"val": 14
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 4 places of decimal",
				"code": "MCQ",
				"pic": {
				"image": "ch1a22.jpg",
				"width": "336",
				"height": "34"
				},
				"options": [
					"(a) 4 places of decimal",
					"(b) 3 places of decimal",
					"(c) 2 places of decimal",
					"(d) Never terminates"
				],
				"val": 15
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": "0.022222... is a __________",
				"ans": "(c) rational number",
				"code": "MCQ",
				"options": [
					"(a) integer",
					"(b) zero",
					"(c) rational number",
					"(d) irrational number"
				],
				"val": 16
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) None of these.",
				"code": "MCQ",
				"pic": {
				"image": "ch1a23.jpg",
				"width": "541",
				"height": "29"
				},
				"options": [
					"(a) q = 3<sup>m</sup> × 2<sup>n</sup>, where m and n are whole numbers.",
					"(b) q = 3<sup>m</sup> × 7<sup>n</sup>, where m and n are whole numbers.",
					"(c) q = 3<sup>m</sup> × 5<sup>n</sup>, where m and n are whole numbers.",
					"(d) None of these."
				],
				"val": 17
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) terminating decimal expansion",
				"code": "MCQ",
				"pic": {
				"image": "ch1a24.jpg",
				"width": "228",
				"height": "38"
				},
				"options": [
					"(a) terminating decimal expansion",
					"(b) non-terminating decimal expansion",
					"(c) non-terminating repeating decimal expansion",
					"(d) non-terminating, non-repeating expansion."
				],
				"val": 18
	},
	
	{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) q can't be expressed as 2<sup>m</sup> × 5<sup>n</sup>",
				"code": "MCQ",
				"pic": {
				"image": "ch1a25.jpg",
				"width": "514",
				"height": "32"
				},
				"options": [
					"(a) q can't be expressed as 3<sup>m</sup> × 5<sup>n</sup>",
					"(b) q can be expressed as 2<sup>m</sup> × 5<sup>n</sup>",
					"(c) q can't be expressed as 2<sup>m</sup> × 5<sup>n</sup>",
					"(d) q can be expressed as 2<sup>m</sup> × 3<sup>n</sup>"
				],
				"val": 19
	},
	
	
	
	],
    [],
    [],
    [],
    [],
    [],
    [
      {
        "heading": "Answer the following questions in short.",
        "qus": "Show that 1196 and 5265 are not coprime.",
        "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": "ch1a5.jpg",
          "width": "421",
          "height": "289"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Using Euclid's Division Algorithm, find the HCF of the numbers 867 and 255.",
        "ans": "867 = 255 × 3 + 102 <br/> 255 = 102 × 2 + 51 <br/> 102 = 51 × 2 + 0 <br/> HCF (867, 255)= 51",
        "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": "On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?",
        "ans": "Here, minimum distance that each of 3 persons walk to cover in complete steps = LCM (40, 42, 45) <br/> Now by prime factorisation, 40 = 2<sup>3</sup> × 5 <br/> 42 = 2 × 3 × 7 <br/> 45 = 3 × 3 × 5 = 3<sup>2</sup> × 5 <br/> ∴ LCM (40, 42, 45) = 2<sup>3</sup> × 3<sup>2</sup> × 5 × 7 = 2520 cm = 25.20 m [Ans: 2520 cm = 25.20 m]",
        "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 HCF of 90 and 126 by Euclid’s Division Algorithm. Also, find their LCM and verify that HCF × LCM = Product of numbers.",
        "ans": "Applying Euclid’s Division Algorithm to 90 and 126, <br/> 126 = 90 × 1 + 36 <br/> 90 = 36 × 2 + 18 <br/> 36 = 18 × 2 = 0 ∴ HCF (90, 126) = 18 <br/> By prime factorisation 90 = 2 × 3<sup>2</sup> × 5 <br/> 126 = 2 × 3<sup>2</sup> × 7 <br/> ∴ LCM (90, 126) = Product of highest powers of prime factors. <br/> = 2 × 3<sup>2</sup> × 5 × 7 = 630 <br/>  Now, HCF × LCM = 18 × 630 <br/> = 11340 <br/> And produce of numbers = 90 × 126 = 11340 <br/> So, HCF × LCM = Product of two numbers. [Ans: HCF = 18, LCM = 630]",
        "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 LCM of 92 and 510. Also, find their HCF by using LCM.",
        "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": "ch1a10.jpg",
          "width": "395",
          "height": "236"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Check whether 14<sup>n</sup> can end with digit zero for any natural number n.",
        "ans": "Let us suppose 14<sup>n</sup> end with 0. <br/> 14<sup>n</sup> in divisible by 5. <br/> Prime factorisation of 14<sup>n</sup> must contain prime number 5, but 14<sup>n</sup> = (2 × 7)<sup>n</sup> = 2<sup>n</sup> × 7<sup>n</sup>. <br/> This means only primes in the factorisation of 14n are 2 and 7. <br/> Also, we know from the fundamental theorem of arithmetic that the prime factorisation of each number is unique except the order in which they can be written. <br/>∴ 14<sup>n</sup> can never end with 0.",
        "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": "Using prime factorisation method, find HCF and LCM of 72, 126 and 168. Also, show that HCF × LCM ≠ Product of three numbers.",
        "ans": "72 = 2<sup>3</sup> × 3<sup>2</sup> <br/> 126 = 2<sup>1</sup> × 3<sup>2</sup> × 7 <br/> 168 = 2<sup>3</sup> × 3<sup>1</sup> × 7<sup>1</sup> <br/> ∴ HCF (72, 126, 168) = 2 × 3 = 6 <br/> LCM (72, 126, 168) = 2<sup>3</sup> × 3<sup>2</sup> × 7 = 504 <br/> HCF × LCM = 6 × 504 = 3024 <br/> Also product of three numbers = 72 × 126 × 168 <br/> = 1524096 <br/> as 3024 ≠ 1524096 <br/> Thus, HCF × LCM ≠ Product of three numbers <br/> [Ans: HCF = 6, LCM = 504]",
        "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": "The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.",
        "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": "ch1a11.jpg",
          "width": "270",
          "height": "253"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The traffic lights of three consecutive different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 am, at what time will they change simultaneously again?",
        "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": "ch1a12.jpg",
          "width": "427",
          "height": "225"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "6 retired teachers, 8 retired doctors and 10 retired defence officers are willing to render their services to a village. Each of the doctors, teachers and defence officers serves equal number of different persons in that village. Find least number of persons served by each.",
        "ans": "Least number of persons served by each as LCM of 6, 8, 10 <br/> By prime fractorisation of 6 = 2 × 3 <br/> 8 = 2<sup>3</sup> <br/> 10 = 2 × 5 <br/> ∴ LCM = 2<sup>3</sup> × 3 × 5 = 120 <br/> So, with a minimum of 120 different village people, each of the 6 retired teachers serves 20, each of the 8 retired doctors serves 15 and each of the 10 retired defence officers serves 12 residents of village. <br/> [Ans: 20, 15, 12]",
        "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": "State fundamental Theorem of Arithmetic. Is it possible that HCF and LCM of two numbers be 24 and 540 respectively?",
        "ans": "“Every composite number can be expressed as product of primes in one and only one way except for the order in which they are written.” <br/> HCF always divides LCM of same numbers. But here, since 24 does not divide 540 exactly it is not possible that HCF and LCM of two numbers be 24 and 540 respectively. [Ans: No]",
        "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": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 12,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch1a16.jpg",
          "width": "405",
          "height": "22"
        },
        "ansimg": {
          "image": "ch1a17.jpg",
          "width": "544",
          "height": "193"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 13,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch1a18.jpg",
          "width": "240",
          "height": "28"
        },
        "ansimg": {
          "image": "ch1a19.jpg",
          "width": "470",
          "height": "255"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 14,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch1a20.jpg",
          "width": "201",
          "height": "27"
        },
        "ansimg": {
          "image": "ch1a21.jpg",
          "width": "527",
          "height": "314"
        }
      },
	  
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 15,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch1a30.jpg",
          "width": "387",
          "height": "24"
        },
        "ansimg": {
          "image": "ch1a31.jpg",
          "width": "478",
          "height": "633"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Use Euclid's Division Lemma to show that the square of any positive integer is either of the form 3 m or 3 m + 1 for some integer m.",
        "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": "ch1a32.jpg",
          "width": "388",
          "height": "513"
        }
      },
	  
    ],
    [
      {
        "heading": "Very short answer type questions.",
        "qus": "What is the HCF of smallest prime number and smallest composite number?",
        "ans": "Smallest prime number = 2 = 2<sup>1</sup> <br/> Smallest composite number = 4 = 22 <br/> ∴ HCF (2, 4) = 2<sup>1</sup> = 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": 1
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "The values of remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Is it true? Justify your answer.",
        "ans": "No, it is false. <br/> According to Euclid’s Division Lemma <br/> a = bq + r; <br/> where 0 ≤ r < b <br/> Here, b = 3 &nbsp;&nbsp;&nbsp;&nbsp; 0 ≤ r < 3 &nbsp;&nbsp;&nbsp;&nbsp; Ans: No",
        "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 largest number which divides 70 and 125 leaving remainders 5 and 8, respectively.",
        "ans": "Required number is HCF of 70 – 5 = 65 and 125 – 8 = 117 <br/> Applying Euclid’s Division Algorithm to 65 and 117 <br/> 117 = 65 × 1 + 52 <br/> 65 = 52 × 1 + 13 <br/> 52 = 13 × 4 + 0 <br/> ∴ HCF (65, 117) = 13 <br> Thus, required largest number is 13.",
        "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": "Explain why (17 × 11 × 2 + 17 × 11 × 5) is a composite number.",
        "ans": "17 × 11 × 2 + 17 × 11 × 5 <br/> = 17 × 11 × (2 + 5) = 17 × 11 × 7 <br/> Since 17 × 11 × 2 + 17 × 11 × 5 can be expressed as a product of primes it is a composite 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": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch1a6.jpg",
          "width": "542",
          "height": "18"
        },
        "ansimg": {
          "image": "ch1a7.jpg",
          "width": "520",
          "height": "72"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Complete the following factor tree and find the composite number x.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch1a8.jpg",
          "width": "206",
          "height": "199"
        },
        "ansimg": {
          "image": "ch1a9.jpg",
          "width": "380",
          "height": "205"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In a school, the duration of a period in junior section is 40 minutes and in senior section is 1 hour. If the first bell for each section rings at 9:00 am, when will the two bells ring together again?",
        "ans": "1 hour = 60 min <br/> Prime factors of 40 = 2 × 2 × 2 × 5 = 2<sup>3</sup> × 5 <br/> 60 = 2 × 2 × 3 × 5 = 2<sup>2</sup> × 3 × 5 <br/> ∴ LCM (40, 60) = 2<sup>3</sup> × 3 × 5 = 120 <br/> ∴ Two bells will ring together after 120 min = 2 hrs. <br/> Thus, the two bells will ring together again at <br/> 9 : 00 + 2 : 00 = 11 : 00 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": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch1a14.jpg",
          "width": "438",
          "height": "24"
        },
        "ansimg": {
          "image": "ch1a15.jpg",
          "width": "303",
          "height": "202"
        },
        "val": 8
      },
	  
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch1a26.jpg",
          "width": "430",
          "height": "41"
        },
        "ansimg": {
          "image": "ch1a27.jpg",
          "width": "241",
          "height": "190"
        },
        "val": 9
      },
	  
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch1a28.jpg",
          "width": "433",
          "height": "30"
        },
        "ansimg": {
          "image": "ch1a29.jpg",
          "width": "307",
          "height": "218"
        },
        "val": 10
      },
    ],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "grade": "Grade 10",
  "co": "ch1_co",
  "mcq": "ch1_mcq",
  "saq": "ch1_saq",
  "fib": "ch1_fib",
  "mtf": "ch1_mtf",
  "pbq": "ch1_pbq",
  "snc": "ch1_snc",
  "ctt": "ch1_ctt",
  "un": "ch1_un",
  "afq": "ch1_afq",
  "gowf": "ch1_gowf",
  "dtf": "ch1_dtf",
  "afow": "ch1_afow",
  "grf": "ch1_grf",
  "tf": "ch1_tf",
  "jtf": "ch1_jtf",
  "nf": "ch1_nf",
  "map": "ch1_map",
  "yn": "ch1_yn",
  "laq": "ch1_laq",
  "vsaq": "ch1_vsaq",
  "cs": "ch1_cs",
  "ctco": "ch1_ctco"
},

{
  "subject": "Mathematics",
  "chapter": "ch2",
  "chapterName": "Chapter 2 - Polynomials",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "The linear polynomial p(x) = 7x – 3 has the zero _____________ .",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch2a2.jpg",
				"width": "39",
				"height": "36"
				},
				"options": [
					"ch2a1.jpg",
					"ch2a2.jpg",
					"ch2a3.jpg",
					"ch2a4.jpg"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The cubic polynomial p(x) = x<sup>3</sup> – x has _____________ zeros.",
				"ans": "(d) 3",
				"code": "MCQ",
				"options": [
					"(a) 0",
					"(b) 1",
					"(c) 2",	
					"(d) 3"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The graph of p(x) = 3x – 2 – x<sup>2</sup> intersects the X-axis in _____________ points.",
				"ans": "(c) 2",
				"code": "MCQ",
				"options": [
					"(a) 0",
					"(b) 1",
					"(c) 2",	
					"(d) 3"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The graph of p(x) = 3x + 5 represents _____________.",
				"ans": "(a) a straight line",
				"code": "MCQ",
				"options": [
					"(a) a straight line",
					"(b) parabola open upwards",
					"(c) parabola open downwards",	
					"(d) a ray"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A quadratic polynomial has no zero. Its graph _____________.",
				"ans": "(c) does not intersect X-axis at two distinct points.",
				"code": "MCQ",
				"options": [
					"(a) touches X-axis at any point",
					"(b) intersects X-axis at two distinct points.",
					"(c) does not intersect X-axis at two distinct points.",	
					"(d) is in any one half place of X-axis."
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For the graph, y = p(x) has _____________ zeros.",
				"ans": "(c) 3",
				"code": "MCQ",
				"pic": {
				"image": "ch2a5.jpg",
				"width": "170",
				"height": "162"
				},
				"options": [
					"(a) 1",
					"(b) 2",
					"(c) 3",	
					"(d) 4"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "a = 3, b = 5, c = 7, d = 11 in the standard notation gives the cubic polynomial _____________.",
				"ans": "(d) 3x<sup>3</sup> + 5x<sup>2</sup> + 7x + 11",
				"code": "MCQ",
				"options": [
					"(a) 3x<sup>3</sup> + 5x<sup>2</sup> – 7x – 11",
					"(b) 3x<sup>3</sup> – 5x<sup>2</sup> + 7x – 11",
					"(c) 3x<sup>3</sup> + 5x<sup>2</sup> – 7x +11",	
					"(d) 3x<sup>3</sup> + 5x<sup>2</sup> + 7x + 11"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the graph of the polynomial does not intersect x-axis, then the number of zeros of the polynomial is",
				"ans": "(d) 0",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) 3",
					"(c) 1",	
					"(d) 0"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is not the graph of quadratic polynomial?",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch2a8.jpg",
				"width": "157",
				"height": "131"
				},
				"options": [
					"ch2a6.jpg",
					"ch2a7.jpg",
					"ch2a8.jpg",
					"ch2a9.jpg"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The sum of the zeros of 3x<sup>2</sup> + 5x – 2 is _____________.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch2a15.jpg",
				"width": "48",
				"height": "34"
				},
				"options": [
					"ch2a12.jpg",
					"ch2a13.jpg",
					"ch2a14.jpg",
					"ch2a15.jpg"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The product of the zeros of x<sup>2</sup> –4x + 3 is _____________.",
				"ans": "(b) 3",
				"code": "MCQ",
				"options": [
					"(a) 1",
					"(b) 3",
					"(c) 4",
					"(d) –4"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the zeros of the quadratic polynomial x<sup>2</sup> + 7x + 10.",
				"ans": "(a) –2, –5",
				"code": "MCQ",
				"options": [
					"(a) –2, –5",
					"(b) –2, +5",
					"(c) 2, 5",
					"(d) 2, –5"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the sum and product of zeros of the polynomial x<sup>2</sup> – 3.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch2a16.jpg",
				"width": "68",
				"height": "38"
				},
				"options": [
					"ch2a16.jpg",
					"(b) 0, 0",
					"(c) 3, 0",
					"(d) 1, 1"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find a quadratic polynomial, the sum and product of whose zeros are –3 and 2.",
				"ans": "(d) x<sup>2</sup> + 3x + 2",
				"code": "MCQ",
				"options": [
					"(a) x<sup>2</sup> + 3x – 2",
					"(b) x<sup>2</sup> – 3x + 2",
					"(c) x<sup>2</sup> – 3x – 2",
					"(d) x<sup>2</sup> + 3x + 2"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The number of polynomials having zeros as –2 and 5 is",
				"ans": "(d) more than 3",
				"code": "MCQ",
				"options": [
					"(a) 1",
					"(b) 2",
					"(c) 3",
					"(d) more than 3"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If one of the zeros of the cubic polynomial x<sup>3</sup> + ax<sup>2</sup> + bx + c is –1, then the product of the other two zeros is _____________.",
				"ans": "(a) b – a + 1",
				"code": "MCQ",
				"options": [
					"(a) b – a + 1",
					"(b) b – a –1",
					"(c) a – b + 1",
					"(d) a – b – 1"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The zeros of the quadratic polynomial x<sup>2</sup> + kx + k, k ≠ 0",
				"ans": "(a) cannot both be positive",
				"code": "MCQ",
				"options": [
					"(a) cannot both be positive",
					"(b) cannot both be negative",
					"(c) are always unequal",
					"(d) are always equal"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the zeros of the quadratic polynomial ax<sup>2</sup> + bx + c, a ≠ 0, are equal, then",
				"ans": "(c) c and a have the same signs",
				"code": "MCQ",
				"options": [
					"(a) c and a have opposite signs",
					"(b) c and b have opposite signs",
					"(c) c and a have the same signs",
					"(d) c and b have the same signs"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Dividing 2x<sup>2</sup> + 3x + 1 by x + 2, the quotient is _______________.",
				"ans": "(c) 2x – 1",
				"code": "MCQ",
				"options": [
					"(a) 2x",
					"(b) 2x + 1",
					"(c) 2x – 1",
					"(d) 2x + x"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The remainder obtained on dividing 3x<sup>3</sup> + x<sup>2</sup> + 2x + 5 by 1 + 2x + x<sup>2</sup> is ______________ .",
				"ans": "(a) 9x + 10",
				"code": "MCQ",
				"options": [
					"(a) 9x + 10",
					"(b) 0",
					"(c) 2x + 3",
					"(d) 1"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Dividing 3x<sup>2</sup> – x<sup>3</sup> – 3x + 5 by x – 1 – x<sup>2</sup>, the quotient is _______________.",
				"ans": "(d) 2x + x + 1",
				"code": "MCQ",
				"options": [
					"(a) x",
					"(b) x – 2",
					"(c) x + 1",
					"(d) 2x + x + 1"
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the quotient obtained on dividing 2x<sup>4</sup> – 3x<sup>3</sup> – 3x<sup>2</sup> + 6x – 2 by x<sup>2</sup> – 2.",
				"ans": "(d) 2x<sup>2</sup> – 3x + 1",
				"code": "MCQ",
				"options": [
					"(a) 2x<sup>2</sup> + 3x + 2",
					"(b) 2x<sup>2</sup> – x + 1",
					"(c) 2x<sup>2</sup> + 2x – 2",
					"(d) 2x<sup>2</sup> – 3x + 1"
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a polynomial of degree 5 is divided by a polynomial of degree 3, then the degree of the quotient is",
				"ans": "(b) equal to 2",
				"code": "MCQ",
				"options": [
					"(a) less than 2",
					"(b) equal to 2",
					"(c) equal to 4",
					"(d) more than 4"
				],
				"val": 22
			},
			
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 1,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch2a28.jpg",
          "width": "442",
          "height": "35"
        },
        "ansimg": {
          "image": "ch2a29.jpg",
          "width": "318",
          "height": "379"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 2,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch2a30.jpg",
          "width": "600",
          "height": "58"
        },
        "ansimg": {
          "image": "ch2a31.jpg",
          "width": "272",
          "height": "515"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "On dividing 10t<sup>4</sup> – 6t<sup>3</sup> – 40t<sup>2</sup> + 41t – 5 by a polynomial g(t), the quotient and remainder were 5t – 3 and 2t + 4 respectively. Find g(t).",
        "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": "ch2a34.jpg",
          "width": "375",
          "height": "390"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "What must be subtracted from the polynomial x<sup>3</sup> + 13x<sup>2</sup> + 35x + 25 so that the resulting polynomial is exactly divisible by x<sup>2</sup> + 11x + 10?",
        "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": "ch2a35.jpg",
          "width": "378",
          "height": "339"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "What should be added in the polynomial x<sup>3</sup> + 2x<sup>2</sup> – 9x + 1 so that it is completely divisible by x + 4?",
        "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": "ch2a36.jpg",
          "width": "543",
          "height": "430"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
         "image": "ch2a37.jpg",
          "width": "543",
          "height": "55"
        },
        "ansimg": {
          "image": "ch2a38.jpg",
          "width": "548",
          "height": "381"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If a polynomial x<sup>4</sup> + 7x<sup>3</sup> + 7x<sup>2</sup> + px + q is exactly divisible by x<sup>2</sup> + 7x + 12, then find the value of p and q.",
        "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": "ch2a39.jpg",
          "width": "307",
          "height": "316"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 8,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
         "image": "ch2a40.jpg",
          "width": "541",
          "height": "25"
        },
        "ansimg": {
          "image": "ch2a41.jpg",
          "width": "273",
          "height": "518"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Divide the polynomial 3x<sup>3</sup> – 6x<sup>2</sup> – 20x+ 14 by the polynomial x<sup>2</sup> – 5x + 6 and verify the division algorithm.",
        "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": "ch2a42.jpg",
          "width": "306",
          "height": "238"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 10,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
         "image": "ch2a43.jpg",
          "width": "543",
          "height": "52"
        },
        "ansimg": {
          "image": "ch2a44.jpg",
          "width": "319",
          "height": "491"
        }
      },
	  
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "Draw the graph of quadratic polynomial f(x) = x<sup>2</sup>.",
        "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": "ch2a10.jpg",
          "width": "394",
          "height": "243"
        },
        "val": 1
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Draw the graph of the polynomial f(x) = 2 ax",
        "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": "ch2a11.jpg",
          "width": "396",
          "height": "246"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If (x + a) is a zero of the polynomial 2x<sup>2</sup> + 3ax + 1, find the value of a.",
        "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": "ch2a17.jpg",
          "width": "212",
          "height": "144"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch2a18.jpg",
          "width": "446",
          "height": "25"
        },
        "ansimg": {
          "image": "ch2a19.jpg",
          "width": "198",
          "height": "172"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the zeros of the quadratic polynomial 6x<sup>2</sup> – 3 – 7x and verify the relationship between zeros and coefficients of the polynomial.",
        "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": "ch2a20.jpg",
          "width": "317",
          "height": "336"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the zeros of the polynomial p(x) as shown in graph and hence find the polynomial.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch2a21.jpg",
          "width": "303",
          "height": "248"
        },
        "ansimg": {
          "image": "ch2a22.jpg",
          "width": "267",
          "height": "197"
        },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If one zero of the polynomial p(x) = (a<sup>2</sup> + 9)x<sup>2</sup> + 45x + 6a is reciprocal of the other, find the value of a.",
        "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": "ch2a23.jpg",
          "width": "248",
          "height": "208"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch2a24.jpg",
          "width": "541",
          "height": "36"
        },
        "ansimg": {
          "image": "ch2a25.jpg",
          "width": "298",
          "height": "514"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch2a26.jpg",
          "width": "465",
          "height": "25"
        },
        "ansimg": {
          "image": "ch2a27.jpg",
          "width": "255",
          "height": "127"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch2a32.jpg",
          "width": "482",
          "height": "24"
        },
        "ansimg": {
          "image": "ch2a33.jpg",
          "width": "231",
          "height": "24"
        },
        "val": 10
      },
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch2_mcq",
  "co": "ch2_co",
  "nf": "ch2_nf",
  "saq": "ch2_saq",
  "fib": "ch2_fib",
  "vsaq": "ch2_vsaq",
  "tf": "ch2_tf",
  "mtf": "ch2_mtf",
  "laq": "ch2_laq",
  "jtf": "ch2_jtf",
  "ctt": "ch2_ctt",
  "snc": "ch2_snc",
  "grade": "Grade 10",
  "gowf": "ch2_gowf",
  "afow": "ch2_afow",
  "cs": "ch2_cs",
  "ctco": "ch2_ctco",
  "map": "ch2_map",
  "dtf": "ch2_dtf",
  "grf": "ch2_grf",
  "afq": "ch2_afq",
  "pbq": "ch2_pbq",
  "yn": "ch2_yn",
  "un": "ch2_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch3",
  "chapterName": "Chapter 3 - Pair of Linear Equations in Two Variables",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 3x – 2y – 6 = 0",
				"code": "MCQ",
				"pic": {
				"image": "ch3a1.jpg",
				"width": "456",
				"height": "38"
				},
				"options": [
					"(a) 2x – 3y – 6 = 0",
					"(b) 3x – 2y – 6 = 0",
					"(c) 3x – 2y = 1",
					"(d) 2x – 3y= 3"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The pair of equations x = a and y = b graphically represents lines which are",
				"ans": "(d) intersecting at (a, b)",
				"code": "MCQ",
				"options": [
					"(a) parallel",
					"(b) intersecting at (b, a)",
					"(c) coincident",
					"(d) intersecting at (a, b)"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The pair of equations y = 0 and y = –1 has",
				"ans": "(d) no solution",
				"code": "MCQ",
				"options": [
					"(a) one solution",
					"(b) two solutions",
					"(c) infinitely many solutions",	
					"(d) no solution"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Graphically, the pair of equations 6x – 3y + 10 = 0, 2x – y + 9 = 0 represents two lines which are",
				"ans": "(d) parallel",
				"code": "MCQ",
				"options": [
					"(a) intersecting at exactly one point",
					"(b) intersecting at exactly two points",
					"(c) coincident",	
					"(d) parallel"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have",
				"ans": "(d) no solution",
				"code": "MCQ",
				"options": [
					"(a) a unique solution",
					"(b) exactly two solutions",
					"(c) infinitely many solutions",	
					"(d) no solution"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a pair of linear equations is consistent, then the lines will be",
				"ans": "(c) intersecting or coincident",
				"code": "MCQ",
				"options": [
					"(a) parallel",
					"(b) always coincident",
					"(c) intersecting or coincident",	
					"(d) always intersecting"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be",
				"ans": "(d) 10x – 14y = –4",
				"code": "MCQ",
				"options": [
					"(a) 10x + 14y + 4 = 0",
					"(b) –10x – 14y + 4 = 0",
					"(c) –10x + 14y + 4 = 0",	
					"(d) 10x – 14y = –4"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The pair of linear equations 2x + 7y = k, kx + 21y = 18 has infinitely many solutions if",
				"ans": "(b) k = 6",
				"code": "MCQ",
				"options": [
					"(a) k = 3",
					"(b) k = 6",
					"(c) k = 9",	
					"(d) k = 18"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The solution set of x – 3y = 1 and 3x + y = 3 is _________________ .",
				"ans": "(c) {(1, 0)}",
				"code": "MCQ",
				"options": [
					"(a) {(0, 1)}",
					"(b) {(1, 1)}",
					"(c) {(1, 0)}",	
					"ch3a9.jpg"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the solution of the following equations: 7x – 15y = 2 and x + 2y = 3",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch3a10.jpg",
				"width": "80",
				"height": "39"
				},
				"options": [
					"ch3a10.jpg",
					"ch3a11.jpg",
					"ch3a12.jpg",	
					"ch3a13.jpg"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the solution of the following equations: s – 7 = 7 (t –7) and s + 3 = 3 (t + 3)",
				"ans": "(c) s = 42, t = 12",
				"code": "MCQ",
				"options": [
					"(a) s = 42, t = 18",
					"(b) s = 21, t = 9",
					"(c) s = 42, t = 12",	
					"(d) s = 61, t = 19"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is correct for given equations: 2x + 3y = 9, 4x + 6y = 18",
				"ans": "(c) infinitely many solutions",
				"code": "MCQ",
				"options": [
					"(a) no solution",
					"(b) null set",
					"(c) infinitely many solutions",	
					"(d) common outcome"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The solution set of 2x + y = 6 and 4x + 2y = 5 is _____________.",
				"ans": "(c) ∲",
				"code": "MCQ",
				"options": [
					"(a) {(x, y) | 2x + y = 6; x, y ∈ R}",
					"(b) {(x, y) | 2x + y = 0; x, y ∈ R}",
					"(c) ∲",	
					"(d) infinite set"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "To eliminate x from 3x + y = 7 and –x + 2y = 2, second equation is multiplied by __________.",
				"ans": "(c) 3",
				"code": "MCQ",
				"options": [
					"(a) 1",
					"(b) 2",
					"(c) 3",	
					"(d) –1"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 2x + 3y = 7 and 3x + 2y = 3, then x – y = _____________.",
				"ans": "(b) –4",
				"code": "MCQ",
				"options": [
					"(a) 4",
					"(b) –4",
					"(c) 2",	
					"(d) –2"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The solution set of 2x + 4y = 8 and x + 2y = 4 is ___________.",
				"ans": "(c) infinite set",
				"code": "MCQ",
				"options": [
					"(a) {(2, 1)}",
					"(b) empty set",
					"(c) infinite set",	
					"(d) {(0, 0)}"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save ₹2000 per month, find their monthly incomes.",
				"ans": "(a) (₹18000, ₹14000)",
				"code": "MCQ",
				"options": [
					"(a) (₹18000, ₹14000)",
					"(b) (₹1000, ₹3000)",
					"(c) (₹5000, ₹7000)",	
					"(d) (₹9000, ₹11000)"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is correct for given equations: 2x + 3y = 9, 4x + 6y = 18 ?",
				"ans": "(b) Infinitely no solution",
				"code": "MCQ",
				"options": [
					"(a) Infinitely many solutions",
					"(b) Infinitely no solution",
					"(c) {(3, 2)}",	
					"(d) {(1, 8)}"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The sum of a two-digit number and the number obtained by reversing the digit is 66. If the digits of the number differ by 2, find the number.",
				"ans": "(a) 24",
				"code": "MCQ",
				"options": [
					"(a) 24",
					"(b) 32",
					"(c) 48",	
					"(d) 13"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the pair of linear equations ax + 2y = 7 and 2x + 3y = 8 has a unique solution, then a ≠",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch3a31.jpg",
				"width": "43",
				"height": "34"
				},
				"options": [
					"ch3a29.jpg",
					"ch3a30.jpg",
					"ch3a31.jpg",	
					"ch3a32.jpg"
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For which values of p does the pair of equations given has unique solution: 4x + py + 8 = 0 and 2x + 2y + 2 = 0?",
				"ans": "(a) p ≠ 4",
				"code": "MCQ",
				"options": [
					"(a) p ≠ 4",
					"(b) p = 5",
					"(c) p ≠ 9",	
					"(d) p"
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If in a two-digit number, the digit at unit place is x and the digit at tens place is 5, then the number is ___________.",
				"ans": "(c) x + 50",
				"code": "MCQ",
				"options": [
					"(a) 50x + 5",
					"(b) 30x + 5",
					"(c) x + 50",	
					"(d) 10x + 5"
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In a two-digit number, the digit at tens place is 7 and the sum of the digits is 8 times the digit at unit place. Then the number is ___________.",
				"ans": "(b) 71",
				"code": "MCQ",
				"options": [
					"(a) 70",
					"(b) 71",
					"(c) 17",	
					"(d) 78"
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The sum of two numbers is 10 and the difference of them is 2. Then the greater number of these two is ___________.",
				"ans": "(c) 6",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) 4",
					"(c) 6",	
					"(d) 8"
				],
				"val": 24
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "3 years ago, the sum of ages of a father and his son was 40 years. After 2 years the sum of ages of the father and his son will be__________.",
				"ans": "(c) 50",
				"code": "MCQ",
				"options": [
					"(a) 40",
					"(b) 46",
					"(c) 50",	
					"(d) 60"
				],
				"val": 25
			},
			
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch3a40.jpg",
				"width": "171",
				"height": "41"
				},
				"ansimg": {
				"image": "ch3a41.jpg",
				"width": "113",
				"height": "34"
				},
				"options": [
					"ch3a41.jpg",
					"ch3a42.jpg",
					"(c) x = 2, y = 3",	
					"(d) x = 5"
				],
				"val": 26
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) x = 4, y = 5",
				"code": "MCQ",
				"pic": {
				"image": "ch3a43.jpg",
				"width": "250",
				"height": "42"
				},
				"options": [
					"(a) x = 2, y = 1",
					"(b) x = 4, y = 5",
					"(c) x = 2, y = 3",	
					"(d) x = 2, y = 4"
				],
				"val": 27
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of boat in still water.",
				"ans": "(d) x = 5, y = 11",
				"code": "MCQ",
				"options": [
					"(a) x = 8, y = 3",
					"(b) x = 5, y = 2",
					"(c) x = 7, y = 9",	
					"(d) x = 5, y = 11"
				],
				"val": 28
			},
			
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "Twenty years ago, the age of father was four times the age of his son. After four years from now, the age of father will be double that of his son. Give algebraic and graphical representation of this situation.",
        "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": "ch3a2.jpg",
          "width": "552",
          "height": "941"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Paths of two roads are given by the equations 2y – x = 8 and 5y – x = 14. Represent these graphically and find whether they cross each other or not.",
        "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": "ch3a3.jpg",
          "width": "480",
          "height": "716"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve graphically 3x + y + 1 = 0 and 2x – 3y + 8 = 0. Shade the area of region bounded by the lines and x-axis.",
        "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": "ch3a7.jpg",
          "width": "550",
          "height": "863"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve graphically the pair of linear equations 3x – 4y + 3 = 0 and 3x + 4y – 21 = 0. Find the coordinates of the vertices of triangular region formed by these lines and x-axis. Also, calculate area of this triangle.",
        "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": "ch3a8.jpg",
          "width": "618",
          "height": "899"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve the following system of equations: <br/> 99x + 101y = 499 <br/> 101x + 99y = 501",
        "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": "ch3a22.jpg",
          "width": "285",
          "height": "502"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve for x and y. <br/> x + 4y = 27xy <br/> x + 2y = 21xy",
        "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": "ch3a23.jpg",
          "width": "360",
          "height": "562"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "3 chairs and 2 tables cost `700 and 5 chairs and 3 tables cost `1100. Find the cost of 2 chairs and 2 tables.",
        "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": "ch3a24.jpg",
          "width": "384",
          "height": "550"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 8,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch3a25.jpg",
          "width": "620",
          "height": "60"
        },
        "ansimg": {
		  "image": "ch3a26.jpg",
          "width": "355",
          "height": "262"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 9,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch3a27.jpg",
          "width": "373",
          "height": "33"
        },
        "ansimg": {
		  "image": "ch3a28.jpg",
          "width": "366",
          "height": "327"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Find the value of a and b if the following pair of linear equations has infinite number of solutions. <br/> 3x – (a + 1)y = 2b – 1 <br/> 5x + (1 – 2a)y = 3b",
        "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": "ch3a36.jpg",
          "width": "205",
          "height": "605"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve for x and y: <br/> x + 2y – 3 = 0 <br/> 3x – 2y + 7 = 0",
        "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": "ch3a37.jpg",
          "width": "388",
          "height": "393"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "For what value of p and q will the following pair of linear equations have infinitely many solutions? <br/> 4x + 5y = 2; (2p + 7q)x + (p + 8q)y = 2q – p + 1",
        "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": "ch3a38.jpg",
          "width": "330",
          "height": "625"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve for x and y: <br/> (a – b)x + (a + b) y = a<sup>2</sup> – 2ab – b<sup>2</sup> <br/> (a + b)(x+y) = a<sup>2</sup> + b<sup>2</sup>",
        "ans": ">",
        "code": "SATQ",
        "options": null,
        "val": 13,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": null,
          "width": null,
          "height": null
        },
        "ansimg": {
		  "image": "ch3a39.jpg",
          "width": "585",
          "height": "469"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "The sum of digits of a two-digit number is 12. The number obtained by interchanging the digits exceeds the given number by 18. Find the number.",
        "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": "ch3a44.jpg",
          "width": "247",
          "height": "580"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve the following pairs of equations by reducing them to a pair of linear equations:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 15,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch3a45.jpg",
          "width": "132",
          "height": "40"
        },
        "ansimg": {
		  "image": "ch3a46.jpg",
          "width": "331",
          "height": "560"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Solve the following pairs of equations by reducing them to a pair of linear equations:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 16,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch3a47.jpg",
          "width": "197",
          "height": "42"
        },
        "ansimg": {
		  "image": "ch3a48.jpg",
          "width": "333",
          "height": "576"
        }
      },
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "Find whether the lines representing the following pair of linear equations intersect at a point.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch3a4.jpg",
          "width": "261",
          "height": "43"
        },
        "ansimg": {
          "image": "ch3a5.jpg",
          "width": "217",
          "height": "228"
        },
        "val": 1
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Find the x-coordinate of the point which lies on the line represented by 5x – y – 7 = 0 and whose y-coordinate is 13.",
        "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": "ch3a6.jpg",
          "width": "291",
          "height": "198"
        },
        "val": 2
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Find the solution of the following system of equations by substitution method. <br/> 4x + 9y = 5 <br/> 3x – 5y = 39",
        "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": "ch3a14.jpg",
          "width": "345",
          "height": "412"
        },
        "val": 3
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Find the solution of the following system of equations by substitution method. <br/> 2x + 3y = 17 <br/> 3x – 2y = 6",
        "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": "ch3a15.jpg",
          "width": "351",
          "height": "423"
        },
        "val": 4
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, find the values of a and b.",
        "ans": "Since x = a, y = b is the solution of given equations <br/> ∴ a – b = 2 ...(1) </br> a + b = 4 ...(2) <br/> (1) + (2) ⇒ 2a = 6 ⇒ a = 3 <br/> Put for a in (1), 3 – b = 2 ⇒ b = 1 <br/> [Ans: a = 3, b = 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": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Solve the following pair of linear equations using elimination method. <br/> x – y + 1 = 0, 4x + 3y – 10 = 0",
        "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": "ch3a16.jpg",
          "width": "299",
          "height": "361"
        },
        "val": 6
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Find solution of the following linear equations: <br/> x + y = 3 <br/> 4x – 2y = 0",
        "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": "ch3a17.jpg",
          "width": "346",
          "height": "334"
        },
        "val": 7
      },
      {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch3a59.jpg",
          "width": "204",
          "height": "34"
        },
        "ansimg": {
          "image": "ch3a18.jpg",
          "width": "263",
          "height": "125"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch3a60.jpg",
          "width": "205",
          "height": "42"
        },
        "ansimg": {
          "image": "ch3a19.jpg",
          "width": "351",
          "height": "564"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In the figure, ▭ABCD is a rectangle. Find the values of x and y.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch3a20.jpg",
          "width": "232",
          "height": "121"
        },
        "ansimg": {
          "image": "ch3a21.jpg",
          "width": "350",
          "height": "208"
        },
        "val": 10
      },
	   {
        "heading": "Very short answer type questions.",
        "qus": "Determine the value of k for which the pair of linear equations 2x + 3y – 5 = 0 and kx – 6y – 8 = 0 has a unique solution.",
        "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": "ch3a33.jpg",
          "width": "170",
          "height": "144"
        },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the value of k for which the following pair of linear equations have infinitely many solutions: 2x + 3y = 7; (k–1)x + (k + 2)y = 3k.",
        "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": "ch3a35.jpg",
          "width": "198",
          "height": "300"
        },
        "val": 12
      },
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch3_mcq",
  "co": "ch3_co",
  "nf": "ch3_nf",
  "saq": "ch3_saq",
  "fib": "ch3_fib",
  "vsaq": "ch3_vsaq",
  "tf": "ch3_tf",
  "mtf": "ch3_mtf",
  "laq": "ch3_laq",
  "jtf": "ch3_jtf",
  "ctt": "ch3_ctt",
  "snc": "ch3_snc",
  "grade": "Grade 10",
  "gowf": "ch3_gowf",
  "afow": "ch3_afow",
  "cs": "ch3_cs",
  "ctco": "ch3_ctco",
  "map": "ch3_map",
  "dtf": "ch3_dtf",
  "grf": "ch3_grf",
  "afq": "ch3_afq",
  "pbq": "ch3_pbq",
  "yn": "ch3_yn",
  "un": "ch3_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch4",
  "chapterName": "Chapter 4 - Quadratic Equations",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "If x = 2 is a root of the equation x<sup>2</sup> – 4x + a = 0, then a =",
				"ans": "(d) 4",
				"code": "MCQ",
				"options": [
					"(a) –2",
					"(b) 2",
					"(c) –4",	
					"(d) 4"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 4 is a root of quadratic equation x2 + ax – 8 = 0, then a = ____________.",
				"ans": "(c) –2",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) 4",
					"(c) –2",	
					"(d) –4"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If one of the roots of kx<sup>2</sup> – 7x + 3 = 0 is 3, then k = ___________.",
				"ans": "(d) 2",
				"code": "MCQ",
				"options": [
					"(a) –2",
					"(b) 3",
					"(c) –3",	
					"(d) 2"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 1 is a root of the equations ay<sup>2</sup> + ay + 3 = 0 and y<sup>2</sup> + y + b = 0, then ab equals ___________.",
				"ans": "(a) 3",
				"code": "MCQ",
				"options": [
					"(a) 3",
					"ch4a1.jpg",
					"(c) 6",
					"(d) -3"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is not a quadratic equation?",
				"ans": "(b) x(x + 1) + 8 = (x + 2) (x – 2)",
				"code": "MCQ",
				"options": [
					"(a) (x – 2)<sup>2</sup> + 1 = 2x – 3",
					"(b) x(x + 1) + 8 = (x + 2) (x – 2)",
					"(c) x(2x + 3) = x<sup>2</sup> + 1",
					"(d) (x + 2)<sup>3</sup> = x<sup>2</sup> – 4"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is a quadratic equation?",
				"ans": "(d) x<sup>3</sup> – x<sup>2</sup> = (x – 1)<sup>3</sup>",
				"code": "MCQ",
				"options": [
					"(a) x<sup>2</sup> + 2x + 1 = (4 – x)<sup>2</sup> + 3",
					"ch4a2.jpg",
					"ch4a3.jpg",
					"(d) x<sup>3</sup> – x<sup>2</sup> = (x – 1)<sup>3</sup>"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is not a quadratic equation?",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch4a4.jpg",
				"width": "191",
				"height": "29"
				},
				"options": [
					"(a) 2(x – 1)<sup>2</sup> = 4x<sup>2</sup> – 2x + 1",
					"(b) 2x – x<sup>2</sup> = x<sup>2</sup> + 5",
					"ch4a4.jpg",
					"(d) (x<sup>2</sup> + 2x)<sup>2</sup> = x<sup>4</sup> + 3 + 4x<sup>3</sup>"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "__________ is a solution of quadratic equation x<sup>2</sup> – 3x + 2 = 0.",
				"ans": "(b) 1",
				"code": "MCQ",
				"options": [
					"(a) –3",
					"(b) 1",
					"(c) 3",	
					"(d) -2"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The quadratic equation ___________ has 3 as one of its roots.",
				"ans": "(a) x<sup>2</sup> – x – 6 = 0",
				"code": "MCQ",
				"options": [
					"(a) x<sup>2</sup> – x – 6 = 0",
					"(b) x<sup>2</sup> + x – 6 = 0",
					"(c) x<sup>2</sup> – x + 6 = 0",	
					"(d) x<sup>2</sup> + x + 6 = 0"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The roots of the equation x<sup>2</sup> – 3x – m(m + 3) = 0 where m is a constant are",
				"ans": "(b) –m, m + 3",
				"code": "MCQ",
				"options": [
					"(a) m, m + 3",
					"(b) –m, m + 3",
					"(c) m, –(m + 3)",	
					"(d) –m, –(m + 3)"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The roots of the equation x<sup>2</sup> + x – p(p + 1) = 0 are __________.",
				"ans": "(c) p, –(p + 1)",
				"code": "MCQ",
				"options": [
					"(a) p (p + 1)",
					"(b) –p, (p + 1)",
					"(c) p, –(p + 1)",	
					"(d) –p, –(p + 1)"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the roots of the equation 2x<sup>2</sup> – 5x + 3 = 0, by factorisation.",
				"ansimg": {
				"image": "ch4a8.jpg",
				"width": "59",
				"height": "36"
				},
				"code": "MCQ",
				"options": [
					"ch4a8.jpg",
					"(b) –1, 1",
					"(c) 1, 0",	
					"ch4a9.jpg"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the roots of the equation 6x<sup>2</sup> – x – 2 = 0.",
				"ansimg": {
				"image": "ch4a12.jpg",
				"width": "67",
				"height": "42"
				},
				"code": "MCQ",
				"options": [
					"ch4a10.jpg",
					"ch4a11.jpg",
					"ch4a12.jpg",	
					"ch4a13.jpg"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the roots of equation 3x<sup>2</sup> – 2 √6x + 2 = 0.",
				"ansimg": {
				"image": "ch4a15.jpg",
				"width": "81",
				"height": "44"
				},
				"code": "MCQ",
				"options": [
					"ch4a14.jpg",
					"ch4a15.jpg",
					"ch4a16.jpg",	
					"ch4a17.jpg"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following equations has 2 as a root?",
				"ans": "(c) 2x<sup>2</sup> – 7x + 6 = 0",
				"code": "MCQ",
				"options": [
					"(a) x<sup>2</sup> – 4x + 5 = 0",
					"(b) x<sup>2</sup> + 3x – 12 = 0",
					"(c) 2x<sup>2</sup> – 7x + 6 = 0",	
					"(d) 3x<sup>2</sup> – 6x – 2 = 0"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"pic": {
				"image": "ch4a18.jpg",
				"width": "449",
				"height": "34"
				},
				"ans": "(a) 2",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) – 2",
					"ch4a19.jpg",	
					"ch4a20.jpg"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following equations has the sum of its roots as 3?",
				"ans": "(b) –x<sup>2</sup> + 3x – 3 = 0",
				"code": "MCQ",
				"options": [
					"(a) 2x<sup>2</sup> – 3x + 6 = 0",
					"(b) –x<sup>2</sup> + 3x – 3 = 0",
					"ch4a21.jpg",	
					"(d) 3x<sup>2</sup> – 3x + 3= 10"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The roots of the quadratic equation 2x<sup>2</sup> – x – 6 = 0 are",
				"ans": null,
				"ansimg": {
				"image": "ch4a38.jpg",
				"width": "65",
				"height": "38"
				},
				"code": "MCQ",
				"options": [
					"ch4a36.jpg",
					"ch4a37.jpg",
					"ch4a38.jpg",	
					"ch4a39.jpg"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) x<sup>2</sup> – 4x + 1 = 0",
				"pic": {
				"image": "ch4a40.jpg",
				"width": "456",
				"height": "28"
				},
				"code": "MCQ",
				"options": [
					"(a) x<sup>2</sup> + 4x + 1 = 0",
					"(b) x<sup>2</sup> – 4x + 1 = 0",
					"(c) x<sup>2</sup> + 4x – 1 = 0",	
					"(d) x<sup>2</sup> – 4x – 1 = 0"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the roots of equation 5x<sup>2</sup> – 6x – 2 = 0 by the method of completing square.",
				"ans": "(b) x<sup>2</sup> – 4x + 1 = 0",
				"pic": {
				"image": "ch4a41.jpg",
				"width": "80",
				"height": "41"
				},
				"code": "MCQ",
				"options": [
					"ch4a41.jpg",
					"ch4a42.jpg",
					"ch4a43.jpg",	
					"ch4a44.jpg"
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the roots of 4x<sup>2</sup> + 3x + 5 = 0 by the method of completing square.",
				"ans": null,
				"ansimg": {
				"image": "ch4a46.jpg",
				"width": "54",
				"height": "38"
				},
				"code": "MCQ",
				"options": [
					"ch4a45.jpg",
					"ch4a46.jpg",
					"ch4a47.jpg",	
					"ch4a48.jpg"
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of rectangular plot is 528 m<sup>2</sup>. The length of the plot (in metres) is one more than twice its breadth. Find the length and breadth of the plot.",
				"ans": "(d) 33, 16",
				"code": "MCQ",
				"options": [
					"(a) 20, 15",
					"(b) 30, 18",
					"(c) 15, 14",	
					"(d) 33, 16"
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find two consecutive odd positive integers, sum of whose squares is 290.",
				"ans": "(b) 11, 13",
				"code": "MCQ",
				"options": [
					"(a) 9, 11",
					"(b) 11, 13",
					"(c) 13, 15",	
					"(d) 15, 17"
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A motorboat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.",
				"ans": "(d) 6 km/hr",
				"code": "MCQ",
				"options": [
					"(a) 4 km/hr",
					"(b) 7 km/hr",
					"(c) 8 km/hr",	
					"(d) 6 km/hr"
				],
				"val": 24
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Discriminant D = ____________ for the quadratic equation 5x<sup>2</sup> – 6x + 1 = 0",
				"ans": "(d) 6 km/hr",
				"code": "MCQ",
				"options": [
					"(a) 6",
					"ch4a75.jpg",
					"(c) 4",	
					"(d) 56"
				],
				"val": 25
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The discriminant of x<sup>2</sup> – 3x – k = 0 is 1. A value of x is _________",
				"ans": "(b) –2",
				"code": "MCQ",
				"options": [
					"(a) –4",
					"(b) –2",
					"(c) 2",	
					"(d) 4"
				],
				"val": 26
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A quadratic equation has two equal roots, if ______________",
				"ans": "(c) D = 0",
				"code": "MCQ",
				"options": [
					"(a) D < 0",
					"(b) D > 0",
					"(c) D = 0",	
					"(d) D is non-zero perfect square"
				],
				"val": 27
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the discriminant of the quadratic equation 2x<sup>2</sup> – 4x + 3 = 0 and find the nature of its roots.",
				"ans": "(d) no real roots.",
				"code": "MCQ",
				"options": [
					"(a) real roots",
					"(b) distinct real roots",
					"(c) equal real roots",	
					"(d) no real roots."
				],
				"val": 28
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the distance of BP and AP.",
				"pic": {
				"image": "ch4a76.jpg",
				"width": "149",
				"height": "135"
				},
				"ans": "(a) 5 and 12",
				"code": "MCQ",
				"options": [
					"(a) 5 and 12",
					"(b) 6 and 14",
					"(c) 4 and 11",	
					"(d) 5 and 15"
				],
				"val": 29
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"pic": {
				"image": "ch4a77.jpg",
				"width": "491",
				"height": "29"
				},
				"ans": "(c) two equal real roots",
				"code": "MCQ",
				"options": [
					"(a) real roots",
					"(b) no real roots",
					"(c) two equal real roots",	
					"(d) two distinct real roots."
				],
				"val": 30
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Solve 2x<sup>2</sup> – 5x + 3 by the method of completing square.",
				"ans": "(a) <sup>3</sup>/<sub>2</sub>, 1",
				"code": "MCQ",
				"options": [
					"(a) <sup>3</sup>/<sub>2</sub>, 1",
					"(b) 1, 1",
					"(c) ⅔, ⅔",	
					"(d) 2, 1"
				],
				"val": 31
			}
	],
    [
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery quadratic equation has exactly one root.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery quadratic equation has at least one real root.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery quadratic equation has at least two roots.\n\t\t_________\n\t",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tEvery quadratic equation has at most two roots.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the coefficient of x<sup>2</sup> and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n\t\tIf the coefficient of x<sup>2</sup> and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.\n\t\t_________\n\t",
          "ans": "True",
          "code": "TF",
          "val": 6
        }
      ],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "Three consecutive positive integers are such that the sum of squares of the first and the product of the other two is 46. Find the integers.",
        "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": "ch4a23.jpg",
          "width": "373",
          "height": "625"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "The difference of squares of two numbers is 88. If the larger is 5 less than twice the smaller number, then find the two numbers.",
        "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": "ch4a24.jpg",
          "width": "442",
          "height": "651"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "A train travels 180 km at a uniform speed. If the speed had been 9 km/hour more, it would have taken 1 hour less for same journey. Find the speed of the train.",
        "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": "ch4a25.jpg",
          "width": "238",
          "height": "646"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "A shopkeeper buys some books for `80. If he had bought 4 more books for same amount, each book would have cost ₹1 less. Find the number of books he bought.",
        "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": "ch4a26.jpg",
          "width": "497",
          "height": "573"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch4a27.jpg",
          "width": "443",
          "height": "35"
        },
        "ansimg": {
          "image": "ch4a28.jpg",
          "width": "194",
          "height": "627"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch4a29.jpg",
          "width": "573",
          "height": "61"
        },
        "ansimg": {
          "image": "ch4a30.jpg",
          "width": "341",
          "height": "585"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 7,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch4a31.jpg",
          "width": "574",
          "height": "34"
        },
        "ansimg": {
          "image": "ch4a32.jpg",
          "width": "285",
          "height": "551"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 8,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch4a33.jpg",
          "width": "576",
          "height": "83"
        },
        "ansimg": {
          "image": "ch4a34.jpg",
          "width": "481",
          "height": "577"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "Speed of a boat in still water is 15 km/hour. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.",
        "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": "ch4a35.jpg",
          "width": "281",
          "height": "516"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": "A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?",
        "ans": "Suppose the policeman catches the thief after t minutes. <br/> Uniform speed of the thief = 100 m/min. <br/> ∴ Distance covered by thief in (t + 1) minutes = 100 (t + 1) metres <br/> Distance covered by policemen in t minutes <br/> = Sum of t terms of an AP with first term 100 and common difference 10. <br/> ⇒ 1/2 [2 × 100 + (t – 1)10] m <br/> = t [100 + 5 (t – 1)] <br/> = t (5t + 95) = 5t2 + 95t <br/> When the policeman catches the thief <br/> 5t2 + 95t = 100 (t + 1) <br/> ⇒ 5t2 + 95t = 100t + 100 <br/> ⇒ 5t2 – 5t – 100 = 0 <br/> ⇒ t2 – t – 20 = 0 <br/> ⇒ t = –4 or t = 5 <br/> <br/> Neglecting –ve time, we get = 5. <br/> ∴ Thus, the policeman catches the thief after 5 minutes.",
        "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": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 11,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch4a53.jpg",
          "width": "297",
          "height": "41"
        },
        "ansimg": {
          "image": "ch4a54.jpg",
          "width": "197",
          "height": "266"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 12,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch4a55.jpg",
          "width": "349",
          "height": "35"
        },
        "ansimg": {
          "image": "ch4a56.jpg",
          "width": "251",
          "height": "234"
        }
      },
      {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 13,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a57.jpg",
          "width": "210",
          "height": "26"
        },
        "ansimg": {
          "image": "ch4a58.jpg",
          "width": "203",
          "height": "295"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 14,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a59.jpg",
          "width": "272",
          "height": "39"
        },
        "ansimg": {
          "image": "ch4a60.jpg",
          "width": "366",
          "height": "341"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 15,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a61.jpg",
          "width": "301",
          "height": "37"
        },
        "ansimg": {
          "image": "ch4a62.jpg",
          "width": "333",
          "height": "519"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 16,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a63.jpg",
          "width": "403",
          "height": "35"
        },
        "ansimg": {
          "image": "ch4a64.jpg",
          "width": "216",
          "height": "460"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A motor boat whose speed is 20 km/hour in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.",
        "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": "ch4a65.jpg",
          "width": "567",
          "height": "671"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 18,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a66.jpg",
          "width": "293",
          "height": "39"
        },
        "ansimg": {
          "image": "ch4a67.jpg",
          "width": "193",
          "height": "405"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 19,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a68.jpg",
          "width": "573",
          "height": "57"
        },
        "ansimg": {
          "image": "ch4a69.jpg",
          "width": "290",
          "height": "550"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 20,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a70.jpg",
          "width": "214",
          "height": "54"
        },
        "ansimg": {
          "image": "ch4a72.jpg",
          "width": "413",
          "height": "410"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 20,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a73.jpg",
          "width": "286",
          "height": "37"
        },
        "ansimg": {
          "image": "ch4a74.jpg",
          "width": "277",
          "height": "386"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If ad ≠ bc, then prove that the equation (a<sup>2</sup> + b<sup>2</sup>)x<sup>2</sup> + 2(ac + bd)x + (c<sup>2</sup> + d<sup>2</sup>) = 0 has no real roots.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 21,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": null,
          "width": null,
          "height": null
        },
        "ansimg": {
          "image": "ch4a87.jpg",
          "width": "329",
          "height": "306"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the roots of the equation (c<sup>2</sup> – ab)x<sup>2</sup> – 2(a<sup>2</sup> – bc)x + b<sup>2</sup> – ac = 0 in x are equal, then show that either a = 0 or a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> = 3abc.",
        "ans": "We know that D = B<sup>2</sup> – 4AC <br/> Here, B = –2(a<sup>2</sup> – bc), A = (c<sup>2</sup> – ab), C = b<sup>2</sup> – ac <br/> For equal roots, D = 0 <br/> ⇒ {–2(a<sup>2</sup> – bc)}<sup>2</sup> – 4(c<sup>2</sup> – ab)(b<sup>2</sup> – ac) = 0 <br/> ⇒ 4[a<sup>4</sup> + b<sup>2</sup>c<sup>2</sup> – 2a<sup>2</sup>bc] – 4[b<sup>2</sup>c<sup>2</sup> – ab<sup>3</sup> – ac<sup>3</sup> + a<sup>2</sup>bc] = 0 <br/> ⇒ 4a<sup>4</sup> + 4ab<sup>3</sup> + 4ac<sup>3</sup> – 12a<sup>2</sup>bc = 0 <br/> ⇒ 4a(a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> – 3abc) = 0 <br/> So, either a = 0 or a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> – 3abc = 0 <br/> Hence a = 0 or a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup> = 3abc",
        "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": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 23,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch4a88.jpg",
          "width": "560",
          "height": "30"
        },
        "ansimg": {
          "image": "ch4a89.jpg",
          "width": "368",
          "height": "294"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the equation (1 + m<sup>2</sup>)x<sup>2</sup> + 2mcx + c<sup>2</sup> – a<sup>2</sup> = 0 has equal roots, then show that c<sup>2</sup> = a<sup>2</sup> (1 + m<sup>2</sup>).",
        "ans": "Here, A = (1 + m<sup>2</sup>), B = 2mc, C = (c<sup>2</sup> – a<sup>2</sup>) <br/> ∴ D = B<sup>2</sup> – 4AC <br/> ⇒ D = (2mc)<sup>2</sup> – 4(1 + m<sup>2</sup>) (c<sup>2</sup> – a<sup>2</sup>) <br/> ⇒ D = 4m<sup>2</sup>c<sup>2</sup> – 4(c<sup>2</sup> + m<sup>2</sup>c<sup>2</sup> – a<sup>2</sup> – a<sup>2</sup>m<sup>2</sup>) <br/> ⇒ D = –4(c<sup>2</sup> – a<sup>2</sup> – a<sup>2</sup>m<sup>2</sup>) <br/> For equal roots, D = 0 <br/> ⇒ c<sup>2</sup> – a<sup>2</sup> – a<sup>2</sup>m<sup>2</sup> = 0 <br/> ⇒ c<sup>2</sup> – a<sup>2</sup> (1 + m<sup>2</sup>) = 0 <br/> ⇒ c<sup>2</sup> = a<sup>2</sup> (1 + m<sup>2</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": "Very short answer type questions.",
        "qus": "If x = 3 is one root of the equation x<sup>2</sup> – 2kx – 6 = 0, then find the value of k.",
        "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": "ch4a5.jpg",
          "width": "183",
          "height": "201"
        },
        "val": 1
      },
      {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch4a6.jpg",
          "width": "506",
          "height": "38"
        },
        "ansimg": {
          "image": "ch4a7.jpg",
          "width": "182",
          "height": "308"
        },
        "val": 2
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "For what value k, the roots of the equation x<sup>2</sup> + 4x + k = 0 are real?",
        "ans": "For Real Roots D <u>></u> 0 <br/> Here, D = b<sup>2</sup> – 4ac = (4)<sup>2</sup> – 4(1) (k) = 16 – 4k <br/> D <u>></u> 0 <br/> ⇒ 16 – 4k <u>></u> 0 <br/> ⇒ 16 <u>></u> 4k <br/> ⇒ 4k <u><</u> 16 <br/> ⇒ k <u><</u> 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": 3
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "If b = 0, c < 0, is it true that the roots of x<sup>2</sup> + bx + c = 0 are numerically equal and opposite in sign? Justify.",
        "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": "ch4a22.jpg",
          "width": "326",
          "height": "232"
        },
        "val": 4
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Solve the following quadratic equation for x.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch4a49.jpg",
          "width": "135",
          "height": "25"
        },
        "ansimg": {
          "image": "ch4a50.jpg",
          "width": "202",
          "height": "363"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Solve the quadratic equation 2x<sup>2</sup> + ax – a<sup>2</sup> = 0 for x.",
        "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": "ch4a51.jpg",
          "width": "180",
          "height": "227"
        },
        "val": 6
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Solve the following quadratic equation for x: <br/> 4x<sup>2</sup> – 4a<sup>2</sup>x + (a<sup>4</sup> – b<sup>4</sup>) = 0",
        "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": "ch4a52.jpg",
          "width": "354",
          "height": "207"
        },
        "val": 7
      },
      {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch4a78.jpg",
          "width": "504",
          "height": "24"
        },
        "ansimg": {
          "image": "ch4a79.jpg",
          "width": "135",
          "height": "145"
        },
        "val": 8
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "For what value of k, the roots of the equation 3x<sup>2</sup> – 10x + k = 0 are reciprocal of each other?",
        "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": "ch4a80.jpg",
          "width": "200",
          "height": "134"
        },
        "val": 9
      },
      {
        "heading": "Very short answer type questions.",
        "qus": "Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots.",
        "ans": "D = b<sup>2</sup> – 4ac <br/> = (–3p)<sup>2</sup> – 3p(9) <br/> = 9p<sup>2</sup> – 36p <br/> = 9p (p – 4) <br/> For equal roots D = 0 <br/> ⇒ 9p (p – 4) = 0 <br/> ⇒ 9p = 0 or p – 4 = 0 <br/> ⇒ p = 0 or p = 4 <br/> ∴ p = 0, 4 <br/> [Ans: p = 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": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the value(s) of k so that the quadratic equation x<sup>2</sup> – 4kx + k = 0 has equal roots.",
        "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": "ch4a81.jpg",
          "width": "167",
          "height": "236"
        },
        "val": 11
      },
      {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch4a82.jpg",
          "width": "540",
          "height": "36"
        },
        "ansimg": {
          "image": "ch4a83.jpg",
          "width": "237",
          "height": "645"
        },
        "val": 12
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If –5 is a root of the quadratic equation 2x<sup>2</sup> + px – 15 = 0 and the quadratic equation p(x<sup>2</sup> + x) + k = 0 has equal roots, find the value of k.",
        "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": "ch4a84.jpg",
          "width": "424",
          "height": "275"
        },
        "val": 13
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the value of p for which one root of the quadratic equation px<sup>2</sup> – 14x + 8 = 0 is 6 times of the other.",
        "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": "ch4a85.jpg",
          "width": "473",
          "height": "413"
        },
        "val": 14
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the value of k for which the equation x<sup>2</sup> + k(2x + k – 1) + 2 = 0 has real and equal roots.",
        "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": "ch4a86.jpg",
          "width": "198",
          "height": "235"
        },
        "val": 15
      },
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch4_mcq",
  "co": "ch4_co",
  "nf": "ch4_nf",
  "saq": "ch4_saq",
  "fib": "ch4_fib",
  "vsaq": "ch4_vsaq",
  "tf": "ch4_tf",
  "mtf": "ch4_mtf",
  "laq": "ch4_laq",
  "jtf": "ch4_jtf",
  "ctt": "ch4_ctt",
  "snc": "ch4_snc",
  "grade": "Grade 10",
  "gowf": "ch4_gowf",
  "afow": "ch4_afow",
  "cs": "ch4_cs",
  "ctco": "ch4_ctco",
  "map": "ch4_map",
  "dtf": "ch4_dtf",
  "grf": "ch4_grf",
  "afq": "ch4_afq",
  "pbq": "ch4_pbq",
  "yn": "ch4_yn",
  "un": "ch4_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch5",
  "chapterName": "Chapter 5 - Arithmetic Progressions",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch5a1.jpg",
				"width": "263",
				"height": "56"
				},
				"ansimg": {
				"image": "ch5a2.jpg",
				"width": "74",
				"height": "38"
				},
				"options": [
					"ch5a2.jpg",
					"ch5a3.jpg",
					"ch5a4.jpg",
					"(d) –1, –1"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The next two terms for an A.P. 4, 10, 16, 22, ... is _____________.",
				"ans": "(b) 28, 34",
				"code": "MCQ",
				"options": [
					"(a) 24, 26",
					"(b) 28, 34",
					"(c) 28, 32",
					"(d) 24, 30"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The list of numbers –10, –6, –2, 2, ... is _______________",
				"ans": "(b) an A.P., with d = 4",
				"code": "MCQ",
				"options": [
					"(a) an A.P., with d = –16",
					"(b) an A.P., with d = 4",
					"(c) an A.P. with d = –4",
					"(d) not as A.P."
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) –1",
				"code": "MCQ",
				"pic": {
				"image": "ch5a5.jpg",
				"width": "364",
				"height": "36"
				},
				"options": [
					"(a) P",
					"(b) –P",
					"(c) –1",
					"(d) 1"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a<sub>3</sub> = 8, a<sub>7</sub> = 24, then a<sub>10</sub> = ___________.",
				"ans": "(d) 36",
				"code": "MCQ",
				"options": [
					"(a) –4",
					"(b) 28",
					"(c) 32",
					"(d) 36"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a<sub>3</sub> = 8, a<sub>7</sub> = 24, then a<sub>10</sub> = ___________.",
				"ans": "(d) 36",
				"code": "MCQ",
				"options": [
					"(a) –4",
					"(b) 28",
					"(c) 32",
					"(d) 36"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In the A.P., 5, 7, 9, 11, 13, 15, the sixth term which is prime is _________.",
				"ans": "(b) 19",
				"code": "MCQ",
				"options": [
					"(a) 13",
					"(b) 19",
					"(c) 23",
					"(d) 15"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For A.P., a<sub>18</sub> – a<sub>8</sub> = _________.",
				"ans": "(b) 10<i>d</i>",
				"code": "MCQ",
				"options": [
					"(a) <i>d</i>",
					"(b) 10<i>d</i>",
					"(c) 26<i>d</i>",
					"(d) 2<i>d</i>"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For A.P., a<sub>25</sub> – a<sub>20</sub> = 15 then d = _________.",
				"ans": "(a) 3",
				"code": "MCQ",
				"options": [
					"(a) 3",
					"(b) 5",
					"(c) 20",
					"(d) 25"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a<sub>4</sub> = 7, a<sub>7</sub> = 4, then a<sub>10</sub> = ___________.",
				"ans": "(d) 1",
				"code": "MCQ",
				"options": [
					"(a) 9",
					"(b) 11",
					"(c) -11",
					"(d) 1"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The 10th term for A.P. 2, 7, 12, ... is ___________.",
				"ans": "(c) 47",
				"code": "MCQ",
				"options": [
					"(a) 50",
					"(b) 40",
					"(c) 47",
					"(d) 55"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "a<sub>3</sub> = 5, a<sub>7</sub> = 9, the A.P. is ___________.",
				"ans": "(a) 3, 4, 5, 6, 7 ...",
				"code": "MCQ",
				"options": [
					"(a) 3, 4, 5, 6, 7 ...",
					"(b) 6, 7, 8, 9, 10,...",
					"(c) 1, 2, 3, 4, 5, ...",
					"(d) 4, 5, 6, 7, 8, ..."
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "No. of two-digit numbers divisible by 3 are ___________.",
				"ans": "(b) 30",
				"code": "MCQ",
				"options": [
					"(a) 25",
					"(b) 30",
					"(c) 35",
					"(d) 40"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A sum of ₹1000 is invested at 8% simple interest per year, calculate the interest at the end of each year, the interest at the end of 30 years will be ___________.",
				"ans": "(d) 2400",
				"code": "MCQ",
				"options": [
					"(a) 1800",
					"(b) 2000",
					"(c) 2200",
					"(d) 2400"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In a flower bed, there are 23 rose plants in first row, 21 in second, 19 in third row, 5 rose plants in last row, there are _______ rows in flower bed.",
				"ans": "(c) 10",
				"code": "MCQ",
				"options": [
					"(a) 8",
					"(b) 9",
					"(c) 10",
					"(d) 11"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "30th term of the A.P., 10, 7, 4, ...",
				"ans": "(c) -77",
				"code": "MCQ",
				"options": [
					"(a) 97",
					"(b) 77",
					"(c) -77",
					"(d) -87"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 22",
				"code": "MCQ",
				"pic": {
				"image": "ch5a8.jpg",
				"width": "278",
				"height": "34"
				},
				"options": [
					"(a) 28",
					"(b) 22",
					"(c) –38",
					"(d) –40"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In an A.P., if d = –4, n = 7, a<sub>n</sub> = 4, then a = ___________.",
				"ans": "(d) 28",
				"code": "MCQ",
					"options": [
					"(a) 6",
					"(b) 7",
					"(c) 20",
					"(d) 28"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In an A.P., if a = 3.5, d = 0, n = 101, a<sub>n</sub> = ___________.",
				"ans": "(b) 3.5",
				"code": "MCQ",
					"options": [
					"(a) 0",
					"(b) 3.5",
					"(c) 103.5",
					"(d) 104.5"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 20",
				"pic": {
				"image": "ch5a10.jpg",
				"width": "315",
				"height": "32"
				},
				"code": "MCQ",
					"options": [
					"(a) –20",
					"(b) 20",
					"(c) –30",
					"(d) 30"
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the 2nd term of an A.P. is 13, and 5th term is 25, the 7th term is ___________.",
				"ans": "(b) 33",
				"code": "MCQ",
					"options": [
					"(a) 30",
					"(b) 33",
					"(c) 37",
					"(d) 38"
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If d = 5, then a<sub>18</sub> – a<sub>13</sub> = ___________.",
				"ans": "(c) 25",
				"code": "MCQ",
					"options": [
					"(a) 5",
					"(b) 20",
					"(c) 25",
					"(d) 30"
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a<sub>18</sub> – a<sub>14</sub> = 32 then d =___________.",
				"ans": "(a) 8",
				"code": "MCQ",
					"options": [
					"(a) 8",
					"(b) -8",
					"(c) -4",
					"(d) 4"
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then its 18th term will be ________",
				"ans": "(d) 0",
				"code": "MCQ",
					"options": [
					"(a) 7",
					"(b) 11",
					"(c) 18",
					"(d) 0"
				],
				"val": 24
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The 4th term from the end of A.P.: –11, –8, –5, ... –49 is ___________.",
				"ans": "(b) 40",
				"code": "MCQ",
					"options": [
					"(a) 37",
					"(b) 40",
					"(c) 43",
					"(d) 58"
				],
				"val": 25
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If d = –2, n = 5, a<sub>n</sub> = 0 then a = ___________.",
				"ans": "(d) 8",
				"code": "MCQ",
					"options": [
					"(a) 10",
					"(b) 5",
					"(c) –8",
					"(d) 8"
				],
				"val": 26
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In an A.P., if a = –10, n = 6, a<sub>n</sub> = 10, d = ___________.",
				"ans": "(b) 4",
				"code": "MCQ",
					"options": [
					"(a) 0",
					"(b) 4",
					"(c) –4",
					"(d) 10/3"
				],
				"val": 27
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If d = 3, then a<sub>20</sub> – a<sub>15</sub> is ___________.",
				"ans": "(c) 15",
				"code": "MCQ",
					"options": [
					"(a) 5",
					"(b) 3",
					"(c) 15",
					"(d) 20"
				],
				"val": 28
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The value of a<sub>30</sub> – a<sub>20</sub> for A.P. 2, 7, 12, 17, ... is: ___________.",
				"ans": "(c) 15",
				"code": "MCQ",
					"options": [
					"(a) 100",
					"(b) 10",
					"(c) 50",
					"(d) 20"
				],
				"val": 29
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the sum of three consecutive terms of A.P. is 48 and the product of first and last term is 252, then d = _______.",
				"ans": "(a) 2",
				"code": "MCQ",
					"options": [
					"(a) 2",
					"(b) 3",
					"(c) 4",
					"(d) 16"
				],
				"val": 30
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a = 2, d = 4, then S<sub>20</sub> = _________.",
				"ans": "(b) 800",
				"code": "MCQ",
					"options": [
					"(a) 600",
					"(b) 800",
					"(c) 78",
					"(d) 80"
				],
				"val": 31
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 3 + 5 + 7 + 9 ... up to n terms = 288, then n = _________.",
				"ans": "(c) 16",
				"code": "MCQ",
					"options": [
					"(a) 12",
					"(b) 15",
					"(c) 16",
					"(d) 17"
				],
				"val": 32
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Four numbers are in A.P. and the sum is 72 and the largest of them is twice the smallest, then the numbers are ___________.",
				"ans": "(b) 12, 16, 20, 24",
				"code": "MCQ",
					"options": [
					"(a) 4, 8, 12, 16",
					"(b) 12, 16, 20, 24",
					"(c) 10, 12, 14, 16",
					"(d) 2, 4, 6, 8"
				],
				"val": 33
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If S<sub>1</sub> = 2 + 4 + ... + 2n and S<sub>2</sub> = 1 + 3 + ... + (2n – 1), then S<sub>1</sub> : S<sub>2</sub> = _________.",
				"ans": null,
				"ansimg": {
				"image": "ch5a18.jpg",
				"width": "57",
				"height": "35"
				},
				"code": "MCQ",
					"options": [
					"ch5a18.jpg",
					"ch5a19.jpg",
					"(c) n<sup>2</sup>",
					"(d) (n + 1)"
				],
				"val": 34
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For A.P. <br/> S<sub>n</sub> – 2S<sub>n –1</sub> + S<sub>n–2</sub> = ______ (n > 2)",
				"ans": "(b) d",
				"code": "MCQ",
					"options": [
					"(a) 2d",
					"(b) d",
					"(c) a",
					"(d) (a + d)"
				],
				"val": 35
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If S<sub>m</sub> = n and S<sub>n</sub> = m, then Sm + n = __________.",
				"ans": "(a) – (m + n)",
				"code": "MCQ",
					"options": [
					"(a) – (m + n)",
					"(b) 0",
					"(c) m + n",
					"(d) 2m – 2n"
				],
				"val": 36
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 2K + 1, 13, 5K – 3 are three consecutive terms of A.P., then K = _________.",
				"ans": "(c) 4",
				"code": "MCQ",
					"options": [
					"(a) 17",
					"(b) 13",
					"(c) 4",
					"(d) 9"
				],
				"val": 37
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If S<sub>n</sub> = 2n<sup>2</sup> + 3n, then d = _________.",
				"ans": "(b) 4",
				"code": "MCQ",
					"options": [
					"(a) 13",
					"(b) 4",
					"(c) 9",
					"(d) -2"
				],
				"val": 38
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For A.P., 8, 3, –2, ... S<sub>22</sub> = _________.",
				"ans": "(c) –979",
				"code": "MCQ",
					"options": [
					"(a) –950",
					"(b) –969",
					"(c) –979",
					"(d) –999"
				],
				"val": 39
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "S<sub>14</sub> = 1050, a = 10, a<sub>20</sub> = ____________",
				"ans": "(b) 200",
				"code": "MCQ",
					"options": [
					"(a) 180",
					"(b) 200",
					"(c) 220",
					"(d) 240"
				],
				"val": 40
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For A.P., 24, 21, 18, ..., S<sub>n</sub> = 78, n = ____________",
				"ans": "(a) 4 or 13",
				"code": "MCQ",
					"options": [
					"(a) 4 or 13",
					"(b) 6 or 18",
					"(c) 9 or 15",
					"(d) 10 or 12"
				],
				"val": 41
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Sum of first 1000 positive integers is ___________",
				"ans": "(a) 500500",
				"code": "MCQ",
					"options": [
					"(a) 500500",
					"(b) 51051",
					"(c) 5000",
					"(d) 5100"
				],
				"val": 42
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Sum of first n term of an A.P. is __________",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch5a19.jpg",
				"width": "71",
				"height": "35"
				},
					"options": [
					"(a) n",
					"ch5a18.jpg",
					"ch5a19.jpg",
					"ch5a20.jpg"
				],
				"val": 43
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a<sub>n</sub> = 3 + 2n, then S<sub>24</sub> = _________",
				"ans": "(b) 672",
				"code": "MCQ",
					"options": [
					"(a) 680",
					"(b) 672",
					"(c) 600",
					"(d) 610"
				],
				"val": 44
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "a<sub>3</sub> = 600, a<sub>7</sub> = 700, a = _________.",
				"ans": "(a) 550",
				"code": "MCQ",
					"options": [
					"(a) 550",
					"(b) 650",
					"(c) 750",
					"(d) 850"
				],
				"val": 45
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "a<sub>3</sub> = 600, a<sub>7</sub> = 700, S<sub>7</sub> = _________.",
				"ans": "(c) 4375",
				"code": "MCQ",
					"options": [
					"(a) 4100",
					"(b) 4205",
					"(c) 4375",
					"(d) 4400"
				],
				"val": 46
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Sum of first 20 odd natural numbers is _____________",
				"ans": "(c) 400",
				"code": "MCQ",
					"options": [
					"(a) 100",
					"(b) 210",
					"(c) 400",
					"(d) 420"
				],
				"val": 47
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If nth term of an A.P. is (2n + 1), then sum of first three terms is _______.",
				"ans": "(b) 15",
				"code": "MCQ",
					"options": [
					"(a) 6n + 3",
					"(b) 15",
					"(c) 12",
					"(d) 21"
				],
				"val": 48
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If K, 2K –1 and 2K + 1 are three consecutive terms of an A.P., then the value of K is ________.",
				"ans": "(b) 3",
				"code": "MCQ",
					"options": [
					"(a) 2",
					"(b) 3",
					"(c) -3",
					"(d) 5"
				],
				"val": 49
			},
			
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.",
        "ans": "Let the three numbers be (a – d), a, (a + d) <br/> Given that, sum of three numbers <br/> = (a – d) + a + (a + d) = 12 <br/> ⇒ 3a = 12 ⇒ a = 4 <br/> ∴ The numbers are (4 – d), 4, (4 + d) <br/> Also, (4 – d)<sup>3</sup> + 4<sup>3</sup> + (4 + d)<sup>3</sup> = 288 <br/> ⇒ [64 – d<sup>3</sup> – 12d (4 – d)] + 64 <br/> + [64 + d<sup>3</sup> + 12d (4 + d)] = 288 ⇒ 192 + 24d<sup>2</sup> = 288 <br/> ⇒ 24d<sup>2</sup> = 46 <br/> ⇒ d<sup>2</sup> = 4 ⇒ d = ±2 <br/> When d = 2, <br/> required numbers are 4 – 2, 4, 4 + 2 or 2, 4, 6. <br/> When d = –2, <br/> required numbers are 4 – (–2), 4, 4 + (–2) or 6, 4, 2 <br/> Thus, the required number are 2, 4, 6",
        "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 sum of four consecutive numbers in an A.P. is 32 and the ratio of the product of the first and the last terms to the product of two middle terms is 7 : 15. Find the numbers.",
        "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": "ch5a43.jpg",
          "width": "463",
          "height": "368"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.",
        "ans": "Here, a<sub>4</sub> = 9 and a<sub>6</sub> + a<sub>13</sub> = 40 <br/> ⇒ a + 3d = 9 ...(1) <br/> and (a + 5d) + (a + 12d) = 40 <br/> ⇒ 2a + 17d = 40 ...(2) <br/> Multiplying (1) by 2 and subtracting from (2) <br/> 2a + 17d – 2(a + 3d) = 40 – 2 × 9 <br/> ⇒ 11d = 22 <br/> ⇒ d = 2 <br/> Put d = 2 in (1). We get a + (3) (2) = 9 = a = 3 <br/> Thus, the required AP is 3, 5, 7, 9, .... <br/> [Ans: 3, 5, 7, 9, ...]",
        "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": "The sum of the 5th and the 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.",
        "ans": "Given that (a<sub>5</sub> + a<sub>9</sub> = 30 and a<sub>25</sub> = 3a<sub>8</sub> <br/> ⇒ (a + 4d) + (a + 8d) = 30 and <br/> a + 24d = 3 (a + 7d) <br/> ⇒ 2a + 12d = 30 ...(1) <br/> and a + 24d = 3a + 21d <br/> ⇒ 3d = 2a ...(2) <br/> From (1) and (2) <br/> 3d + 12d = 30 <br/> ⇒ 15d = 30 <br/> ⇒ d = 2 <br/> Put d in (1), 3(2) = 2a = 6 ⇒ a = 3 <br/> Thus, the required AP is 3, 5, 7, ... <br/> [Ans: 3, 5, 7, ...]",
        "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": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch5a14.jpg",
          "width": "411",
          "height": "41"
        },
        "ansimg": {
          "image": "ch5a15.jpg",
          "width": "343",
          "height": "662"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch5a16.jpg",
          "width": "468",
          "height": "34"
        },
        "ansimg": {
          "image": "ch5a17.jpg",
          "width": "326",
          "height": "533"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the pth term of an A.P. is q and qth term is p, prove that its nth term is (p + q – n)",
        "ans": "Let a, d be first term and common difference respectively of given A.P <br/> Then, a<sub>p</sub>= q ⇒ a + (p – 1)d = q ...(1) <br/> a<sub>q</sub> = p ⇒ a + (q – 1)d = p ...(2) <br/> Subtracting (2) from (1) <br/> (p – q)d = q – p <br/> ⇒ d = –1 <br/> Put for d in (1), we get <br/> a = p + q – 1 <br/> Now, a<sub>n</sub> = a + (n – 1)d <br/> = (p + q – 1) + (n – 1) (–1) <br/> = (p + q – n) <br/> = p + q – n.",
        "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": "In an A.P., the sum of first ten terms is –150 and the sum of its next ten terms is –550. Find the A.P.",
        "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": "ch5a26.jpg",
          "width": "328",
          "height": "656"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the sum of all multiples of 7 lying between 500 and 900.",
        "ans": "First multiple of 7 between 500 and 900 = 504 <br/> Last multiple of 7 between 500 and 900 = 896. <br/> ∴ Required multiples of 7 are <br/> 504, 511, 518, ..., 896 <br/> Here, a = 504, d = 7 <br/> Let a<sub>n</sub> = l = 896 <br/> Now, <br/> ⇒ a + (n – 1)d = 896 <br/> ⇒ 504 + (n – 1)7 = 896 <br/> ⇒ 7n + 497 = 896 <br/> ⇒ 7n = 399 <br/> ⇒ n = 57 <br/> Required sum S<sub>57</sub> = 57/2[a + l] <br/> = (57/2) [504 + 896] <br/> = 57 × 700 <br/> = 39900 <br/> Thus, the sum of all multiples of 7 lying between 500 and 900 is 39900. <br/> [Ans: 39900]",
        "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": "The sum of first seven terms of an A.P. is 182. If its 4th and 17th terms are in the ratio 1 : 5, find the A.P.",
        "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": "ch5a27.jpg",
          "width": "326",
          "height": "373"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The 14th term of an A.P. is twice its 8th term. If its 6th term is –8, then find the sum of its first 20 terms.",
        "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": "ch5a28.jpg",
          "width": "400",
          "height": "392"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If S<sub>n</sub> denotes the sum of first n terms of A.P, prove that S<sub>12</sub> = 3 (S<sub>8</sub> – S<sub>4</sub>).",
        "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": "ch5a29.jpg",
          "width": "359",
          "height": "359"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the ratio of the sum of first n terms of two A.P.'s is (7n + 1) : (4n + 27), then find the ratio of their mth terms.",
        "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": "ch5a30.jpg",
          "width": "501",
          "height": "697"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 14,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch5a31.jpg",
          "width": "378",
          "height": "35"
        },
        "ansimg": {
          "image": "ch5a32.jpg",
          "width": "279",
          "height": "439"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.",
        "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": "ch5a33.jpg",
          "width": "469",
          "height": "684"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the common difference of A.P. whose first term is 5 and the sum of whose first four terms is half the sum of next four terms.",
        "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": "ch5a34.jpg",
          "width": "325",
          "height": "472"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Sum of the first 14 terms of an A.P. is 1505 and its first term is 10. Find its 25th term.",
        "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": "ch5a35.jpg",
          "width": "254",
          "height": "281"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "In an A.P. of 50 terms, the sum of first 10 terms is 210 and sum of its last 15 terms is 2565. Find the A.P.",
        "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": "ch5a36.jpg",
          "width": "329",
          "height": "609"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the 60th term of the A.P.: 8, 10, 12, ..., if it has a total of 60 terms and hence, find the sum of its last 10 terms.",
        "ans": "Here, a = 8, d = 10 – 8 = 2 <br/> a<sub>60</sub> = a + (60 – 1)d <br/> = 8 + 59 × 2 = 126 <br/> Sum of last 10 terms <br/> = a<sub>51</sub> + a<sub>52</sub> + ... + a<sub>60</sub> <br/> = 10/2 [a<sub>51</sub> + a<sub>60</sub>] (Sn = n/2 [a + l]) <br/> = 5[(a + 50d] + (a + 59d)] = 5{2a + 109d} <br/> = 5[2 × 8 + 109 × 2] <br/> = 5[16 + 218] <br/> = 5 × 234 = 1170. <br/> The 60th term is 126 and sum of 10 terms is 1170. <br/> [Ans: 60th term = 126, sum = 1170]",
        "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": "Ramkali required ₹ 2500 after 12 weeks to send her daughter to school. She saved ₹ 100 in the first week and increased her weekly saving by ₹ 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.",
        "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": "ch5a37.jpg",
          "width": "578",
          "height": "287"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 21,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch5a38.jpg",
          "width": "578",
          "height": "35"
        },
        "ansimg": {
          "image": "ch5a39.jpg",
          "width": "326",
          "height": "640"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The ratio of the sums of first m and first n terms of an A.P. is m<sup>2</sup> : n<sup>2</sup>. Show that the ratio of its mth and nth terms is (2m – 1) : (2n – 1).",
        "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": "ch5a40.jpg",
          "width": "352",
          "height": "444"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the sum of first m terms of an A.P. is the same as the sum of its n terms, show that the sum of its first (m + n) terms is zero.",
        "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": "ch5a41.jpg",
          "width": "348",
          "height": "253"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The houses in a row are numbered consecutively from 1 to 49. Show that these exists a value of x such that sum of numbers of houses preceding the houses numbered x is equal to sum of the numbers of houses following x.",
        "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": "ch5a42.jpg",
          "width": "461",
          "height": "550"
        }
      }
	  
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "For what value of k will k + 9, 2k – 1 and 2k + 1 be the consecutive terms of an A.P.?",
        "ans": "k + 9, 2k – 1, 2k + 1 are consecutive terms of an A.P. <br/> ⇒ 2 (2k – 1) = k + 9 + 2k + 1 <br/> ⇒ 4k – 2 = 3k + 10 <br/> ⇒ k = 12 <br/> Thus, k = 12 <br/> [Ans: k = 12]",
        "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": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch5a6.jpg",
          "width": "451",
          "height": "40"
        },
        "ansimg": {
          "image": "ch5a7.jpg",
          "width": "223",
          "height": "253"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ... 185.",
        "ans": "Here, a = 5, d = 9 – 5 = 4, <i>l</i> = 185 <br/> n<sup>th</sup> term from end = <i>l</i> – (n – 1) <i>d</i> <br/> = 185 – (9 – 1)4 <br/> = 185 – 32 <br/> = 153 <br/> Thus, the 9th term from the end is 153. <br/> [Ans: 153]",
        "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 an A.P. if the common difference d = –4 and seventh term (a<sub>7</sub>) is 4, then find the first term.",
        "ans": "a<sub>7</sub> = a + 6d <br/> ⇒ 4 = a + (6)(–4) <br/> ⇒ a = 4 + 24 = 28 <br/> Thus, the first term is 28. <br/> [Ans: 28]",
        "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": "Find the value of middle term of the following A.P.: –6, –2, 2, ... 58.",
        "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": "ch5a11.jpg",
          "width": "224",
          "height": "368"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Determine the A.P. whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.",
        "ans": "Given, a<sub>4</sub> = 18 and a<sub>15</sub> – a<sub>9</sub> = 30 <br/> ⇒ a + 3d = 18 ...(1) <br/> and (a + 14d) – (a + 8d) = 30 <br/> ⇒ 6d = 30 <br/> ⇒ d = 5 ...(2) <br/> (1) and (2) ⇒ a + 3(5) = 18 <br/> ∴ a = 18 – 15 = 3 <br/> Thus, the required A.P is 3, 8, 13, ... <br/> [Ans: 3, 8, 13, ...]",
        "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": "Find how many two-digit numbers are divisible by 6.",
        "ans": "Two-digit numbers divisible by 6 are: <br/> 12, 18, 24, ..., 96 <br/> Here a = 12, d = 6 <br/> Let nth term be last term, i.e. 96 <br/> a<sub>n</sub> = 96 <br/> ⇒ 12 + (n – 1)6 = 96 <br/> ⇒ 6n + 6 = 96 <br/> ⇒ n = 15 <br/> Thus, 15 two-digit numbers are divisible by 6. <br/> [Ans: 15]",
        "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": "Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.",
        "ans": "LCM (2, 5) = 10 <br/> ∴ Numbers divisible by 2 and 5 are actually numbers divisible by 10. <br/> First such number = 110 <br/> Last such number = 990. <br/> an = 990 ⇒ a + (n – 1)d = 990 <br/> ⇒ 110 + (n – 1)10 = 990 <br/> ⇒ 10n = 890 <br/> ⇒ n = 89 <br/> Thus, number of natural numbers between 101 and 999 is 89. <br/> [Ans: 89]",
        "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": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch5a12.jpg",
          "width": "437",
          "height": "38"
        },
        "ansimg": {
          "image": "ch5a13.jpg",
          "width": "270",
          "height": "405"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find how many integers between 200 and 500 are divisible by 8.",
        "ans": "Numbers between 200 and 500 which are divisible by 8 are 208, 216, 224, ..., 496, which is an A.P with a = 208, <br/> d = 8 <br/> Here a<sub>n</sub> = 496 <br/> ⇒ a + (n – 1)d = 496 <br/> ⇒ 208 + (n – 1) (8) = 496 <br/> ⇒ 8n = 296 <br/> ⇒ n = 37 <br/> Thus, there are 37 such integers. <br/> [Ans: 37 integers]",
        "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": "The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.",
        "ans": "Let a, d be first term and common difference of an A.P respectively <br/> t<sub>4</sub> = 0 <br/> ⇒ a + 3d = 0 <br/> ⇒ a = –3d ...(1) <br/> t<sub>25</sub> = a + 24d <br/> = –3d + 24d <br/> = 21d [Using (1)] <br/> t<sub>11</sub> = a + 10d <br/> ⇒ t<sub>11</sub> = –3d + 10d = 7d <br/> ⇒ t<sub>25</sub> = 3 × t<sub>11</sub> (∵ 21d = 3 × 7d) <br/> Thus, 25th term is three times the 11th term.",
        "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": "If the sum of p terms of an A.P. is ap<sup>2</sup> + bp, find its common difference.",
        "ans": "t<sub>1</sub> = s<sub>1</sub> <br/> = a(1)<sup>2</sup> + b(1) = a + b <br/> t<sub>2</sub> = s<sub>2</sub> – s <br/> = (4a + 2b) – (a + b) <br/> = 3a + b <br/> d = t<sub>2</sub> – t<sub>1</sub> = (3a + b) – (a + b) = 2a <br/> Thus, the common difference is 2a. <br/> [Ans: 2a]",
        "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": "In an A.P., the first term is 2, the last term is 29 and sum of the terms is 155. Find the common difference of A.P.",
        "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": "ch5a23.jpg",
          "width": "192",
          "height": "420"
        },
        "val": 13
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In an A.P., if S<sub>5</sub> + S<sub>7</sub> = 167 and S<sub>10</sub> = 235, then find the A.P., where S<sub>n</sub> denotes the sum of its first n terms.",
        "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": "ch5a24.jpg",
          "width": "374",
          "height": "555"
        },
        "val": 14
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "How many terms of the A.P.: 18, 16, 14, ..., be taken so that their sum is zero?",
        "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": "ch5a25.jpg",
          "width": "202",
          "height": "260"
        },
        "val": 15
      },	  
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch5_mcq",
  "co": "ch5_co",
  "nf": "ch5_nf",
  "saq": "ch5_saq",
  "fib": "ch5_fib",
  "vsaq": "ch5_vsaq",
  "tf": "ch5_tf",
  "mtf": "ch5_mtf",
  "laq": "ch5_laq",
  "jtf": "ch5_jtf",
  "ctt": "ch5_ctt",
  "snc": "ch5_snc",
  "grade": "Grade 10",
  "gowf": "ch5_gowf",
  "afow": "ch5_afow",
  "cs": "ch5_cs",
  "ctco": "ch5_ctco",
  "map": "ch5_map",
  "dtf": "ch5_dtf",
  "grf": "ch5_grf",
  "afq": "ch5_afq",
  "pbq": "ch5_pbq",
  "yn": "ch5_yn",
  "un": "ch5_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch6",
  "chapterName": "Chapter 6 - Triangles",
  "all": [
    [
		{
				"heading": "Multiple Choice Question.",
				"qus": "All regular polygons of same number of sides are ________.",
				"ans": "(b) similar",
				"code": "MCQ",
				"options": [
					"(a) congruent",
					"(b) similar",
					"(c) not similar",
					"(d) not congruent"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A polygon of 10 sides is ____________ to a polygon of 11 sides.",
				"ans": "(c) not similar",
				"code": "MCQ",
				"options": [
					"(a) congruent",
					"(b) similar",
					"(c) not similar",
					"(d) isomorphic"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Two circles of radii 5.2 cm each are ___________.",
				"ans": "(c) similar",
				"code": "MCQ",
				"options": [
					"(a) not congruent",
					"(b) not similar",
					"(c) similar"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In figure, if AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm, then",
				"ans": "(a) 624",
				"code": "MCQ",
				"pic": {
				"image": "ch6a5.jpg",
				"width": "218",
				"height": "244"
				},
				"ansimg": {
				"image": "ch6a3.jpg",
				"width": "158",
				"height": "24"
				},
				"options": [
					"ch6a2.jpg",
					"ch6a3.jpg",
					"ch6a4.jpg",
					"(d) None of these."
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) 18 cm",
				"code": "MCQ",
				"pic": {
				"image": "ch6a6.jpg",
				"width": "584",
				"height": "292"
				},
				"options": [
					"(a) 12 cm",
					"(b) 24 cm",
					"(c) 15 cm",
					"(d) 18 cm"
				],
				"val": 5
			},	
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 17.5 cm",
				"code": "MCQ",
				"pic": {
				"image": "ch6a8.jpg",
				"width": "280",
				"height": "242"
				},
				"options": [
					"(a) 17.5 cm",
					"(b) 35 cm",
					"(c) 42 cm",
					"(d) 25 cm"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch6a29.jpg",
				"width": "345",
				"height": "204"
				},
				"ansimg": {
				"image": "ch6a33.jpg",
				"width": "62",
				"height": "40"
				},
				"options": [
					"ch6a30.jpg",
					"ch6a31.jpg",
					"ch6a32.jpg",
					"ch6a33.jpg"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 70°",
				"code": "MCQ",
				"pic": {
				"image": "ch6a34.jpg",
				"width": "477",
				"height": "202"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 100°",
					"(b) 70°",
					"(c) 60°",
					"(d) 50°"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In figure, ΔPQR ∼ ΔPDE, the measure of ∠Q is:",
				"ans": "(b) 80°",
				"code": "MCQ",
				"pic": {
				"image": "ch6a35.jpg",
				"width": "148",
				"height": "146"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 60°",
					"(b) 80°",
					"(c) 100°",
					"(d) 30°"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) 3 cm",
				"code": "MCQ",
				"pic": {
				"image": "ch6a36.jpg",
				"width": "220",
				"height": "227"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 3.6 cm",
					"(b) 6.3 cm",
					"(c) 3 cm",
					"(d) 6 cm"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A vertical pole 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is:",
				"ans": "(a) 100 m",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 100 m",
					"(b) 120 m",
					"(c) 200 m",
					"(d) 25 m"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 25 : 4",
				"code": "MCQ",
				"pic": {
				"image": "ch6a50.jpg",
				"width": "450",
				"height": "206"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 25 : 4",
					"(b) 2 : 5",
					"(c) 4 : 25",
					"(d) 5 : 2"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The areas of two similar triangles are 9 cm<sup>2</sup> and 16 cm<sup>2</sup> respectively. The ratio of their corresponding sides is:",
				"ans": "(b) 3 : 4",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 9 : 16",
					"(b) 3 : 4",
					"(c) 4 : 3",
					"(d) 2 : 3"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) 9 : 16",
				"code": "MCQ",
				"pic": {
				"image": "ch6a51.jpg",
				"width": "420",
				"height": "37"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 2 : 5",
					"(b) 4 : 25",
					"(c) 9 : 16",
					"(d) 8 : 12"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of their corresponding height is:",
				"ans": "(a) 4: 5",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 4: 5",
					"(b) 5 : 4",
					"(c) 3 : 2",
					"(d) 5 : 7"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In figure, if QR = 26 cm, DP= 6 cm and DR = 8 cm, then value of PR and QP respectively is:",
				"ans": "(b) 10 cm, 24 cm",
				"code": "MCQ",
				"pic": {
				"image": "ch6a62.jpg",
				"width": "189",
				"height": "206"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 24 cm, 10 cm",
					"(b) 10 cm, 24 cm",
					"(c) 12 cm, 16 cm",
					"(d) 16 cm, 12 cm"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) 3 CD<sup>2</sup>",
				"code": "MCQ",
				"pic": {
				"image": "ch6a63.jpg",
				"width": "366",
				"height": "27"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"ch6a64.jpg",
					"(b) 2 DC<sup>2</sup>",
					"(c) 3 CD<sup>2</sup>",
					"(d) 4 DC<sup>2</sup>"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Two poles of height 6 m and 10 m stand vertically upright on a plane ground. If the distance between their feet is 3 m, the distance between their tops is:",
				"ans": "(c) 5 m",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 7 m",
					"(b) 4 m",
					"(c) 5 m",
					"(d) 12 m"
				],
				"val": 18
			},
			
			
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "Prove that the ratio of the perimeters of the similar triangles is equal to the ratio of their corresponding sides.",
        "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": "ch6a25.jpg",
          "width": "552",
          "height": "456"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 2,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch6a26.jpg",
          "width": "304",
          "height": "262"
        },
        "ansimg": {
          "image": "ch6a27.jpg",
          "width": "444",
          "height": "525"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.",
        "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": "ch6a28.jpg",
          "width": "361",
          "height": "534"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 4,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch6a44.jpg",
          "width": "431",
          "height": "61"
        },
        "ansimg": {
          "image": "ch6a45.jpg",
          "width": "499",
          "height": "668"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch6a46.jpg",
          "width": "444",
          "height": "232"
        },
        "ansimg": {
          "image": "ch6a47.jpg",
          "width": "544",
          "height": "421"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch6a48.jpg",
          "width": "456",
          "height": "264"
        },
        "ansimg": {
          "image": "ch6a49.jpg",
          "width": "287",
          "height": "499"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that the area of the equilateral triangle described on the side of an isosceles right-angled triangle is half the area of equilateral triangle described on its hypotenuse.",
        "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": "ch6a60.jpg",
          "width": "495",
          "height": "552"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the area of two similar triangles are equal, prove that they are congruent.",
        "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": "ch6a61.jpg",
          "width": "411",
          "height": "480"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 9,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch6a70.jpg",
          "width": "403",
          "height": "310"
        },
        "ansimg": {
          "image": "ch6a71.jpg",
          "width": "328",
          "height": "370"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "O is any point inside a square □PQRS. Prove that OP<sup>2</sup> + OR<sup>2</sup> = OQ<sup>2</sup> + OS<sup>2</sup>.",
        "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": "ch6a72.jpg",
          "width": "426",
          "height": "535"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "Fill in the blanks. <br/> (i) The polygons of same number of sides are similar, if <br/> (a) _____________________ <br/> (b) ____________________ <br/> (ii) All congruent figures are ________________",
        "ans": "(i) (a) corresponding angles are equal. <br/> (b) their corresponding sides are proportional <br/> (ii) similar",
        "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": "State whether the pair of geometrical figures given below are similar or not.",
        "ans": "The given geometrical figures are similar",
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a1.jpg",
          "width": "368",
          "height": "165"
        },
        "ansimg": {
          "image": null,
          "width": null,
          "height": null
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In figure, ΔAHK is similar to ΔABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find AC.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a9.jpg",
          "width": "245",
          "height": "109"
        },
        "ansimg": {
          "image": "ch6a10.jpg",
          "width": "304",
          "height": "210"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a11.jpg",
          "width": "408",
          "height": "270"
        },
        "ansimg": {
          "image": "ch6a12.jpg",
          "width": "113",
          "height": "241"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In figure, if AD = 6 cm, DB = 9 cm, AE = 8 cm and EC = 12 cm and ∠ADE = 48°. Find ∠ABC.",
        "ans": "201",
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a13.jpg",
          "width": "206",
          "height": "271"
        },
        "ansimg": {
          "image": "ch6a14.jpg",
          "width": "378",
          "height": "211"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a15.jpg",
          "width": "593",
          "height": "257"
        },
        "ansimg": {
          "image": "ch6a16.jpg",
          "width": "168",
          "height": "255"
        },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a17.jpg",
          "width": "495",
          "height": "40"
        },
        "ansimg": {
          "image": "ch6a18.jpg",
          "width": "581",
          "height": "381"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a19.jpg",
          "width": "307",
          "height": "36"
        },
        "ansimg": {
          "image": "ch6a20.jpg",
          "width": "345",
          "height": "269"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a21.jpg",
          "width": "308",
          "height": "236"
        },
        "ansimg": {
          "image": "ch6a22.jpg",
          "width": "153",
          "height": "205"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a23.jpg",
          "width": "582",
          "height": "61"
        },
        "ansimg": {
          "image": "ch6a24.jpg",
          "width": "584",
          "height": "406"
        },
        "val": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Is ΔABC similar to ΔPQR?",
        "ans": "Using angle sum property <br/> ∠A = 180° – (40° + 80°) <br/> = 60° <br/> ∠P = 180° – (80° + 50°) <br/> = 50° <br/> ∠A ≠ ∠P <br/> ∠B ≠ ∠Q <br/> ∠C ≠ ∠R <br/> ∴ AAA similarity is violated <br/> ∴ΔABC  ΔPQR",
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a37.jpg",
          "width": "379",
          "height": "190"
        },
        "ansimg": {
          "image": null,
          "width": null,
          "height": null
        },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "State which pairs of triangles in the given figure are similar. Also, state the similarity criterion used.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a38.jpg",
          "width": "550",
          "height": "174"
        },
        "ansimg": {
          "image": "ch6a39.jpg",
          "width": "232",
          "height": "333"
        },
        "val": 12
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a40.jpg",
          "width": "387",
          "height": "22"
        },
        "ansimg": {
          "image": "ch6a41.jpg",
          "width": "500",
          "height": "382"
        },
        "val": 13
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a42.jpg",
          "width": "581",
          "height": "51"
        },
        "ansimg": {
          "image": "ch6a43.jpg",
          "width": "533",
          "height": "419"
        },
        "val": 14
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a52.jpg",
          "width": "582",
          "height": "283"
        },
        "ansimg": {
          "image": "ch6a53.jpg",
          "width": "275",
          "height": "284"
        },
        "val": 15
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If ΔABC ∼ ΔDEF and BC = 3 cm, EF = 4 cm, ar(ΔABC) = 54 cm2, then find ar(ΔDEF).",
        "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": "ch6a54.jpg",
          "width": "461",
          "height": "165"
        },
        "val": 16
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a55.jpg",
          "width": "315",
          "height": "44"
        },
        "ansimg": {
          "image": "ch6a56.jpg",
          "width": "494",
          "height": "88"
        },
        "val": 17
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Let ΔABC ∼ ΔDEF, if ar(ΔABC) = 100 cm<sup>2</sup>, ar(ΔDEF) = 196 cm<sup>2</sup> and DE = 7 cm, then find AB.",
        "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": "ch6a57.jpg",
          "width": "560",
          "height": "480"
        },
        "val": 18
      },
	   {
        "heading": "Very short answer type questions.",
        "qus": "Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a58.jpg",
          "width": "446",
          "height": "233"
        },
        "ansimg": {
          "image": "ch6a59.jpg",
          "width": "582",
          "height": "250"
        },
        "val": 19
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a65.jpg",
          "width": "511",
          "height": "28"
        },
        "ansimg": {
          "image": "ch6a66.jpg",
          "width": "315",
          "height": "401"
        },
        "val": 20
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "□ABCD is a rhombus. Prove that 4BC<sup>2</sup> = AC<sup>2</sup> + BD<sup>2</sup>",
        "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": "ch6a67.jpg",
          "width": "557",
          "height": "291"
        },
        "val": 21
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In the figure, find AD, if it is given that AC = 6 cm, BC = 9 cm and BD = 7 cm.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch6a68.jpg",
          "width": "117",
          "height": "243"
        },
        "ansimg": {
          "image": "ch6a69.jpg",
          "width": "296",
          "height": "229"
        },
        "val": 22
      }
	  
	  
	],
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  "mcq": "ch6_mcq",
  "co": "ch6_co",
  "nf": "ch6_nf",
  "saq": "ch6_saq",
  "fib": "ch6_fib",
  "vsaq": "ch6_vsaq",
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  "jtf": "ch6_jtf",
  "ctt": "ch6_ctt",
  "snc": "ch6_snc",
  "grade": "Grade 10",
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  "cs": "ch6_cs",
  "ctco": "ch6_ctco",
  "map": "ch6_map",
  "dtf": "ch6_dtf",
  "grf": "ch6_grf",
  "afq": "ch6_afq",
  "pbq": "ch6_pbq",
  "yn": "ch6_yn",
  "un": "ch6_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch7",
  "chapterName": "Chapter 7 - Coordinate Geometry",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) P(2, 0)",
				"code": "MCQ",
				"pic": {
				"image": "c7a1.jpg",
				"width": "417",
				"height": "23"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) P(2, 1)",
					"(b) P(–1, 0)",
					"(c) P(2, 0)",
					"(d) P(0, 0)"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If one of the end points of a circle having centre at origin is A(3, –2), then the other end point of the diameter has the coordinates.",
				"ans": "(a) (–3, 2)",
				"code": "MCQ",
				"options": [
					"(a) (–3, 2)",
					"c7a2.jpg",
					"c7a3.jpg",
					"(d) None of these"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The distance of A (x, y) from origin is ___________.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "c7a4.jpg",
				"width": "83",
				"height": "32"
				},
				"options": [
					"(a) x<sup>2</sup> + y<sup>2</sup>",
					"(b) |x – y|",
					"(c) |x + y|",
					"c7a4.jpg"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The foot of the perpendicular from P(–3, 2) to Y-axis is M. Coordinates of M are_________.",
				"ans": "(b) (0, 2)",
				"code": "MCQ",
				"options": [
					"(a) (3, 0)",
					"(b) (0, 2)",
					"c7a5.jpg",
					"(d) 1"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The coordinates of the foot of the perpendicular from P(5, –1) to x-axis are___________.",
				"ans": "(d) (5, 0)",
				"code": "MCQ",
				"options": [
					"c7a6.jpg",
					"(b) (–5, 1)",
					"(c) (0, –1)",
					"(d) (5, 0)"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) –8",
				"code": "MCQ",
				"pic": {
				"image": "c7a7.jpg",
				"width": "584",
				"height": "64"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) –8",
					"(b) 3",
					"(c) –4",
					"(d) 4"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If A and B are the points (–6, 7) and (–1, –5) respectively, then the distance 2AB is equal to _______.",
				"ans": "(b) 26",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 13",
					"(b) 26",
					"(c) 169",
					"(d) 238"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The midpoint of the segment AB is the point P(0, 4). If the coordinates of B are (–2, 3), then the coordinates of A are",
				"ans": "(a) (2, 5)",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (2, 5)",
					"(b) (–2, –5)",
					"(c) (2, 9)",
					"(d) (–2, 11)"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of centre are (–2, 5), then the coordinates of the other end of diameter are",
				"ans": "(a) (–6, 7)",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (–6, 7)",
					"(b) (6, –7)",
					"(c) (6, 7)",
					"(d) (–6, 7)"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The distance of the point (–3, 4) from the x-axis is __________.",
				"ans": "(c) 4",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 3",
					"(b) –3",
					"(c) 4",
					"(d) 5"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3), D(0, 3), then length of one of its diagonals is ______________.",
				"ans": "(a) 5",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 5",
					"(b) 4",
					"(c) 3",
					"(d) 25"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The distance between the points A(0, 6) and B(0, 2) is _________.",
				"ans": "(b) 8",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 6",
					"(b) 8",
					"(c) 4",
					"(d) 2"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The distance of the point P(–6, 8) from the origin is___________.",
				"ans": "(c) 10",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 8",
					"(b) 2√7",
					"(c) 10",
					"(d) 6"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The coordinates of the point which is equidistant from the three vertices of ΔAOB as shown in the figure are",
				"ans": "(a) (x, y)",
				"code": "MCQ",
				"pic": {
				"image": "c7a8.jpg",
				"width": "177",
				"height": "172"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (x, y)",
					"(b) (y, x)",
					"c7a9.jpg",
					"c7a10.jpg"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the distance between the points (4, P) and (1, 0) is 5, then the value of P is ____________.",
				"ans": "(b) ±4",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 4",
					"(b) ±4",
					"(c) –4",
					"(d) 0"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "c7a11.jpg",
				"width": "581",
				"height": "54"
				},
				"ansimg": {
				"image": "c7a15.jpg",
				"width": "76",
				"height": "43"
				},
				"options": [
					"c7a12.jpg",
					"c7a13.jpg",
					"c7a14.jpg",
					"c7a15.jpg"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then",
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": "c7a18.jpg",
				"width": "97",
				"height": "36"
				},
				"options": [
					"c7a16.jpg",
					"(b) AP = AB",
					"c7a17.jpg",
					"c7a18.jpg"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The coordinates of the point which divides the line segment joining the points (4, –3) and (8, 5) in the ratio 3:1 are",
				"ans": "(d) (7, 3)",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (4, 2)",
					"(b) (7, 0)",
					"(c) (5, 1)",
					"(d) (7, 3)"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The point (–4, 6) divides the line segment joining the points A(–6, 10) and B(3, –8) in the ratio of _____.",
				"ans": "(a) 2:7",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 2:7",
					"(b) 1:5",
					"(c) 3:5",
					"(d) 2:9"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The coordinates of the points of trisection of the line segment joining the points A(2, –2) and B(–7, 4) are __________.",
				"ans": "(a) (–1, 0)(–4, 2)",
				"code": "MCQ",
				"pic": {
				"image": "c7a29.jpg",
				"width": "279",
				"height": "53"
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (–1, 0)(–4, 2)",
					"(b) (0, 1)(2, 3)",
					"(c) (–1, 2)(–3, 1)",
					"(d) (–1, –1)(–3, 3)"
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the points A(6, 1), B(18, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, the value of p is__________.",
				"ans": "(c) 7",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 3",
					"(b) 5",
					"(c) 7",
					"(d) 9"
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The point P which divides the line segment joining the points A (2, –5) and B(5, 2) in the ratio 2:3 lies in the quadrant",
				"ans": "(d) IV",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) I",
					"(b) II",
					"(c) III",
					"(d) IV"
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2:1 are ___________.",
				"ans": "(b) (3, 5)",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (2, 4)",
					"(b) (3, 5)",
					"(c) (4, 2)",
					"(d) (5, 3)"
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the point C(k, 4) divides the join of points A(2, 6) and B(5, 1) in the ratio 2:3, then the value of k is _________.",
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": "c7a31.jpg",
				"width": "51",
				"height": "37"
				},
				"options": [
					"(a) 16",
					"c7a30.jpg",
					"c7a31.jpg",
					"c7a32.jpg"
				],
				"val": 24
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The fourth vertex D of a parallelogram ABCD whose three vertices are A(–2, 3), B(6, 7) and C(8, 3) is _______________.",
				"ans": "(b) (0, –1)",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (0, 1)",
					"(b) (0, –1)",
					"(c) (–1, 0)",
					"(d) (1, 0)"
				],
				"val": 25
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A(0, 0), B(3, 0), C(3, 4) are the vertices of a _______triangle.",
				"ans": "(a) right-angled",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) right-angled",
					"(b) equilateral",
					"(c) isosceles",
					"(d) acute-angled"
				],
				"val": 26
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "(1, 0), (0, 1), (1, 1) are the coordinates of vertices of a triangle. The triangle is an ______ triangle.",
				"ans": "(c) isosceles",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) acute-angled",
					"(b) obtuse-angled",
					"(c) isosceles",
					"(d) equilateral"
				],
				"val": 27
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A(1, 2), B(2, 3), C(3, 4) are given points __________ of the following is true.",
				"ans": "(b) AB + BC = AC",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) AC + BC + AB",
					"(b) AB + BC = AC",
					"(c) A is the midpoint of BC",
					"(d) A, B, C are non-collinear."
				],
				"val": 28
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the points A(x, 2), B(–3, –4) and C(7, –5) are collinear, then the value of x is __________.",
				"ans": "(a) –63",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) –63",
					"(b) 63",
					"(c) 60",
					"(d) –60"
				],
				"val": 29
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then __________.",
				"ans": "(c) 2a = b",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) a = b",
					"(b) a = 2b",
					"(c) 2a = b",
					"(d) a = –b"
				],
				"val": 30
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is __________.",
				"ans": "(b) 0",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) (a + b+ c)<sup>2</sup>",
					"(b) 0",
					"(c) a + b + c",
					"(d) abc"
				],
				"val": 31
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of triangle with vertices A (3, 0), B(7, 0) and C(8, 4) is __________.",
				"ans": "(c) 8",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 14",
					"(b) 28",
					"(c) 8",
					"(d) 6"
				],
				"val": 32
			}		
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "Find a point P on the y-axis which is equidistant from the points A(4, 8) and B(–6, 6). Also, find the distance AP.",
        "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": "c7a27.jpg",
          "width": "268",
          "height": "339"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A point A(2, –1) is equidistant from the points (b, –7) and (–3, b). Find b.",
        "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": "c7a28.jpg",
          "width": "360",
          "height": "188"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 3,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "c7a37.jpg",
          "width": "584",
          "height": "54"
        },
        "ansimg": {
          "image": "c7a38.jpg",
          "width": "407",
          "height": "503"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 4,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "c7a39.jpg",
          "width": "584",
          "height": "59"
        },
        "ansimg": {
          "image": "c7a40.jpg",
          "width": "307",
          "height": "636"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The vertices of parallelogram ABCD are A(3, –4), B(–1, –3), C(–6, 2). Find the coordinates of the fourth vertex D and also find the area of parallelogram ABCD.",
        "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": "c7a41.jpg",
          "width": "399",
          "height": "632"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "c7a44.jpg",
          "width": "571",
          "height": "55"
        },
        "ansimg": {
          "image": "c7a45.jpg",
          "width": "389",
          "height": "597"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If R(x, y) is a point on the line segment joining the points P(a, b) and Q(b, a), then prove that x + y = a + b.",
        "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": "c7a46.jpg",
          "width": "435",
          "height": "256"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If two vertices of an equilateral triangle are (3, 0) and (6, 0), then find the third vertex.",
        "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": "c7a47.jpg",
          "width": "408",
          "height": "794"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the points A(–2, 1), B(a, b) and C(4, –1) are collinear and a – b = 1, then find the values of a and b.",
        "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": "c7a48.jpg",
          "width": "371",
          "height": "326"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the area of the triangle ΔABC with A(1, –4) and the midpoints of sides through A being (2, –1) and (0, –1).",
        "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": "c7a49.jpg",
          "width": "579",
          "height": "543"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, then find the values of a and b. Hence, find lengths of its sides.",
        "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": "c7a50.jpg",
          "width": "454",
          "height": "473"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Show that ΔABC where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 4) are similar triangles.",
        "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": "c7a51.jpg",
          "width": "359",
          "height": "321"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 13,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "c7a52.jpg",
          "width": "578",
          "height": "57"
        },
        "ansimg": {
          "image": "c7a53.jpg",
          "width": "336",
          "height": "495"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b), then prove that bx = ay.",
        "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": "c7a54.jpg",
          "width": "413",
          "height": "271"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that the area of a triangle with vertices (t, t – 2), (t + 2, t + 2) and (t + 3, t) is independent of t.",
        "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": "c7a55.jpg",
          "width": "390",
          "height": "345"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 16,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "c7a56.jpg",
          "width": "577",
          "height": "195"
        },
        "ansimg": {
          "image": "c7a57.jpg",
          "width": "563",
          "height": "863"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k –1, 5k) are collinear, then find the value of k.",
        "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": "c7a58.jpg",
          "width": "561",
          "height": "344"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If a ≠ b, a ≠ 0, b ≠ 0, prove that the points (a, a2), (b, b2), (0, 0) will not be collinear.",
        "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": "c7a59.jpg",
          "width": "339",
          "height": "327"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?",
        "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": "c7a19.jpg",
          "width": "390",
          "height": "211"
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the distance of a point P(x, y) from origin.",
        "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": "c7a20.jpg",
          "width": "331",
          "height": "113"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0).",
        "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": "c7a21.jpg",
          "width": "402",
          "height": "293"
		  },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the value of y for which the distance between the points A(3, –1) and B(11, y) is 10 units.",
        "ans": "Given that, AB = 10 <br/> ⇒ AB<sup>2</sup> = 100 <br/> ⇒ (11 – 3)<sup>2</sup> + (y + 1)<sup>2</sup> = 100 <br/> ⇒ 64 + y<sup>2</sup> + 1 + 2y = 100 <br/> ⇒ y<sup>2</sup> + 2y – 35 = 0 <br/> ⇒ y<sup>2</sup> + 7y – 5y – 35 = 0 <br/> ⇒ y(y + 7) – 5 (y + 7) = 0 <br/> ⇒ (y + 7) (y – 5) = 0 <br/> ⇒ y = –7, 5 <br/> Thus, y = –7, 5",
        "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 a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), then find the value of p.",
        "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": "c7a22.jpg",
          "width": "261",
          "height": "161"
		  },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right-angled triangle, right-angled at B. Find the value of p.",
        "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": "c7a23.jpg",
          "width": "553",
          "height": "313"
		  },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find coordinates of P.",
        "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": "c7a24.jpg",
          "width": "277",
          "height": "269"
		  },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Prove that the points (3, 0), (6, 4) and (–1, 3) are vertices of a right-angled isosceles triangle.",
        "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": "c7a25.jpg",
          "width": "395",
          "height": "372"
		  },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y.",
        "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": "c7a26.jpg",
          "width": "261",
          "height": "238"
		  },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "c7a33.jpg",
          "width": "584",
          "height": "62"
        },
        "ansimg": {
          "image": "c7a34.jpg",
          "width": "525",
          "height": "541"
		  },
        "val": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–1, –4). Also, find the coordinates of the print of division.",
        "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": "c7a35.jpg",
          "width": "419",
          "height": "398"
		  },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Let P and Q be the points of trisection of the line segment joining the points A(2, –2) and B(–7, 4) such that P is nearer to A. Find coordinates of P and Q.",
        "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": "c7a36.jpg",
          "width": "586",
          "height": "339"
		  },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the relation between x and y if the points A(x, y), B(–5, 7) and C(–4, 5) are collinear.",
        "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": "c7a42.jpg",
          "width": "285",
          "height": "133"
		  },
        "val": 12
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the area of the quadrilateral the coordinates of whose vertices are (5, –2), (1, 1), (3, 4) and (4, –3).",
        "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": "c7a43.jpg",
          "width": "538",
          "height": "640"
		  },
        "val": 13
      } 
	],
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  "mcq": "ch7_mcq",
  "co": "ch7_co",
  "nf": "ch7_nf",
  "saq": "ch7_saq",
  "fib": "ch7_fib",
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  "ctt": "ch7_ctt",
  "snc": "ch7_snc",
  "grade": "Grade 10",
  "gowf": "ch7_gowf",
  "afow": "ch7_afow",
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  "ctco": "ch7_ctco",
  "map": "ch7_map",
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  "grf": "ch7_grf",
  "afq": "ch7_afq",
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  "un": "ch7_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch8",
  "chapterName": "Chapter 8 - Introduction to Trigonometry",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "In the figure, AD = 4 cm, BD = 3 cm, CB = 12 cm, thus value of cot θ is",
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch8a5.jpg",
				"width": "210",
				"height": "134"
				},
				"ansimg": {
				"image": "ch8a1.jpg",
				"width": "50",
				"height": "34"
				},
				"options": [
					"ch8a1.jpg",
					"ch8a2.jpg",
					"ch8a3.jpg",
					"ch8a4.jpg"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 7",
				"code": "MCQ",
				"pic": {
				"image": "ch8a6.jpg",
				"width": "239",
				"height": "33"
				},
				"options": [
					"(a) 7",
					"(b) 3",
					"(c) 4",
					"(d) 20"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "ΔABC is right-angled at A; the value of tan B × tan C is",
				"ans": "(a) 1",
				"code": "MCQ",
				"options": [
					"(a) 1",
					"(b) zero",
					"(c) tan B",
					"(d) tan C"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If C is an acute angle in a right ΔABC, right-angled at B, then the value of sin C + cos C is equal to",
				"ans": "(d) greater than one",
				"code": "MCQ",
				"options": [
					"(a) 1",
					"(b) 2",
					"(c) less than one",
					"(d) greater than one"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 1",
				"code": "MCQ",
				"pic": {
				"image": "ch8a15.jpg",
				"width": "136",
				"height": "37"
				},
				"options": [
					"(a) 1",
					"(b) 2",
					"(c) 0",
					"(d) can’t be determined"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 60º, 30º",
				"code": "MCQ",
				"pic": {
				"image": "ch8a16.jpg",
				"width": "546",
				"height": "36"
				},
				"options": [
					"(a) 30º, 60º",
					"(b) 60º, 30º",
					"(c) 45º, 45º",
					"(d) 65º, 65º"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If tan<sup>2</sup> 45º – cos<sup>2</sup> 30º = x sin 45º cos 45º, then x equals",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch8a18.jpg",
				"width": "42",
				"height": "34"
				},
				"options": [
					"(a) – 2",
					"(b) 2",
					"ch8a17.jpg",
					"ch8a18.jpg"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) sin 30º",
				"code": "MCQ",
				"pic": {
				"image": "ch8a19.jpg",
				"width": "138",
				"height": "36"
				},
				"options": [
					"(a) sin 60º",
					"(b) cos 60º",
					"(c) tan 60º",
					"(d) sin 30º"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) –1",
				"code": "MCQ",
				"pic": {
				"image": "ch8a20.jpg",
				"width": "206",
				"height": "35"
				},
				"options": [
					"(a) 0",
					"(b) 1",
					"(c) 2",
					"(d) –1"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Given that sin 3A = cos (A – 26º) and if 3A is an acute angle, then measure of A is",
				"ans": "(b) 29º",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 52º",
					"(b) 29º",
					"(c) 13º",
					"(d) 78º"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If θ and (2θ – 45º) are acute angles such that sin θ = cos (2θ – 45º), then value of tan θ is",
				"ans": "(c) 1",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) √3",
					"ch8a29.jpg",
					"(c) 1",
					"(d) –1"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch8a30.jpg",
				"width": "362",
				"height": "36"
				},
				"ansimg": {
				"image": "ch8a32.jpg",
				"width": "67",
				"height": "35"
				},
				"options": [
					"ch8a31.jpg",
					"ch8a32.jpg",
					"ch8a33.jpg",
					"ch8a34.jpg"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) 1",
				"code": "MCQ",
				"pic": {
				"image": "ch8a35.jpg",
				"width": "203",
				"height": "38"
				},
				"options": [
					"ch8a36.jpg",
					"ch8a37.jpg",
					"(c) 1",
					"(d) 2"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 2",
				"code": "MCQ",
				"pic": {
				"image": "ch8a50.jpg",
				"width": "201",
				"height": "36"
				},
				"options": [
					"(a) 2",
					"(b) 4",
					"(c) 1",
					"(d) 3"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If sec<sup>2</sup> θ (1 + sin θ) (1 – sin θ) = K, then value of K is",
				"ans": "(d) 1",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) 3",
					"ch8a51.jpg",
					"(d) 1"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch8a52.jpg",
				"width": "324",
				"height": "36"
				},
				"ansimg": {
				"image": "ch8a55.jpg",
				"width": "49",
				"height": "37"
				},
				
				"options": [
					"ch8a53.jpg",
					"(b) 3",
					"ch8a54.jpg",
					"ch8a55.jpg"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 18",
				"code": "MCQ",
				"pic": {
				"image": "ch8a56.jpg",
				"width": "240",
				"height": "31"
				},			
				"options": [
					"(a) 9",
					"(b) 18",
					"(c) 27",
					"(d) 20"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The value of (sec θ + tan θ) (1 – sin θ) is equal to",
				"ans": "(d) cos θ",
				"code": "MCQ",		
				"options": [
					"(a) sec θ",
					"(b) sin θ",
					"(c) cosec θ",
					"(d) cos θ"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If cosec θ = 4 and cot θ = √3 k, then k =_________.",
				"ans": "(c) √5",
				"code": "MCQ",		
				"options": [
					"(a) 1",
					"(b) 2",
					"(c) √5",
					"(d) 5"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If sec θ + tan θ = x, then sec θ is equal to",
				"ans": null,
				"code": "MCQ",	
				"ansimg": {
				"image": "ch8a62.jpg",
				"width": "70",
				"height": "39"
				},				
				"options": [
					"ch8a59.jpg",
					"ch8a60.jpg",
					"ch8a61.jpg",
					"ch8a62.jpg"
				],
				"val": 20
			}
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "If ΔABC is right-angled at B, BC = 7 cm, AC – AB = 1 cm, then find the value of cos A + sin A.",
        "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": "ch8a14.jpg",
          "width": "407",
          "height": "329"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 2,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a26.jpg",
          "width": "262",
          "height": "42"
        },
        "ansimg": {
          "image": "ch8a27.jpg",
          "width": "403",
          "height": "462"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Evaluate without using trigonometric tables.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 3,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a40.jpg",
          "width": "330",
          "height": "39"
        },
        "ansimg": {
          "image": "ch8a41.jpg",
          "width": "574",
          "height": "199"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If A, B and C are interior angles of a ΔABC, prove that",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 4,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a42.jpg",
          "width": "237",
          "height": "67"
        },
        "ansimg": {
          "image": "ch8a43.jpg",
          "width": "408",
          "height": "418"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a44.jpg",
          "width": "468",
          "height": "38"
        },
        "ansimg": {
          "image": "ch8a45.jpg",
          "width": "583",
          "height": "300"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a46.jpg",
          "width": "421",
          "height": "54"
        },
        "ansimg": {
          "image": "ch8a47.jpg",
          "width": "517",
          "height": "356"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 7,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a48.jpg",
          "width": "494",
          "height": "57"
        },
        "ansimg": {
          "image": "ch8a49.jpg",
          "width": "570",
          "height": "364"
        }
      },
	  
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 8,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a77.jpg",
          "width": "275",
          "height": "34"
        },
        "ansimg": {
          "image": "ch8a78.jpg",
          "width": "371",
          "height": "353"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that 2 sec<sup>2</sup> θ – sec<sup>4</sup> θ – 2 cosec<sup>2</sup> θ + cosec<sup>4</sup> θ = cot<sup>4</sup> θ – tan<sup>4</sup> θ.",
        "ans": "R.H.S. = cot<sup>4</sup> θ – tan<sup>4</sup> θ <br/> = (cot<sup>2</sup> θ)<sup>2</sup> – (tan<sup>2</sup> θ)<sup>2</sup> <br/> = (cot<sup>2</sup> θ – tan<sup>2</sup> θ) (cot<sup>2</sup> θ + tan<sup>2</sup> θ) <br/> = [cosec<sup>2</sup> θ – 1) – (sec<sup>2</sup> θ – 1)] [cosec<sup>2</sup> θ – 1) + (sec<sup>2</sup> θ – 1)] <br/> = (cosec<sup>2</sup> θ – sec<sup>2</sup> θ) (cosec<sup>2</sup> θ + sec<sup>2</sup> θ – 2) <br/> = (cosec<sup>2</sup> θ – sec<sup>2</sup> θ) (cosec<sup>2</sup> θ + sec<sup>2</sup> θ) – 2 (cosec<sup>2</sup> θ – sec<sup>2</sup> θ) <br/> = (cosec<sup>4</sup> θ – sec<sup>4</sup> θ) – 2cosec<sup>2</sup> θ + 2sec<sup>2</sup> θ <br/> = cosec<sup>4</sup> θ – sec<sup>4</sup> θ – 2cosec<sup>2</sup> θ + 2sec<sup>2</sup> θ <br/> = 2sec<sup>2</sup> θ – sec<sup>4</sup> θ – 2cosec<sup>2</sup> θ + cosec<sup>4</sup> θ <br/> = L.H.S.",
        "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": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 10,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a79.jpg",
          "width": "272",
          "height": "44"
        },
        "ansimg": {
          "image": "ch8a80.jpg",
          "width": "579",
          "height": "348"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that sec<sup>2</sup> θ – cos<sup>2</sup> θ = sin<sup>2</sup> θ (sec<sup>2</sup> θ + 1).",
        "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": "ch8a81.jpg",
          "width": "191",
          "height": "342"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 12,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a82.jpg",
          "width": "214",
          "height": "43"
        },
        "ansimg": {
          "image": "ch8a83.jpg",
          "width": "168",
          "height": "273"
        }
      },
	   {
        "heading": "Answer the following questions in short.",
        "qus": "Prove the following identity: <br/> (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) = 1",
        "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": "ch8a84.jpg",
          "width": "315",
          "height": "208"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 14,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a85.jpg",
          "width": "333",
          "height": "35"
        },
        "ansimg": {
          "image": "ch8a86.jpg",
          "width": "333",
          "height": "448"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 15,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a87.jpg",
          "width": "295",
          "height": "38"
        },
        "ansimg": {
          "image": "ch8a88.jpg",
          "width": "345",
          "height": "198"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 16,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a89.jpg",
          "width": "297",
          "height": "42"
        },
        "ansimg": {
          "image": "ch8a90.jpg",
          "width": "226",
          "height": "445"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 17,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch8a91.jpg",
          "width": "246",
          "height": "39"
        },
        "ansimg": {
          "image": "ch8a92.jpg",
          "width": "265",
          "height": "454"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If cot θ + tan θ = x and sec θ – cos θ = y. Prove that <br/> (x<sup>2</sup> y)<sup>2/3</sup> – (xy<sup>2</sup>)<sup>2/3</sup> = 1.",
        "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": "ch8a99.jpg",
          "width": "350",
          "height": "900"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If x sin<sup>3</sup> θ + y cos<sup>3</sup> θ = sin θ cos θ and x sin θ = y cos θ, prove that x<sup>2</sup> + y<sup>2</sup> = 1.",
        "ans": "x sin<sup>3</sup> θ + y cos<sup>3</sup> θ = sin θ cos θ <br/> ⇒ x sin<sup>3</sup> θ + cos<sup>2</sup> θ (y cos θ) = sin θ cos θ <br/> ⇒ x sin<sup>3</sup> θ + cos<sup>2</sup> θ (x sin θ) = sin θ cos θ [Given that y cos θ = x sin θ] <br/> ⇒ x sin θ (sin<sup>2</sup> θ + cos<sup>2</sup> θ) = sin θ cos θ <br/> ⇒ x sin θ (1) = sin θ cos θ <br/> ⇒ x = cos θ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ...(1) <br/> By putting x cos θ in x sin θ = y cos θ, we get <br/> cos θ sin θ = y cos θ <br/> ⇒ y = sin θ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ...(2) <br/> Adding (1) and (2), we get <br/> x<sup>2</sup> + y<sup>2</sup> = 1 ( sin<sup>2</sup> θ + cos<sup>2</sup> θ = 1)",
        "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": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 20,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
           "image": "ch8a93.jpg",
          "width": "496",
          "height": "33"
        },
        "ansimg": {
          "image": "ch8a94.jpg",
          "width": "473",
          "height": "676"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 21,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
           "image": "ch8a95.jpg",
          "width": "361",
          "height": "65"
        },
        "ansimg": {
          "image": "ch8a96.jpg",
          "width": "475",
          "height": "347"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 22,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
           "image": "ch8a97.jpg",
          "width": "245",
          "height": "38"
        },
        "ansimg": {
          "image": "ch8a98.jpg",
          "width": "290",
          "height": "321"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a7.jpg",
          "width": "288",
          "height": "29"
        },
        "ansimg": {
          "image": "ch8a8.jpg",
          "width": "197",
          "height": "271"
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a9.jpg",
          "width": "330",
          "height": "34"
        },
        "ansimg": {
          "image": "ch8a10.jpg",
          "width": "290",
          "height": "301"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a11.jpg",
          "width": "468",
          "height": "45"
        },
        "ansimg": {
          "image": "ch8a12.jpg",
          "width": "376",
          "height": "581"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In a right ΔABC, right-angled at B, if 15 cot A = 8, then find sin A and sec A.",
        "ans": "centimetres",
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": null,
          "width": null,
          "height": null
        },
        "ansimg": {
          "image": "ch8a13.jpg",
          "width": "311",
          "height": "333"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a21.jpg",
          "width": "197",
          "height": "40"
        },
        "ansimg": {
          "image": "ch8a22.jpg",
          "width": "329",
          "height": "151"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "What is the value of (cos<sup>2</sup> 67º – sin2 23º)?",
        "ans": "67° + 23° = 90° <br/> ∴ cos<sup>2</sup> 67° – sin<sup>2</sup> 23° = cos<sup>2</sup> (90° – 23°) – sin<sup>2</sup> 23° <br/> = sin<sup>2</sup> 23° – sin2 23° <br/> = 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": "Find the value of tan<sup>2</sup> 10º – cot<sup>2</sup> 80º.",
        "ans": "tan<sup>2</sup> 10° – cot<sup>2</sup> 80° = tan<sup>2</sup> (90° – 80°) – cot<sup>2</sup> 80° <br/> = cot<sup>2</sup> 80° – cot<sup>2</sup> 80° <br/> = 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": "If tan x = sin 45º cos 45º + sin 30º, then find the value of x.",
        "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": "ch8a23.jpg",
          "width": "249",
          "height": "209"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Without using trigonometric tables, find the value of the following expression:",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a24.jpg",
          "width": "361",
          "height": "38"
        },
        "ansimg": {
          "image": "ch8a25.jpg",
          "width": "360",
          "height": "274"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Express cosec 48º + tan 88º in terms of T-ratios of angles between 0º and 45º. <br/> ",
        "ans": "cosec 48º = cosec (90° – 42º) = sec 42° (∵ cosec (90° – θ) = sec θ) <br/> tan 88º = tan (90° – 2º) = cot 2° (∵ tan (90° – θ) = cot θ) <br/> ∴ cosec 48º + tan 88° = sec 42º + cot 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": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If tan A = cot (A + 10º), then find A.",
        "ans": "tan A = cot (A + 10°) <br/> ⇒ cot (90º – A) = cot (A + 10°) <br/> ⇒ 90º – A = A + 10° <br/> ⇒ 2A = 80° <br/> ⇒ A = 40°",
        "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": "If A and B are acute angles and sin A = cos B, then find the value of A + B.",
        "ans": "Given that A and B are acute angles. <br/> sin A = cos B = sin (90° – B) <br/> ⇒ A = 90º – B <br/> ⇒ A + B = 90º",
        "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": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a38.jpg",
          "width": "430",
          "height": "34"
        },
        "ansimg": {
          "image": "ch8a39.jpg",
          "width": "331",
          "height": "259"
        },
        "val": 13
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If x = 3 sec<sup>2</sup> θ – 1 and y = 3 tan<sup>2</sup>θ –2 , then find (x – y).",
        "ans": "x – y = (3 sec<sup>2</sup>θ – 1) – (3 tan<sup>2</sup>θ – 2) <br/> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 3 sec<sup>2</sup>θ – 3 tan<sup>2</sup>θ – 1 + 2 <br/> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 3 (sec<sup>2</sup>θ – tan<sup>2</sup>θ) + 1 <br/> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 3 (1) + 1 <br/> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 3 + 1 <br/> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 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": 14
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a63.jpg",
          "width": "235",
          "height": "65"
        },
        "ansimg": {
          "image": "ch8a64.jpg",
          "width": "285",
          "height": "194"
        },
        "val": 15
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a65.jpg",
          "width": "337",
          "height": "39"
        },
        "ansimg": {
          "image": "ch8a66.jpg",
          "width": "289",
          "height": "410"
        },
        "val": 16
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a67.jpg",
          "width": "324",
          "height": "34"
        },
        "ansimg": {
          "image": "ch8a68.jpg",
          "width": "198",
          "height": "157"
        },
        "val": 17
      },
	  	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a69.jpg",
          "width": "222",
          "height": "37"
        },
        "ansimg": {
          "image": "ch8a70.jpg",
          "width": "253",
          "height": "302"
        },
        "val": 18
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a71.jpg",
          "width": "375",
          "height": "40"
        },
        "ansimg": {
          "image": "ch8a72.jpg",
          "width": "333",
          "height": "555"
        },
        "val": 19
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the value of cosec 30° geometrically.",
        "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": "ch8a73.jpg",
          "width": "370",
          "height": "468"
        },
        "val": 20
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If x = a cos θ – b sin θ and y = a sin θ + b cos θ, then prove that a<sup>2</sup> + b<sup>2</sup> = x<sup>2</sup> + y<sup>2</sup>.",
        "ans": "x<sup>2</sup> = a<sup>2</sup>cos<sup>2</sup> θ + b<sup>2</sup>sin<sup>2</sup> θ – 2ab sin θ cos θ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ...(1) <br/> y<sup>2</sup> = a<sup>2</sup>sin<sup>2</sup> θ + b<sup>2</sup>cos<sup>2</sup> θ + 2ab sin θ cos θ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ...(2) <br/> Adding (1) and (2), we get <br/> x<sup>2</sup> + y<sup>2</sup> = a<sup>2</sup> (cos<sup>2</sup> θ + sin<sup>2</sup> θ) + b<sup>2</sup> (sin<sup>2</sup> θ + cos<sup>2</sup> θ) <br/>  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = a<sup>2</sup> (1) + b<sup>2</sup> (1) ( cos<sup>2</sup> θ + sin<sup>2</sup> θ = 1) <br/> ⇒  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  x<sup>2</sup> + y<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>",
        "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": 21
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Express sin A and cos A in terms of cot A.",
        "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": "ch8a74.jpg",
          "width": "346",
          "height": "307"
        },
        "val": 22
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch8a75.jpg",
          "width": "379",
          "height": "37"
        },
        "ansimg": {
           "image": "ch8a76.jpg",
          "width": "302",
          "height": "347"
        },
        "val": 23
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Prove that sec<sup>4</sup> θ – sec<sup>2</sup> θ = tan<sup>4</sup> θ + tan<sup>2</sup> θ.",
        "ans": "L.H.S. = sec<sup>4</sup> θ – sec<sup>2</sup> θ <br/>  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (sec<sup>2</sup> θ)<sup>2</sup> – (1 + tan<sup>2</sup> θ) <br/>  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (1 + tan<sup>2</sup> θ)<sup>2</sup> – 1 – tan<sup>2</sup> θ <br/>  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 1 + tan<sup>4</sup> θ + 2 tan<sup>2</sup> θ – 1 – tan<sup>2</sup> θ <br/>  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = tan<sup>4</sup> θ + tan<sup>2</sup> θ",
        "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": 24
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "If tan A + cot A = 2, then find the value of tan<sup>2</sup> A + cot<sup>2</sup> A.",
        "ans": "Given that tan A + cot A = 2 <br/> Squaring both sides, we get <br/>   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (tan A + cot A)<sup>2</sup> = (2)<sup>2</sup> <br/>⇒ &nbsp;&nbsp;&nbsp;&nbsp; tan<sup>2</sup>A + cot<sup>2</sup>A + 2 tan A cot A = 4 <br/>⇒ &nbsp;&nbsp;&nbsp;&nbsp; tan<sup>2</sup>A + cot<sup>2</sup>A + 2 × 1 = 4 <br/>⇒ &nbsp;&nbsp;&nbsp;&nbsp; tan<sup>2</sup>A + cot<sup>2</sup>A = 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": 25
      } 
	],
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  "mcq": "ch8_mcq",
  "co": "ch8_co",
  "nf": "ch8_nf",
  "saq": "ch8_saq",
  "fib": "ch8_fib",
  "vsaq": "ch8_vsaq",
  "tf": "ch8_tf",
  "mtf": "ch8_mtf",
  "laq": "ch8_laq",
  "jtf": "ch8_jtf",
  "ctt": "ch8_ctt",
  "snc": "ch8_snc",
  "grade": "Grade 10",
  "gowf": "ch8_gowf",
  "afow": "ch8_afow",
  "cs": "ch8_cs",
  "ctco": "ch8_ctco",
  "map": "ch8_map",
  "dtf": "ch8_dtf",
  "grf": "ch8_grf",
  "afq": "ch8_afq",
  "pbq": "ch8_pbq",
  "yn": "ch8_yn",
  "un": "ch8_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch9",
  "chapterName": "Chapter 9 - Some Applications of Trigonometry",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "A tower stands vertically on the ground. From a point on the ground which is 25 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45°. Then the height (in metres) of the tower is",
				"ans": "(c) 25",
				"code": "MCQ",
				"options": [
					"(a) 25√2",
					"(b) 25√3",
					"(c) 25",
					"(d) 12.5"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A kite is flying at a height of 30 m from the ground. The length of string from the kite to the ground is 60 m. Assuming that there is no slack in the string, the angle of elevation of the kite at the ground is",
				"ans": "(b) 30°",
				"code": "MCQ",
				"options": [
					"(a) 45°",
					"(b) 30°",
					"(c) 60°",
					"(d) 90°"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The length of shadow of a tower on the plane ground is 3 times the height of the tower. The angle of elevation of the sun is",
				"ans": "(b) 30°",
				"code": "MCQ",
				"options": [
					"(a) 45°",
					"(b) 30°",
					"(c) 60°",
					"(d) 90°"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The angle of depression of a car, standing on the ground, from the top of a 75 m high tower is 30°. The distance of the car from the base of the tower (in m) is",
				"ans": "(c) 75√3",
				"code": "MCQ",
				"options": [
					"(a) 25√3",
					"(b) 50√3",
					"(c) 75√3",
					"(d) 150"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A ladder makes an angle of 60° with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is",
				"ans": "(d) 4",
				"code": "MCQ",
				"options": [
					"ch9a1.jpg",
					"(b) 4√3",
					"(c) 2√2",
					"(d) 4"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The length of string between a kite and a point on the ground is 90 m. If the string makes an angle θ with level ground such that tan θ = 15/8. Assuming that there is no slack in the string, height of the kite is",
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": "ch9a4.jpg",
				"width": "65",
				"height": "33"
				},
				"options": [
					"ch9a2.jpg",
					"ch9a3.jpg",
					"ch9a4.jpg",
					"ch9a5.jpg"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the ratio of length of a pole to its height is √3 : 1, then elevation of the sun is",
				"ans": "(c) 60°",
				"code": "MCQ",
				"pic": {
				"image": null,
				"width": null,
				"height": null
				},
				"ansimg": {
				"image": null,
				"width": null,
				"height": null
				},
				"options": [
					"(a) 30°",
					"(b) 45°",
					"(c) 60°",
					"(d) 75°"
				],
				"val": 7
			}
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 15 seconds, the angle of deviation changes to 30°. If the jet plane is flying at a constant height of 1500 3 m, find the speed of the jet 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": "ch9a15.jpg",
          "width": "550",
          "height": "588"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.",
        "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": "ch9a16.jpg",
          "width": "394",
          "height": "572"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of boat in m/hr.",
        "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": "ch9a17.jpg",
          "width": "500",
          "height": "513"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Find the distance of the hill from the ship and the height of the hill.",
        "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": "ch9a18.jpg",
          "width": "504",
          "height": "591"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. (Use √3 = 1.73)",
        "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": "ch9a19.jpg",
          "width": "525",
          "height": "587"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The angles of elevation and depression of the top and the bottom of a tower from the top of a building 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them.",
        "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": "ch9a20.jpg",
          "width": "411",
          "height": "482"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is 30°. Find the height of the tower.",
        "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": "ch9a21.jpg",
          "width": "416",
          "height": "563"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point 10 m vertically above the first, its angle of elevation is 30°. Find the height of the tower.",
        "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": "ch9a22.jpg",
          "width": "520",
          "height": "503"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are 30° and 60° respectively. Find <br/> (i) the difference between the heights of the lighthouse and the building. <br/> (ii) the distance between the lighthouse and the building.",
        "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": "ch9a23.jpg",
          "width": "470",
          "height": "441"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower to the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.",
        "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": "ch9a24.jpg",
          "width": "455",
          "height": "492"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake at A is 60°. Find the distance of the cloud from A.",
        "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": "ch9a25.jpg",
          "width": "525",
          "height": "550"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "From a point P on the ground, the angle of elevation of the top of a tower is 30° and that of top of a flag staff fixed on the top of the tower is 60°. If the length of the flag staff is 5 m, find the height of the tower.",
        "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": "ch9a26.jpg",
          "width": "579",
          "height": "459"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45°. Find the height of the tower PQ and the distance PX. (Use √3 = 1.73)",
        "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": "ch9a27.jpg",
          "width": "416",
          "height": "585"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 30° respectively. Find the width of the river. (Use √3 = 1.732)",
        "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": "ch9a28.jpg",
          "width": "487",
          "height": "497"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A bird is sitting on the top of 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Find the speed of flying of the bird. (Take √3 = 1.732)",
        "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": "ch9a29.jpg",
          "width": "476",
          "height": "442"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of there points from the top of the tower are 60° and 45° respectively. If the height of the tower is 15 m, then find the distance between these points.",
        "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": "ch9a30.jpg",
          "width": "426",
          "height": "408"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "An observer finds the angle of elevation of the top of the tower from a certain point on the ground as 30°. If the observer moves 20 m towards the base of the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.",
        "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": "ch9a31.jpg",
          "width": "563",
          "height": "657"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "In the figure, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the ladder. (Use √3 = 1.73)",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch9a6.jpg",
          "width": "232",
          "height": "237"
        },
        "ansimg": {
          "image": "ch9a7.jpg",
          "width": "229",
          "height": "338"
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.",
        "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": "ch9a8.jpg",
          "width": "313",
          "height": "208"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "From the top of a vertical tower, the angles of depression of two cars, in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower. (Use √3 = 1.73)",
        "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": "ch9a9.jpg",
          "width": "326",
          "height": "511"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the cars. (Use √3 = 1.73)",
        "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": "ch9a10.jpg",
          "width": "488",
          "height": "546"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The angles of depression of the top and bottom of a tower as seen from the top of a 60√3 high cliff are 45° and 60° respectively. Find the height of the tower.",
        "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": "ch9a11.jpg",
          "width": "458",
          "height": "675"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The angles of depression of two ships from the top of a lighthouse and on the same side of it are found to be 45° and 30°. If the ships are 200 m apart, find the height of the lighthouse.",
        "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": "ch9a12.jpg",
          "width": "583",
          "height": "741"
        },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The horizontal distance between two poles is 15 m. The angles of depression of the top of first pole as seen from the top of second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. (Use √3 = 1.732)",
        "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": "ch9a13.jpg",
          "width": "390",
          "height": "393"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Two ships are there in the sea on either side of a lighthouse in such a way that the ships and the lighthouse are in the same straight line. The angles of depression of two ships as observed from the top of the lighthouse are 60° and 45°. If the height of the lighthouse is 200 m, find the distance between the two ships. (Use √3 = 1.732)",
        "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": "ch9a14.jpg",
          "width": "429",
          "height": "493"
        },
        "val": 8
      }	  
	],
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  "mcq": "ch9_mcq",
  "co": "ch9_co",
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  "grade": "Grade 10",
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},

{
  "subject": "Mathematics",
  "chapter": "ch10",
  "chapterName": "Chapter 10 - Circles",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 17",
				"code": "MCQ",
				"pic": {
				"image": "ch10a1.jpg",
				"width": "546",
				"height": "24"
				},
				"options": [
					"(a) 17",
					"(b) 13",
					"(c) 23",	
					"(d) 7"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A tangent from P, a point in the exterior of a circle, touches the circle at Q. If OP = 13, PQ = 5, then the diameter of the circle is ________.",
				"ans": "(d) 24",
				"code": "MCQ",
				"options": [
					"(a) 576",
					"(b) 15",
					"(c) 8",	
					"(d) 24"
				],
				
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 8",
				"code": "MCQ",
				"pic": {
				"image": "ch10a2.jpg",
				"width": "451",
				"height": "27"
				},
				"options": [
					"(a) 8",
					"(b) 10",
					"(c) 7",	
					"(d) 6"	
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 5",
				"code": "MCQ",
				"pic": {
				"image": "ch10a3.jpg",
				"width": "525",
				"height": "137"
				},
				"options": [
					"(a) 11",
					"(b) 10",
					"(c) 14",	
					"(d) 15"	
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 4 cm",
				"code": "MCQ",
				"pic": {
				"image": "ch10a4.jpg",
				"width": "525",
				"height": "137"
				},
				"options": [
					"(a) 3 cm",
					"(b) 4 cm",
					"(c) 5 cm",	
					"(d) 6 cm"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 7.5",
				"code": "MCQ",
				"pic": {
				"image": "ch10a5.jpg",
				"width": "581",
				"height": "193"
				},
				"options": [
					"(a) 7.5",
					"(b) 15",
					"(c) 10",	
					"(d) 9"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is _________ .",
				"ans": "(b) 6 cm",
				"code": "MCQ",
				"options": [
					"(a) 3 cm",
					"(b) 6 cm",
					"(c) 9 cm",	
					"(d) 1 cm"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 50",
				"code": "MCQ",
				"pic": {
				"image": "ch10a17.jpg",
				"width": "465",
				"height": "28"
				},
				"options": [
					"(a) 80",
					"(b) 50",
					"(c) 10",	
					"(d) 100"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In ΔABC, AB = 3, BC = 4, AC = 5, then the radius of the circle touching all the three sides is _________ .",
				"ans": "(b) 1",
				"code": "MCQ",
				"options": [
					"(a) 2",
					"(b) 1",
					"(c) 4",	
					"(d) 3"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 5",
				"code": "MCQ",
				"pic": {
				"image": "ch10a18.jpg",
				"width": "575",
				"height": "57"
				},
				"options": [
					"(a) 5",
					"(b) 20",
					"(c) 60",	
					"(d) 10"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The points of contact of the tangent from an exterior point P to the circle with centre O are A and B. If m ∠OPB = 30°, then m ∠AOB = _________ .",
				"ans": "(d) 120°",
				"code": "MCQ",
				"options": [
					"(a) 30°",
					"(b) 60°",
					"(c) 90°",	
					"(d) 120°"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) 120°",
				"code": "MCQ",
				"pic": {
				"image": "ch10a19.jpg",
				"width": "576",
				"height": "158"
				},
				"ansimg": {
				"image": "ch10a20.jpg",
				"width": "54",
				"height": "35"
				},
				"options": [
					"ch10a20.jpg",
					"ch10a21.jpg",
					"ch10a22.jpg",	
					"ch10a23.jpg"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 55°",
				"code": "MCQ",
				"pic": {
				"image": "ch10a24.jpg",
				"width": "585",
				"height": "165"
				},
				"options": [
					"(a) 55°",
					"(b) 70°",
					"(c) 45°",	
					"(d) 35°"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 30º",
				"code": "MCQ",
				"pic": {
				"image": "ch10a25.jpg",
				"width": "550",
				"height": "30"
				},
				"options": [
					"(a) 30º",
					"(b) 60º",
					"(c) 90º",	
					"(d) 15º"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In the figure, a circle with centre O is inscribed in a quadrilateral ABCD such that it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90º and DS = 5 cm, then the radius of the circle is _______ cm.",
				"ans": "(a) 11",
				"code": "MCQ",
				"pic": {
				"image": "ch10a26.jpg",
				"width": "147",
				"height": "132"
				},
				"options": [
					"(a) 11",
					"(b) 18",
					"(c) 6",	
					"(d) 15"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) 90º",
				"code": "MCQ",
				"pic": {
				"image": "ch10a27.jpg",
				"width": "574",
				"height": "55"
				},
				"options": [
					"(a) 30º",
					"(b) 45º",
					"(c) 60º",	
					"(d) 90º"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 5√2",
				"code": "MCQ",
				"pic": {
				"image": "ch10a28.jpg",
				"width": "552",
				"height": "142"
				},
				"options": [
					"(a) 5√2",
					"(b) 10√2",
					"ch10a29.jpg",	
					"(d) 10"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) 50º",
				"code": "MCQ",
				"pic": {
				"image": "ch10a30.jpg",
				"width": "583",
				"height": "198"
				},
				"options": [
					"(a) 65º",
					"(b) 60º",
					"(c) 50º",	
					"(d) 40º"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) 6",
				"code": "MCQ",
				"pic": {
				"image": "ch10a31.jpg",
				"width": "572",
				"height": "50"
				},
				"options": [
					"(a) 4",
					"(b) 5",
					"(c) 6",	
					"(d) 8"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 60",
				"code": "MCQ",
				"pic": {
				"image": "ch10a32.jpg",
				"width": "575",
				"height": "180"
				},
				"options": [
					"(a) 60",
					"(b) 65",
					"(c) 30",	
					"(d) 32.5"
				],
				"val": 20
			}	
	],
    [],
    [],
    [],
    [],
    [],
    [
	{
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 1,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch10a51.jpg",
          "width": "586",
          "height": "367"
        },
        "ansimg": {
          "image": "ch10a52.jpg",
          "width": "300",
          "height": "886"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.",
        "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": "ch10a53.jpg",
          "width": "571",
          "height": "697"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "In the figure, a circle is inscribed in a ΔPQR with PQ = 10 cm, QR = 8 cm and PR = 12 cm. Find lengths of QM, RN and PL.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 3,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch10a54.jpg",
          "width": "293",
          "height": "279"
        },
        "ansimg": {
         "image": "ch10a55.jpg",
          "width": "375",
          "height": "606"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that the parallelogram circumscribing a circle is a rhombus.",
        "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": "ch10a56.jpg",
          "width": "571",
          "height": "393"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that the lengths of tangents drawn from an external point to a circle are equal.",
        "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": "ch10a57.jpg",
          "width": "442",
          "height": "423"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.",
        "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": "ch10a58.jpg",
          "width": "586",
          "height": "495"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 7,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch10a59.jpg",
          "width": "591",
          "height": "188"
        },
        "ansimg": {
          "image": "ch10a60.jpg",
          "width": "478",
          "height": "735"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Prove that the tangents drawn at midpoint of an arc of a circle is parallel to the chord joining the end points of the arc.",
        "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": "ch10a61.jpg",
          "width": "583",
          "height": "525"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 9,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch10a62.jpg",
          "width": "576",
          "height": "204"
        },
        "ansimg": {
          "image": "ch10a63.jpg",
          "width": "275",
          "height": "278"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 10,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch10a64.jpg",
          "width": "586",
          "height": "212"
        },
        "ansimg": {
          "image": "ch10a65.jpg",
          "width": "341",
          "height": "498"
        }
      }
	],
    [
	{
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a6.jpg",
          "width": "531",
          "height": "184"
        },
        "ansimg": {
          "image": "ch10a7.jpg",
          "width": "527",
          "height": "437"
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a8.jpg",
          "width": "583",
          "height": "160"
        },
        "ansimg": {
          "image": "ch10a9.jpg",
          "width": "346",
          "height": "341"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a10.jpg",
          "width": "578",
          "height": "209"
        },
        "ansimg": {
          "image": "ch10a11.jpg",
          "width": "463",
          "height": "522"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Two concentric circles are of radii 7 cm and r cm respectively, where r >7. A chord of the larger circle of length 48 cm touches the smaller circle. Find the value of r.",
        "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": "ch10a12.jpg",
          "width": "472",
          "height": "471"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a13.jpg",
          "width": "578",
          "height": "207"
        },
        "ansimg": {
          "image": "ch10a14.jpg",
          "width": "322",
          "height": "636"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a15.jpg",
          "width": "579",
          "height": "347"
        },
        "ansimg": {
          "image": "ch10a16.jpg",
          "width": "575",
          "height": "447"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a33.jpg",
          "width": "577",
          "height": "191"
        },
        "ansimg": {
          "image": "ch10a34.jpg",
          "width": "434",
          "height": "231"
        },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a35.jpg",
          "width": "577",
          "height": "53"
        },
        "ansimg": {
          "image": "ch10a36.jpg",
          "width": "450",
          "height": "445"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a37.jpg",
          "width": "579",
          "height": "192"
        },
        "ansimg": {
          "image": "ch10a38.jpg",
          "width": "419",
          "height": "160"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a39.jpg",
          "width": "575",
          "height": "223"
        },
        "ansimg": {
          "image": "ch10a40.jpg",
          "width": "565",
          "height": "620"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a41.jpg",
          "width": "573",
          "height": "234"
        },
        "ansimg": {
          "image": "ch10a42.jpg",
          "width": "575",
          "height": "854"
        },
        "val": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a43.jpg",
          "width": "574",
          "height": "207"
        },
        "ansimg": {
          "image": "ch10a44.jpg",
          "width": "369",
          "height": "258"
        },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a45.jpg",
          "width": "574",
          "height": "172"
        },
        "ansimg": {
          "image": "ch10a46.jpg",
          "width": "427",
          "height": "257"
        },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a47.jpg",
          "width": "581",
          "height": "205"
        },
        "ansimg": {
          "image": "ch10a48.jpg",
          "width": "422",
          "height": "505"
        },
        "val": 12
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch10a49.jpg",
          "width": "578",
          "height": "185"
        },
        "ansimg": {
          "image": "ch10a50.jpg",
          "width": "265",
          "height": "430"
        },
        "val": 13
      } 
	],
    [],
    [],
    [],
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    [],
    [],
    [],
    [],
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    [],
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  "mcq": "ch10_mcq",
  "co": "ch10_co",
  "nf": "ch10_nf",
  "saq": "ch10_saq",
  "fib": "ch10_fib",
  "vsaq": "ch10_vsaq",
  "tf": "ch10_tf",
  "mtf": "ch10_mtf",
  "laq": "ch10_laq",
  "jtf": "ch10_jtf",
  "ctt": "ch10_ctt",
  "snc": "ch10_snc",
  "grade": "Grade 10",
  "gowf": "ch10_gowf",
  "afow": "ch10_afow",
  "cs": "ch10_cs",
  "ctco": "ch10_ctco",
  "map": "ch10_map",
  "dtf": "ch10_dtf",
  "grf": "ch10_grf",
  "afq": "ch10_afq",
  "pbq": "ch10_pbq",
  "yn": "ch10_yn",
  "un": "ch10_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch11",
  "chapterName": "Chapter 11 - Constructions",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) 12",
				"code": "MCQ",
				"pic": {
				"image": "ch11a1.jpg",
				"width": "572",
				"height": "49"
				},
				"options": [
					"(a) 8",
					"(b) 10",
					"(c) 11",	
					"(d) 12"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) A<sub>9</sub>",
				"code": "MCQ",
				"pic": {
				"image": "ch11a2.jpg",
				"width": "570",
				"height": "54"
				},
				"options": [
					"(a) A<sub>12</sub>",
					"(b) A<sub>11</sub>",
					"(c) A<sub>12</sub>",	
					"(d) A<sub>9</sub>"
				],
				
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) A<sub>5</sub>, and B<sub>6</sub>",
				"code": "MCQ",
				"pic": {
				"image": "ch11a3.jpg",
				"width": "578",
				"height": "51"
				},
				"options": [
					"(a) A<sub>5</sub>, and B<sub>6</sub>",
					"(b) A<sub>6</sub> and B<sub>5</sub>",
					"(c) A<sub>4</sub>, and B<sub>5</sub>",	
					"(d) A<sub>5</sub> and B<sub>4</sub>"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) B<sub>7</sub> to C",
				"code": "MCQ",
				"pic": {
				"image": "ch11a4.jpg",
				"width": "572",
				"height": "80"
				},
				"options": [
					"(a) B<sub>1</sub> to C",
					"(b) B to C",
					"(c) B<sub>7</sub> to C",	
					"(d) B<sub>4</sub> to C"	
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 6",
				"code": "MCQ",
				"pic": {
				"image": "ch11a5.jpg",
				"width": "576",
				"height": "86"
				},
				"options": [
					"(a) 5",
					"(b) 6",
					"(c) 13",	
					"(d) 3"		
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be",
				"ans": "(d) 120°",
				"code": "MCQ",
				"options": [
					"(a) 135°",
					"(b) 90°",
					"(c) 60°",	
					"(d) 120°"		
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is not a step in the construction of tangent from an external point P to a circle of centre O?",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch11a26.jpg",
				"width": "294",
				"height": "34"
				},
				"options": [
					"ch11a24.jpg",
					"ch11a25.jpg",
					"(c) With M as centre and radius equal to MP, draw a circle intersecting given circle at T<sub>1</sub> and T<sub>2</sub>.",	
					"ch11a26.jpg"		
				],
				"val": 7
			}		
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 1,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a9.jpg",
          "width": "577",
          "height": "53"
        },
        "ansimg": {
          "image": "ch11a10.jpg",
          "width": "509",
          "height": "552"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 2,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a11.jpg",
          "width": "578",
          "height": "64"
        },
        "ansimg": {
          "image": "ch11a12.jpg",
          "width": "549",
          "height": "692"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 3,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a13.jpg",
          "width": "577",
          "height": "58"
        },
        "ansimg": {
          "image": "ch11a14.jpg",
          "width": "572",
          "height": "617"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 4,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a15.jpg",
          "width": "576",
          "height": "58"
        },
        "ansimg": {
          "image": "ch11a16.jpg",
          "width": "540",
          "height": "639"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a17.jpg",
          "width": "572",
          "height": "55"
        },
        "ansimg": {
          "image": "ch11a18.jpg",
          "width": "520",
          "height": "735"
        }
      },
	   {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a19.jpg",
          "width": "582",
          "height": "56"
        },
        "ansimg": {
          "image": "ch11a20.jpg",
          "width": "563",
          "height": "619"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Construct a ΔABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°. Construct another ΔAB′C′ similar to ΔABC with base AB' = 8 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": "ch11a21.jpg",
          "width": "571",
          "height": "705"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 8,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a22.jpg",
          "width": "575",
          "height": "56"
        },
        "ansimg": {
          "image": "ch11a23.jpg",
          "width": "585",
          "height": "404"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Draw a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.",
        "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": "ch11a27.jpg",
          "width": "584",
          "height": "712"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Construct a tangent of a circle of radius 4 cm from a point on the concentric circle of radius 6 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": "ch11a28.jpg",
          "width": "553",
          "height": "501"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also, measure its length.",
        "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": "ch11a29.jpg",
          "width": "483",
          "height": "465"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 12,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch11a30.jpg",
          "width": "572",
          "height": "52"
        },
        "ansimg": {
          "image": "ch11a31.jpg",
          "width": "567",
          "height": "645"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "Draw a line segment of length 6 cm. Using compass and ruler, find a point P on it which divides it in the ratio 3:4.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch11a6.jpg",
          "width": "584",
          "height": "423"
        },
        "ansimg": {
          "image": null,
          "width": null,
          "height": null
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch11a7.jpg",
          "width": "570",
          "height": "35"
        },
        "ansimg": {
          "image": "ch11a8.jpg",
          "width": "193",
          "height": "402"
        },
        "val": 2
      }
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch11_mcq",
  "co": "ch11_co",
  "nf": "ch11_nf",
  "saq": "ch11_saq",
  "fib": "ch11_fib",
  "vsaq": "ch11_vsaq",
  "tf": "ch11_tf",
  "mtf": "ch11_mtf",
  "laq": "ch11_laq",
  "jtf": "ch11_jtf",
  "ctt": "ch11_ctt",
  "snc": "ch11_snc",
  "grade": "Grade 10",
  "gowf": "ch11_gowf",
  "afow": "ch11_afow",
  "cs": "ch11_cs",
  "ctco": "ch11_ctco",
  "map": "ch11_map",
  "dtf": "ch11_dtf",
  "grf": "ch11_grf",
  "afq": "ch11_afq",
  "pbq": "ch11_pbq",
  "yn": "ch11_yn",
  "un": "ch11_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch12",
  "chapterName": "Chapter 12 - Areas Related to Circles",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the area and the circumference of a circle are numerically equal, then r = _______________.",
				"ans": "(d) 2",
				"code": "MCQ",
				"options": [
					"(a) π",
					"ch12a1.jpg",
					"(c) 1",	
					"(d) 2"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the radius of a circle is increased by 10%, then corresponding increase in the area of the circle is . (π = 3.14)",
				"ans": "(c) 21%",
				"code": "MCQ",
				"options": [
					"(a) 9%",
					"(b) 10%",
					"(c) 21%",	
					"(d) 20%"
				],
				
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the ratio of the area of two circles is 1 : 4, then the ratio of their circumference is ______________.",
				"ans": "(b) 1 : 2",
				"code": "MCQ",
				"options": [
					"(a) 1 : 4",
					"(b) 1 : 2",
					"(c) 4 : 1",	
					"(d) 2 : 1"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The cost of fencing a circular field at the rate of ₹24 per metre is ₹5280. The field is to be ploughed at the rate of ₹0.50 per m². Find the cost of ploughing field.",
				"ans": "(a) ₹1925",
				"code": "MCQ",
				"options": [
					"(a) ₹1925",
					"(b) ₹2100",
					"(c) ₹2560",	
					"(d) ₹2810"	
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The perimeter (in cm) of a square circumscribing a circle of radius a cm is",
				"ans": "(a) 8a",
				"code": "MCQ",
				"options": [
					"(a) 8a",
					"(b) 4a",
					"(c) 2a",	
					"(d) 16a"		
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The radii of two circles are 4 cm and 3 cm respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm) is ____________.",
				"ans": "(c) 10",
				"code": "MCQ",
				"options": [
					"(a) 5",
					"(b) 7",
					"(c) 10",	
					"(d) 14"		
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The radius of the circle whose perimeter and area are numerically equal is _____________.",
				"ans": "(b) 2",
				"code": "MCQ",
				"options": [
					"(a) 1",
					"(b) 2",
					"(c) 4",	
					"ch12a2.jpg"		
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The radius of the circle whose perimeter and area are numerically equal is _____________.",
				"ans": "(b) 44 cm",
				"code": "MCQ",
				"pic": {
				"image": "ch12a3.jpg",
				"width": "581",
				"height": "47"
				},
				"options": [
					"(a) 154 cm",
					"(b) 44 cm",
					"(c) 14 cm",	
					"(d) 7 cm"		
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the sum of the areas of two circles with radii R1 and R2 is equal to the area of circle with radius R<sub>1</sub> then :  _____________.",
				"ans": "(b) R<sub>1</sub><sup>2</sup> + R<sub>2</sub><sup>2</sup> = R<sup>2</sup>",
				"code": "MCQ",
				"options": [
					"(a) R<sub>1</sub> + R<sub>2</sub> = R",
					"(b) R<sub>1</sub><sup>2</sup> + R<sub>2</sub><sup>2</sup> = R<sup>2</sup>",
					"(c) R<sub>1</sub> + R<sub>2</sub> < R",	
					"(d) R<sub>1</sub><sup>2</sup> + R<sub>2</sub><sup>2</sup> < R<sup>2</sup>"		
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If an arc of a circle subtends an angle of measure θ at the centre, then the area of the minor sector is  _____________.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch12a13.jpg",
				"width": "63",
				"height": "39"
				},
				"options": [
					"ch12a10.jpg",
					"ch12a11.jpg",
					"ch12a12.jpg",	
					"ch12a13.jpg"		
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of the sector is given by the formula _____________.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch12a14.jpg",
				"width": "57",
				"height": "33"
				},
				"options": [
					"ch12a14.jpg",
					"ch12a15.jpg",
					"ch12a16.jpg",	
					"ch12a17.jpg"		
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 63.585",
				"code": "MCQ",
				"pic": {
				"image": "ch12a12a.jpg",
				"width": "650",
				"height": "56"
				},
				"options": [
					"(a) 63.575",
					"(b) 63.585",
					"(c) 63.595",	
					"(d) 63.60"	
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A sector subtends an angle of measure 120° at the centre of a circle having radius of 21 cm. The area of the sector is ___________ cm<sup>2</sup>.",
				"ans": "(a) 462",
				"code": "MCQ",
				"options": [
					"(a) 462",
					"(b) 460",
					"(c) 465",	
					"(d) 470"	
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The length of an arc subtending as angle of measure 60° at the centre of a circle whose area is 616 is ___________.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch12a19.jpg",
				"width": "56",
				"height": "33"
				},
				"options": [
					"ch12a18.jpg",
					"(b) 66",
					"ch12a19.jpg",	
					"(d) 33"	
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 20",
				"code": "MCQ",
				"pic": {
				"image": "ch12a20.jpg",
				"width": "520",
				"height": "22"
				},
				"options": [
					"(a) 30",
					"(b) 20",
					"(c) 90",	
					"(d) 15"	
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The length of minute hand of a clock is 14 cm. If the minute hand moves from 2 to 11 on the circular dial, then the area covered by it is ______________ cm<sup>2</sup>.",
				"ans": "(c) 462",
				"code": "MCQ",
				"options": [
					"(a) 154",
					"(b) 308",
					"(c) 462",	
					"(d) 616"	
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The length of minute hand of a clock is 15 cm. If the minute hand moves for 20 minutes on a circular dial of a clock, the area covered by it is  ______________ cm<sup>2</sup>.",
				"ans": "(a) 235.5",
				"code": "MCQ",
				"options": [
					"(a) 235.5",
					"(b) 471",
					"(c) 141.3",	
					"(d) 706.5"	
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector. (Use π = 3.14)",
				"ans": "(c) 4.19 cm<sup>2</sup>, 46.1 cm<sup>2</sup>",
				"code": "MCQ",
				"pic": {
				"image": "ch12a21.jpg",
				"width": "194",
				"height": "163"
				},
				"options": [
					"(a) 5.64 cm<sup>2</sup>, 51.1 cm<sup>2</sup>",
					"(b) 3.20 cm<sup>2</sup>, 38.2 cm<sup>2</sup>",
					"(c) 4.19 cm<sup>2</sup>, 46.1 cm<sup>2</sup>",	
					"(d) 4.35 cm<sup>2</sup>, 62.3 cm<sup>2</sup>"	
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the area of the segment AYB if radius of the circle is 21 cm and ∠AOB = 120°.",
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch12a22.jpg",
				"width": "156",
				"height": "165"
				},
				"ansimg": {
				"image": "ch12a23.jpg",
				"width": "132",
				"height": "35"
				},
				"options": [
					"(a) 5(11−20√5) cm<sup>2</sup>",
					"(b) 11(9−√7) cm<sup>2</sup>",
					"ch12a23.jpg",	
					"ch12a24.jpg"	
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A chord of a circle subtends a right angle at its centre. The length of the chord is _____________.",
				"ans": "(b) 10√2",
				"code": "MCQ",
				"options": [
					"(a) 5√2",
					"(b) 10√2",
					"ch12a25.jpg",	
					"(d) 10√3"	
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of the largest triangle inscribed in a semi-circle of radius 8 is ____________.",
				"ans": "(c) 64",
				"code": "MCQ",
				"options": [
					"(a) 8",
					"(b) 16",
					"(c) 64",	
					"(d) 256"	
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the circumference of a circle is 44 then the length of a side of a square inscribed in the circle is ___________.",
				"ans": "(b) 7√2",
				"code": "MCQ",
				"options": [
					"ch12a29.jpg",
					"(b) 7√2",
					"(c) 14√2",	
					"ch12a30.jpg"	
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In the given figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of lawn and flower beds.",
				"ans": "(a) 4032 m<sup>2</sup>",
				"code": "MCQ",
				"pic": {
				"image": "ch12a31.jpg",
				"width": "162",
				"height": "178"
				},
				"options": [
					"(a) 4032 m<sup>2</sup>",
					"(b) 5100 m<sup>2</sup>",
					"(c) 3920 m<sup>2</sup>",	
					"(d) 4189 m<sup>2</sup>"	
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the area of shaded region where ABCD is a square of side 14 cm.",
				"ans": "(d) 42 cm<sup>2</sup>",
				"code": "MCQ",
				"pic": {
				"image": "ch12a32.jpg",
				"width": "130",
				"height": "124"
				},
				"options": [
					"(a) 56 cm<sup>2</sup>",
					"(b) 49 cm<sup>2</sup>",
					"(c) 32 cm<sup>2</sup>",	
					"(d) 42 cm<sup>2</sup>"	
				],
				"val": 24
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the area of the shaded design where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as a diameter.",
				"ans": "(b) 57 cm<sup>2</sup>",
				"code": "MCQ",
				"pic": {
				"image": "ch12a33.jpg",
				"width": "193",
				"height": "166"
				},
				"options": [
					"(a) 39 cm<sup>2</sup>",
					"(b) 57 cm<sup>2</sup>",
					"(c) 61 cm<sup>2</sup>",	
					"(d) 40 cm<sup>2</sup>"	
				],
				"val": 25
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameter 16 m and 12 m in a locality. The radius of the new park would be ___________.",
				"ans": "(a) 10 m",
				"code": "MCQ",
				"options": [
					"(a) 10 m",
					"(b) 15 m",
					"(c) 20 m",	
					"(d) 24 m"	
				],
				"val": 26
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of the circle that can be inscribed in a square of side 6 cm is ___________.",
				"ans": "(d) 9 π cm<sup>2</sup>",
				"code": "MCQ",
				"options": [
					"(a) 36 π cm<sup>2</sup>",
					"(b) 18 π cm<sup>2</sup>",
					"(c) 12 π cm<sup>2</sup>",	
					"(d) 9 π cm<sup>2</sup>"	
				],
				"val": 27
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of the square that can be inscribed in a circle of radius 8 cm is ___________.",
				"ans": "(b) 128 cm<sup>2</sup>",
				"code": "MCQ",
				"options": [
					"(a) 256 cm<sup>2</sup>",
					"(b) 128 cm<sup>2</sup>",
					"(c) 64√2 π cm<sup>2</sup>",	
					"(d) 64 π cm<sup>2</sup>"	
				],
				"val": 28
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The diameter of a circle whose area is equal to the sum of the areas of the two circles of each 24 cm and 7 cm is ___________.",
				"ans": "(d) 50 cm",
				"code": "MCQ",
				"options": [
					"(a) 31 cm",
					"(b) 25 cm",
					"(c) 62 cm",	
					"(d) 50 cm"	
				],
				"val": 29
			},
			
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "Find the product of the following:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 1,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a26.jpg",
          "width": "572",
          "height": "302"
        },
        "ansimg": {
          "image": "ch12a27.jpg",
          "width": "418",
          "height": "401"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the area of the shaded region.",
        "ans": "Area of shaded region = Area of the square with side 14 cm – ( Area of square with side 4 cm + 4 × Area of each semicircle with radius 2 cm) <br/> = 14 × 14 – [4 × 4 + 4 × 1/2 × 3.14 × (2)<sup>2</sup>] <br/> = 196 – (16 + 25.12) <br/> = 196 – 41.12 <br/> = 154.88 cm<sup>2</sup>",
        "code": "SATQ",
        "options": null,
        "val": 2,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a28.jpg",
          "width": "508",
          "height": "240"
        },
        "ansimg": {
          "image": null,
          "width": null,
          "height": null
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 3,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a50.jpg",
          "width": "561",
          "height": "257"
        },
        "ansimg": {
          "image": "ch12a51.jpg",
          "width": "578",
          "height": "353"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "In figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. (Use π = 3.14)",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 4,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a52.jpg",
          "width": "204",
          "height": "197"
        },
        "ansimg": {
          "image": "ch12a53.jpg",
          "width": "386",
          "height": "757"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a54.jpg",
          "width": "570",
          "height": "284"
        },
        "ansimg": {
          "image": "ch12a55.jpg",
          "width": "481",
          "height": "237"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
       "pic": {
          "image": "ch12a56.jpg",
          "width": "588",
          "height": "306"
        },
        "ansimg": {
          "image": "ch12a57.jpg",
          "width": "576",
          "height": "284"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 7,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a58.jpg",
          "width": "573",
          "height": "177"
        },
        "ansimg": {
          "image": "ch12a59.jpg",
          "width": "383",
          "height": "476"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 8,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a60.jpg",
          "width": "583",
          "height": "235"
        },
        "ansimg": {
          "image": "ch12a61.jpg",
          "width": "309",
          "height": "800"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 9,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a62.jpg",
          "width": "577",
          "height": "207"
        },
        "ansimg": {
          "image": "ch12a63.jpg",
          "width": "576",
          "height": "672"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 10,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a64.jpg",
          "width": "576",
          "height": "203"
        },
        "ansimg": {
          "image": "ch12a65.jpg",
          "width": "481",
          "height": "313"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 11,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a66.jpg",
          "width": "580",
          "height": "277"
        },
        "ansimg": {
          "image": "ch12a67.jpg",
          "width": "363",
          "height": "346"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 12,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a68.jpg",
          "width": "575",
          "height": "284"
        },
        "ansimg": {
          "image": "ch12a69.jpg",
          "width": "578",
          "height": "950"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 13,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a70.jpg",
          "width": "581",
          "height": "232"
        },
        "ansimg": {
          "image": "ch12a71.jpg",
          "width": "401",
          "height": "830"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "An elastic belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulling. Also, find the shaded area. (Use π = 3.14 and √3 = 1.73)",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 14,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch12a72.jpg",
          "width": "296",
          "height": "129"
        },
        "ansimg": {
          "image": "ch12a73.jpg",
          "width": "423",
          "height": "864"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "In figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square, where O and O′ are centres of the circles. Find the area of shaded region.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 15,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
         "pic": {
          "image": "ch12a74.jpg",
          "width": "191",
          "height": "178"
        },
        "ansimg": {
          "image": "ch12a75.jpg",
          "width": "416",
          "height": "239"
        }
      }	  
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a4.jpg",
          "width": "576",
          "height": "281"
        },
        "ansimg": {
          "image": "ch12a5.jpg",
          "width": "583",
          "height": "318"
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a6.jpg",
          "width": "577",
          "height": "257"
        },
        "ansimg": {
          "image": "ch12a7.jpg",
          "width": "574",
          "height": "259"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a8.jpg",
          "width": "581",
          "height": "253"
        },
        "ansimg": {
          "image": "ch12a9.jpg",
          "width": "401",
          "height": "261"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "□ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. (Take π = 3.14)",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a34.jpg",
          "width": "246",
          "height": "189"
        },
        "ansimg": {
          "image": "ch12a35.jpg",
          "width": "575",
          "height": "336"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a36.jpg",
          "width": "573",
          "height": "233"
        },
        "ansimg": {
          "image": "ch12a37.jpg",
          "width": "572",
          "height": "230"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a38.jpg",
          "width": "572",
          "height": "257"
        },
        "ansimg": {
          "image": "ch12a39.jpg",
          "width": "360",
          "height": "550"
        },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a40.jpg",
          "width": "538",
          "height": "58"
        },
        "ansimg": {
          "image": "ch12a41.jpg",
          "width": "472",
          "height": "578"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a42.jpg",
          "width": "176",
          "height": "177"
        },
        "ansimg": {
          "image": "ch12a43.jpg",
          "width": "439",
          "height": "442"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a44.jpg",
          "width": "575",
          "height": "252"
        },
        "ansimg": {
          "image": "ch12a45.jpg",
          "width": "417",
          "height": "747"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a46.jpg",
          "width": "573",
          "height": "232"
        },
        "ansimg": {
          "image": "ch12a47.jpg",
          "width": "296",
          "height": "278"
        },
        "val": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch12a48.jpg",
          "width": "574",
          "height": "280"
        },
        "ansimg": {
          "image": "ch12a49.jpg",
          "width": "299",
          "height": "236"
        },
        "val": 11
      },
	  
	],
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  "mcq": "ch12_mcq",
  "co": "ch12_co",
  "nf": "ch12_nf",
  "saq": "ch12_saq",
  "fib": "ch12_fib",
  "vsaq": "ch12_vsaq",
  "tf": "ch12_tf",
  "mtf": "ch12_mtf",
  "laq": "ch12_laq",
  "jtf": "ch12_jtf",
  "ctt": "ch12_ctt",
  "snc": "ch12_snc",
  "grade": "Grade 10",
  "gowf": "ch12_gowf",
  "afow": "ch12_afow",
  "cs": "ch12_cs",
  "ctco": "ch12_ctco",
  "map": "ch12_map",
  "dtf": "ch12_dtf",
  "grf": "ch12_grf",
  "afq": "ch12_afq",
  "pbq": "ch12_pbq",
  "yn": "ch12_yn",
  "un": "ch12_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch13",
  "chapterName": "Chapter 13 - Surface Areas and Volumes",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "The diameter of the base of cone is 10 cm and its slant height is 17 cm. Then the curved surface area of the cone is _______ cm<sup>2</sup>.",
				"ans": "(a) 85π",
				"code": "MCQ",
				"options": [
					"(a) 85π",
					"(b) 170π",
					"(c) 95π",	
					"(d) 88π"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The diameter and the height of the cylinder are 14 cm and 10 cm. Then the total surface area is ________ cm<sup>2</sup>.",
				"ans": "(c) 748",
				"code": "MCQ",
				"options": [
					"(a) 44",
					"(b) 308",
					"(c) 748",	
					"(d) 1010"
				],
				
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Mayank has made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird bath.",
				"ans": "(a) 3.3 m<sup>2</sup>",
				"code": "MCQ",
				"pic": {
				"image": "ch13a1.jpg",
				"width": "78",
				"height": "127"
				},
				"options": [
					"(a) 3.3 m<sup>2</sup>",
					"(b) 3 m<sup>2</sup>",
					"(c) 4.5 m<sup>2</sup>",	
					"(d) 4 m<sup>2</sup>"	
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is _______ cm.",
				"ans": "(a) 4.2",
				"code": "MCQ",
				"options": [
					"(a) 4.2",
					"(b) 2.1",
					"(c) 8.4",	
					"(d) 1.05"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If two solid hemispheres of same base radius ‘r’ are joined together along their bases, then curved surface area of this new solid is _______.",
				"ans": "(a) 4π r<sup>2</sup>",
				"code": "MCQ",
				"options": [
					"(a) 4π r<sup>2</sup>",
					"(b) 6π r<sup>2</sup>",
					"(c) 3π r<sup>2</sup>",	
					"(d) 8π r<sup>2</sup>"	
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A right circular cylinder of radius r cm and height h cm, just enclose a sphere of diameter:",
				"ans": "(b) 2 r cm",
				"code": "MCQ",
				"options": [
					"(a) r cm",
					"(b) 2 r cm",
					"(c) h cm",	
					"(d) 2 h cm"	
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The volume of sphere with diameter 1 cm is _________ cm<sup>3</sup>.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch13a15.jpg",
				"width": "53",
				"height": "31"
				},
				"options": [
					"ch13a14.jpg",
					"ch13a15.jpg",
					"ch13a16.jpg",	
					"ch13a17.jpg"	
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The volume of hemisphere with radius 1.2 cm is ________ cm<sup>3</sup>.",
				"ans": "(a) 1.152π",
				"code": "MCQ",
				"options": [
					"(a) 1.152π",
					"(b) 0.96π",
					"(c) 2.152π",	
					"(d) 3.456π"	
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The volume of sphere is 4/3 π cm<sup>3</sup>. Then its diameter is ________ cm.",
				"ans": "(c) 2",
				"code": "MCQ",
				"options": [
					"(a) 0.5",
					"(b) 1",
					"(c) 2",	
					"(d) 2.5"	
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The volume of cone with radius 2 cm and height 6 cm is _________ cm<sup>3</sup>.",
				"ans": "(d) 16π",
				"code": "MCQ",
				"options": [
					"(a) 8π",
					"(b) 2π",
					"(c) 14π",	
					"(d) 16π"	
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The ratio of the radii of two cones having equal height is 2:3. Then, the ratio of their volumes is ______.",
				"ans": "(d) 4:9",
				"code": "MCQ",
				"options": [
					"(a) 4:6",
					"(b) 8:27",
					"(c) 3:2",	
					"(d) 4:9"	
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by ________",
				"ans": "(a) 3",
				"code": "MCQ",
				"options": [
					"(a) 3",
					"(b) 4",
					"(c) 5",	
					"(d) 6"	
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the radius of the base of a right circular cylinder is halved, keeping the height same then the ratio of the volume of cylinder thus obtained to the volume of original cylinder is ________.",
				"ans": "(c) 1:4",
				"code": "MCQ",
				"options": [
					"(a) 1:2",
					"(b) 2:1",
					"(c) 1:4",	
					"(d) 4:1"	
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is _________.",
				"ans": "(b) 5",
				"code": "MCQ",
				"options": [
					"(a) 3",
					"(b) 5",
					"(c) 4",	
					"(d) 6"	
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 142296",
				"code": "MCQ",
				"pic": {
				"image": "ch13a18.jpg",
				"width": "568",
				"height": "54"
				},
				"options": [
					"(a) 142296",
					"(b) 142396",
					"(c) 142496",	
					"(d) 142596"	
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A medicine capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispherical stuck to each to its ends. The length of entire capsule is 2 cm. The capacity of the capsule is: ________.",
				"ans": "(a) 0.36 cm<sup>3</sup>",
				"code": "MCQ",
				"options": [
					"(a) 0.36 cm<sup>3</sup>",
					"(b) 0.35 cm<sup>3</sup>",
					"(c) 0.34 cm<sup>3</sup>",	
					"(d) 0.33 cm<sup>3</sup>"	
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Volume of two spheres are in the ratio 64:27. The ratio of their surface areas is ________.",
				"ans": "(d) 16 : 9",
				"code": "MCQ",
				"options": [
					"(a) 3 : 4",
					"(b) 4 : 3",
					"(c) 9 : 16",	
					"(d) 16 : 9"	
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is ________.",
				"ans": "(a) 64 : 27",
				"code": "MCQ",
				"options": [
					"(a) 64 : 27",
					"(b) 16 : 9",
					"(c) 4 : 3",	
					"(d) 16<sup>3</sup> : 9<sup>3</sup>"	
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the radii of a frustum of a cone are 7 cm and 3 cm and the height is 3 cm, then the curved surface area is ________ cm<sup>2</sup>.",
				"ans": "(a) 50π",
				"code": "MCQ",
				"options": [
					"(a) 50π",
					"(b) 25π",
					"(c) 35π",	
					"(d) 63π"	
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The radii of a frustum of a cone are 5 cm and 9 cm and height is 6 cm, then the volume is _______ cm<sup>3</sup>.",
				"ans": "(c) 302π",
				"code": "MCQ",
				"options": [
					"(a) 320π",
					"(b) 151π",
					"(c) 302π",	
					"(d) 98π"	
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone: _________.",
				"ans": "(d) 1 : 8",
				"code": "MCQ",
				"options": [
					"(a) 1 : 2",
					"(b) 1 : 4",
					"(c) 1 : 6",	
					"(d) 1 : 8"	
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of sphere. Find the radius of the sphere.",
				"ans": "(b) 6 cm",
				"code": "MCQ",
				"options": [
					"(a) 4 cm",
					"(b) 6 cm",
					"(c) 8 cm",	
					"(d) 10 cm"	
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch13a49.jpg",
				"width": "76",
				"height": "28"
				},
				"options": [
					"ch13a49.jpg",
					"ch13a50.jpg",
					"ch13a51.jpg",	
					"ch13a52.jpg"	
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A hemispherical tank full of water is emptied by a pipe at the rate of 3 <sup>4</sup>/<sub>7</sub> <i>l</i> per second. How much time will it take to empty half the tank if it is 3 m in diameter.",
				"ans": "(a) 16–5 mins",
				"code": "MCQ",
				"options": [
					"(a) 16–5 mins",
					"(b) 12 mins",
					"(c) 18 mins",	
					"(d) 15–1 mins"	
				],
				"val": 24
			}	
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 1,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a3.jpg",
          "width": "570",
          "height": "450"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 2,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a4.jpg",
          "width": "573",
          "height": "341"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but height 2.8 m, and the canvas to be used costs ₹100 per square metre, find the amount the associations will have to pay.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 3,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a5.jpg",
          "width": "571",
          "height": "588"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 4,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a6.jpg",
          "width": "567",
          "height": "292"
        },
        "ansimg": {
          "image": "ch13a7.jpg",
          "width": "570",
          "height": "335"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a8.jpg",
          "width": "568",
          "height": "277"
        },
        "ansimg": {
          "image": "ch13a9.jpg",
          "width": "564",
          "height": "433"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a10.jpg",
          "width": "571",
          "height": "338"
        },
        "ansimg": {
          "image": "ch13a11.jpg",
          "width": "250",
          "height": "269"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.",
        "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": "ch13a12.jpg",
          "width": "522",
          "height": "616"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs ₹120 per square metre, find the amount shared by each school to set up the tents. What value is generated by the above problem? (Use π = <sup>22</sup>/<sub>7</sub>)",
        "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": "ch13a13.jpg",
          "width": "494",
          "height": "700"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.",
        "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": "ch13a24.jpg",
          "width": "519",
          "height": "291"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Water in canal 6 m wide and 1.5 m deep is flowing at a speed of 4 km/hour. How much area will it irrigate in 10 minutes if 8 cm of standing water is needed for irrigation?",
        "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": "ch13a25.jpg",
          "width": "446",
          "height": "462"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle if 10% liquid is wasted in this transfer.",
        "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": "ch13a26.jpg",
          "width": "554",
          "height": "646"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence, find its surface area.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 12,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a27.jpg",
          "width": "310",
          "height": "642"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 13,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a28.jpg",
          "width": "565",
          "height": "82"
        },
        "ansimg": {
          "image": "ch13a29.jpg",
          "width": "402",
          "height": "623"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 14,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a30.jpg",
          "width": "403",
          "height": "378"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 15,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a31.jpg",
          "width": "565",
          "height": "51"
        },
        "ansimg": {
          "image": "ch13a32.jpg",
          "width": "335",
          "height": "203"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 16,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a33.jpg",
          "width": "390",
          "height": "171"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.",
        "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": "ch13a34.jpg",
          "width": "526",
          "height": "313"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 square cm, find the volume of the cylinder.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 18,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a35.jpg",
          "width": "520",
          "height": "595"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 19,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a36.jpg",
          "width": "570",
          "height": "81"
        },
        "ansimg": {
          "image": "ch13a37.jpg",
          "width": "455",
          "height": "611"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?",
        "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": "ch13a38.jpg",
          "width": "572",
          "height": "375"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 21,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a39.jpg",
          "width": "566",
          "height": "54"
        },
        "ansimg": {
          "image": "ch13a40.jpg",
          "width": "384",
          "height": "660"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm at the rate of 0.4 metre/second. Determine the rise in level of water in the tank in half an hour.",
        "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": "ch13a41.jpg",
          "width": "569",
          "height": "536"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 23,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a42.jpg",
          "width": "567",
          "height": "81"
        },
        "ansimg": {
          "image": "ch13a43.jpg",
          "width": "472",
          "height": "380"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A well of diameter 3 metres is dug 14 metres deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 metres to form an embankment. Find the height of the embankment.",
        "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": "ch13a45.jpg",
          "width": "378",
          "height": "831"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.",
        "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": "ch13a46.jpg",
          "width": "437",
          "height": "846"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can completly fill the bucket at ₹ 30 per litre.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 26,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a53.jpg",
          "width": "348",
          "height": "412"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 27,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a54.jpg",
          "width": "566",
          "height": "83"
        },
        "ansimg": {
          "image": "ch13a55.jpg",
          "width": "485",
          "height": "869"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 28,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch13a56.jpg",
          "width": "571",
          "height": "79"
        },
        "ansimg": {
          "image": "ch13a57.jpg",
          "width": "404",
          "height": "953"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "Two cubes each of volume 27 cm<sup>3</sup> are joined end to end to form a solid. Find the surface area of the resulting cuboid.",
        "ans": "If a is side of each cube, then volume of cube = a<sup>3</sup> = 27 <br/>⇒ a<sup>3</sup> = (3)<sup>3</sup> <br/> ⇒ a = 3 cm <br/> Surface area of resulting solid = 10a<sup>2</sup> = 10(3)<sup>2</sup> = 90 cm<sup>2</sup>",
        "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": "Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?",
        "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": "ch13a19.jpg",
          "width": "268",
          "height": "157"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch13a20.jpg",
          "width": "479",
          "height": "32"
        },
        "ansimg": {
          "image": "ch13a21.jpg",
          "width": "342",
          "height": "383"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": null,
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch13a22.jpg",
          "width": "454",
          "height": "36"
        },
        "ansimg": {
          "image": "ch13a23.jpg",
          "width": "294",
          "height": "359"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.",
        "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": "ch13a47.jpg",
          "width": "226",
          "height": "287"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A solid sphere of radius 10.5 cm is melted and recast into smaller solid cones each of radius 35 cm and height 3 cm. Find the number of cones so formed.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch13a2.jpg",
          "width": "88",
          "height": "29"
        },
        "ansimg": {
          "image": "ch13a48.jpg",
          "width": "279",
          "height": "255"
        },
        "val": 6
      }
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
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    [],
    [],
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    [],
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    [],
    [],
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    [],
    [],
    [],
    [],
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    [],
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    [],
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    [],
    [],
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    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch13_mcq",
  "co": "ch13_co",
  "nf": "ch13_nf",
  "saq": "ch13_saq",
  "fib": "ch13_fib",
  "vsaq": "ch13_vsaq",
  "tf": "ch13_tf",
  "mtf": "ch13_mtf",
  "laq": "ch13_laq",
  "jtf": "ch13_jtf",
  "ctt": "ch13_ctt",
  "snc": "ch13_snc",
  "grade": "Grade 10",
  "gowf": "ch13_gowf",
  "afow": "ch13_afow",
  "cs": "ch13_cs",
  "ctco": "ch13_ctco",
  "map": "ch13_map",
  "dtf": "ch13_dtf",
  "grf": "ch13_grf",
  "afq": "ch13_afq",
  "pbq": "ch13_pbq",
  "yn": "ch13_yn",
  "un": "ch13_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch14",
  "chapterName": "Chapter 14 - Statistics",
  "all": [
    [
			{
				"heading": "Multiple Choice Question.",
				"qus": "The most stable measure of central tendency is _______.",
				"ans": "(a) mean",
				"code": "MCQ",
				"options": [
					"(a) mean",
					"(b) median",
					"(c) mode",	
					"(d) none of these"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The marks obtained by 30 Students of Class X of certain School in Mathematics are given below. Find mean _______.",
				"ans": "(b) 59.3",
				"code": "MCQ",
				"pic": {
				"image": "ch14a1.jpg",
				"width": "359",
				"height": "52"
				},
				"options": [
					"(a) 78.1",
					"(b) 59.3",
					"(c) 60.9",	
					"(d) 72.5"
				],
				
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the mean for the following data:-",
				"ans": "(a) 62",
				"code": "MCQ",
				"pic": {
				"image": "ch14a2.jpg",
				"width": "317",
				"height": "103"
				},
				"options": [
					"(a) 62",
					"(b) 85",
					"(c) 70",	
					"(d) 59"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Find the mean:-",
				"ans": "(c) 39.71",
				"code": "MCQ",
				"pic": {
				"image": "ch14a3.jpg",
				"width": "390",
				"height": "101"
				},
				"options": [
					"(a) 30.1",
					"(b) 37.1",
					"(c) 39.71",	
					"(d) 32.05"	
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "While computing the mean of grouped data, we assume that the frequencies are",
				"ans": "(b) centred at the class marks of the classes",
				"code": "MCQ",
				"options": [
					"(a) evenly distributed over all classes",
					"(b) centred at the class marks of the classes",
					"(c) centred at upper limits of classes",	
					"(d) centred at lower limits of classes"	
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 0",
				"code": "MCQ",
				"pic": {
				"image": "ch14a4.jpg",
				"width": "574",
				"height": "51"
				},
				"options": [
					"(a) 0",
					"(b) -1",
					"(c) 1",	
					"(d) 2"	
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"pic": {
				"image": "ch14a5.jpg",
				"width": "572",
				"height": "49"
				},
				"ansimg": {
				"image": "ch14a7.jpg",
				"width": "68",
				"height": "36"
				},
				"options": [
					"ch14a6.jpg",
					"(b) h(x<sub>i</sub> −a)",
					"ch14a7.jpg",	
					"ch14a8.jpg"	
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The modal class of the frequency distribution is ___________.",
				"ans": "(c) 30 – 40",
				"code": "MCQ",
				"pic": {
				"image": "ch14a19.jpg",
				"width": "308",
				"height": "57"
				},
				"options": [
					"(a) 10 – 20",
					"(b) 20 – 30",
					"(c) 30 – 40",	
					"(d) 40 – 50"	
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The wickets taken by a bowler in 10 cricket matches are as follows. Find the mode. <br/> 2, 6, 4, 5, 0, 2, 1, 3, 2, 3",
				"ans": "(c) 2",
				"code": "MCQ",
				"options": [
					"(a) 6",
					"(b) 4",
					"(c) 2",	
					"(d) 0"	
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A survey conducted on 20 households in a locality by group of students on number of family members. Find the mode.",
				"ans": "(a) 3.286",
				"code": "MCQ",
				"pic": {
				"image": "ch14a20.jpg",
				"width": "284",
				"height": "51"
				},
				"options": [
					"(a) 3.286",
					"(b) 3",
					"(c) 4.1",	
					"(d) 1.25"	
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For the following distribution:",
				"ans": "(c) 30 – 40",
				"code": "MCQ",
				"pic": {
				"image": "ch14a21.jpg",
				"width": "177",
				"height": "205"
				},
				"options": [
					"(a) 10 – 20",
					"(b) 20 – 30",
					"(c) 30 – 40",	
					"(d) 50 – 60"	
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 25",
				"code": "MCQ",
				"pic": {
				"image": "ch14a38.jpg",
				"width": "346",
				"height": "25"
				},
				"options": [
					"(a) 25",
					"(b) 75",
					"(c) 50",	
					"(d) 0"	
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For some data, Z – M = 2.5, if mean of the data is 20, then Z = ________ .",
				"ans": "(c) 23.75",
				"code": "MCQ",
				"options": [
					"(a) 21.25",
					"(b) 22.75",
					"(c) 23.75",	
					"(d) 22.25"	
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) 23",
				"code": "MCQ",
				"pic": {
				"image": "ch14a39.jpg",
				"width": "274",
				"height": "23"
				},
				"options": [
					"(a) 24",
					"(b) 22",
					"(c) 26",	
					"(d) 23"	
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 20",
				"code": "MCQ",
				"pic": {
				"image": "ch14a40.jpg",
				"width": "209",
				"height": "23"
				},
				"options": [
					"(a) 10",
					"(b) 20",
					"(c) 30",	
					"(d) 40"	
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(c) 25",
				"code": "MCQ",
				"pic": {
				"image": "ch14a41.jpg",
				"width": "208",
				"height": "24"
				},
				"options": [
					"(a) 15",
					"(b) 20",
					"(c) 25",	
					"(d) 30"	
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(b) 25",
				"code": "MCQ",
				"pic": {
				"image": "ch14a42.jpg",
				"width": "210",
				"height": "21"
				},
				"options": [
					"(a) 22",
					"(b) 25",
					"(c) 32",	
					"(d) 66"	
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) 20.67",
				"code": "MCQ",
				"pic": {
				"image": "ch14a43.jpg",
				"width": "251",
				"height": "23"
				},
				"options": [
					"(a) 21.10",
					"(b) 19.67",
					"(c) 20.10",	
					"(d) 20.67"	
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(a) 6",
				"code": "MCQ",
				"pic": {
				"image": "ch14a44.jpg",
				"width": "211",
				"height": "26"
				},
				"options": [
					"(a) 6",
					"(b) 5",
					"(c) 4",	
					"(d) 3"	
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The cumulative frequency of class 20–30 of the frequency distribution given is _______ .",
				"ans": "(b) 35",
				"code": "MCQ",
				"pic": {
				"image": "ch14a45.jpg",
				"width": "321",
				"height": "53"
				},
				"options": [
					"(a) 25",
					"(b) 35",
					"(c) 15",	
					"(d) 40"	
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The median class of the frequency distribution given is _______.",
				"ans": "(c) 20–30",
				"code": "MCQ",
				"pic": {
				"image": "ch14a46.jpg",
				"width": "388",
				"height": "50"
				},
				"options": [
					"(a) 40–50",
					"(b) 30–40",
					"(c) 20–30",	
					"(d) 10–20"	
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The mean and median of the data are 20 and 22 respectively. The value of the mode is _______.",
				"ans": "(b) 26",
				"code": "MCQ",
				"options": [
					"(a) 20",
					"(b) 26",
					"(c) 22",	
					"(d) 21"	
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For a frequency distribution, mean, median and mode are connected by the relation _______.",
				"ans": "(c) Mode = 3 Median – 2 Mean",
				"code": "MCQ",
				"options": [
					"(a) Mode = 3 Mean – 2 Median",
					"(b) Mode = 2 Median – 3 Mean",
					"(c) Mode = 3 Median – 2 Mean",	
					"(d) Mode = 3 Median – 2 Mean"	
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For the following distribution:",
				"ans": "(b) 25",
				"code": "MCQ",
				"pic": {
				"image": "ch14a47.jpg",
				"width": "386",
				"height": "73"
				},
				"options": [
					"(a) 15",
					"(b) 25",
					"(c) 30",	
					"(d) 35"	
				],
				"val": 24
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Consider the following frequency distribution:",
				"ans": "(b) 17.5",
				"code": "MCQ",
				"pic": {
				"image": "ch14a48.jpg",
				"width": "384",
				"height": "77"
				},
				"options": [
					"(a) 7",
					"(b) 17.5",
					"(c) 18",	
					"(d) 18.5"	
				],
				"val": 25
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Consider the data _______.",
				"ans": "(b) 19",
				"code": "MCQ",
				"pic": {
				"image": "ch14a49.jpg",
				"width": "532",
				"height": "99"
				},
				"options": [
					"(a) 0",
					"(b) 19",
					"(c) 20",	
					"(d) 38"	
				],
				"val": 26
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If ‘less than type’ Ogive and ‘more than type’ Ogive intersect each other at (20.5, 15.5) then the median of the given data is:",
				"ans": "(b) 20.5",
				"code": "MCQ",
				"options": [
					"(a) 36.0",
					"(b) 20.5",
					"(c) 15.5",	
					"(d) 5.5"	
				],
				"val": 27
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In a less than type Ogive, the cumulative frequency is plotted against:",
				"ans": "(a) lower limit of the concerned class interval.",
				"code": "MCQ",
				"options": [
					"(a) lower limit of the concerned class interval.",
					"(b) upper limit of the concerned class interval.",
					"(c) class mark of the concerned class interval.",	
					"(d) None of these."	
				],
				"val": 28
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The abscissa of the point of intersection of the less than type and more than type cumulative frequency curves of a grouped data gives its:",
				"ans": "(c) mode",
				"code": "MCQ",
				"options": [
					"(a) mean",
					"(b) median",
					"(c) mode",	
					"(d) all of these."	
				],
				"val": 29
			}
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "In Subzi Mandi, fruit vendors were selling apples in boxes, which carried varying number of apples. The following frequence distribution shows apples according to number of boxes.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 1,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a13.jpg",
          "width": "454",
          "height": "89"
        },
        "ansimg": {
          "image": "ch14a14.jpg",
          "width": "576",
          "height": "442"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the mean of the following distribution by step deviation method:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 2,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a15.jpg",
          "width": "573",
          "height": "64"
        },
        "ansimg": {
          "image": "ch14a16.jpg",
          "width": "573",
          "height": "620"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The mean of the following distribution is 18. Find the frequency f of the class 19-21.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 3,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a17.jpg",
          "width": "441",
          "height": "61"
        },
        "ansimg": {
          "image": "ch14a18.jpg",
          "width": "572",
          "height": "440"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The mode of the following data is 36. Find the missing frequency x in it.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 4,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a28.jpg",
          "width": "524",
          "height": "60"
        },
        "ansimg": {
          "image": "ch14a29.jpg",
          "width": "285",
          "height": "388"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The distribution of sale of shirts sold in a month in a departmental store is as under. Calculate the modal size of shirts sold.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 5,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a30.jpg",
          "width": "543",
          "height": "64"
        },
        "ansimg": {
          "image": "ch14a31.jpg",
          "width": "334",
          "height": "368"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "If the mode of the following distribution is 57.5, find the value of x.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 6,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a32.jpg",
          "width": "479",
          "height": "63"
        },
        "ansimg": {
          "image": "ch14a33.jpg",
          "width": "296",
          "height": "437"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the mean and mode for the following data.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 7,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a34.jpg",
          "width": "477",
          "height": "64"
        },
        "ansimg": {
          "image": "ch14a35.jpg",
          "width": "477",
          "height": "553"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The following distribution gives the weights of 60 students of a class. Find the mean and mode weigths of the students.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 8,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a36.jpg",
          "width": "574",
          "height": "64"
        },
        "ansimg": {
          "image": "ch14a37.jpg",
          "width": "520",
          "height": "579"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The following table shows the distribution of marks obtained by the students in a certain subject:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 9,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a50.jpg",
          "width": "537",
          "height": "82"
        },
        "ansimg": {
          "image": "ch14a51.jpg",
          "width": "570",
          "height": "349"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The table below shows the salaries of 280 persons:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 10,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a52.jpg",
          "width": "323",
          "height": "257"
        },
        "ansimg": {
          "image": "ch14a53.jpg",
          "width": "513",
          "height": "534"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "For Uttarakhand flood victims, money donated by teachers of a school is shown in the following frequency distribution.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 11,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a54.jpg",
          "width": "579",
          "height": "88"
        },
        "ansimg": {
          "image": "ch14a55.jpg",
          "width": "576",
          "height": "717"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Calculate the missing frequency from the following frequency distribution, it is given that the median of the distribution is 24.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 12,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a56.jpg",
          "width": "569",
          "height": "67"
        },
        "ansimg": {
          "image": "ch14a57.jpg",
          "width": "576",
          "height": "583"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Find the mean, mode and median of the following frequency distribution:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 13,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a58.jpg",
          "width": "571",
          "height": "66"
        },
        "ansimg": {
          "image": "ch14a59.jpg",
          "width": "579",
          "height": "842"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "By changing the following frequency distribution to ‘less than type’ distribution, draw its Ogive.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 14,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a68.jpg",
          "width": "563",
          "height": "64"
        },
        "ansimg": {
          "image": "ch14a69.jpg",
          "width": "565",
          "height": "573"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "The following distribution gives the daily income of 50 workers of a factory.",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 15,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a70.jpg",
          "width": "565",
          "height": "87"
        },
        "ansimg": {
          "image": "ch14a71.jpg",
          "width": "565",
          "height": "570"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "In annual day of a school, age-wise participation of students is shown in the following frequency distribution:",
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 16,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch14a72.jpg",
          "width": "571",
          "height": "82"
        },
        "ansimg": {
          "image": "ch14a73.jpg",
          "width": "568",
          "height": "549"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "Find the mean of the data, using an empirical formula, when it is given that mode = 50.5 and median = 45.5.",
        "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": "ch14a9.jpg",
          "width": "252",
          "height": "141"
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The mean monthly salary of 10 members of a group is ₹1445. If one more member whose monthly salary is ₹1500 joins the group, then find the mean monthly salary (in ₹) of 11 members of the group.",
        "ans": "3",
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": null,
          "width": null,
          "height": null
        },
        "ansimg": {
          "image": "ch14a10.jpg",
          "width": "272",
          "height": "210"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In the frequency distribution, if Σf = 50 and Σf<sub>i</sub>x<sub>i</sub> = 2550, then what is the mean of the distribution?",
        "ans": "7",
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": null,
          "width": null,
          "height": null
        },
        "ansimg": {
          "image": "ch14a11.jpg",
          "width": "113",
          "height": "96"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The mean of 11 numbers is 35. If mean of first 6 numbers is 32 and that of last 6 numbers is 37, find 6th number.",
        "ans": "5",
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": null,
          "width": null,
          "height": null
        },
        "ansimg": {
          "image": "ch14a12.jpg",
          "width": "476",
          "height": "397"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find mode of the following frequency distribution.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a22.jpg",
          "width": "413",
          "height": "60"
        },
        "ansimg": {
          "image": "ch14a23.jpg",
          "width": "320",
          "height": "266"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Given below is the distribution of weekly pocket money recieved by students of a class. Calculate the pocket money that is received by most of the students:",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a24.jpg",
          "width": "530",
          "height": "62"
        },
        "ansimg": {
          "image": "ch14a25.jpg",
          "width": "258",
          "height": "252"
        },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Age of the pumps manufactured by a company are given in the following distribution table. Calculate the modal age of pumps.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a26.jpg",
          "width": "509",
          "height": "60"
        },
        "ansimg": {
          "image": "ch14a27.jpg",
          "width": "292",
          "height": "292"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In a certain distribution, mean and median are 9.5 and 10 respectively. Find the mode of the distribution using an empirical relation.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a26.jpg",
          "width": "509",
          "height": "60"
        },
        "ansimg": {
          "image": "ch14a27.jpg",
          "width": "292",
          "height": "292"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "In a certain distribution, mean and median are 9.5 and 10 respectively. Find the mode of the distribution using an empirical relation.",
        "ans": "Empirical relation is: <br/> 3 Median = Mode + 2 Mean <br/> ⇒ Mode = 3 Median – 2 Mean <br/> = 3 × 10 – 2 × 9.5 <br/> = 30 – 19 <br/> = 11",
        "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": "Which central tendency is obtained by abscissa of point of intersection of ‘less than type’ and ‘more than type’ Ogives?",
        "ans": "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": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Given below is a frequency distribution table showing daily income of 100 workers of a factory.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a60.jpg",
          "width": "515",
          "height": "83"
        },
        "ansimg": {
          "image": "ch14a61.jpg",
          "width": "560",
          "height": "262"
        },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Find the ‘More than type’ cumulative frequency of the given distribution.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a62.jpg",
          "width": "515",
          "height": "77"
        },
        "ansimg": {
          "image": "ch14a63.jpg",
          "width": "515",
          "height": "216"
        },
        "val": 12
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Given below is a cumulative frequency distribution of ‘Less than type’.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a64.jpg",
          "width": "533",
          "height": "84"
        },
        "ansimg": {
          "image": "ch14a65.jpg",
          "width": "536",
          "height": "139"
        },
        "val": 13
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The following are the ages of 300 patients getting medical treatment in a hospital on a particular day.",
        "ans": null,
        "code": "VSAQ",
        "option1": null,
        "option2": null,
        "option3": null,
        "aoption1": null,
        "aoption2": null,
        "aoption3": null,
        "pic": {
          "image": "ch14a66.jpg",
          "width": "567",
          "height": "98"
        },
        "ansimg": {
          "image": "ch14a67.jpg",
          "width": "565",
          "height": "187"
        },
        "val": 14
      }
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch14_mcq",
  "co": "ch14_co",
  "nf": "ch14_nf",
  "saq": "ch14_saq",
  "fib": "ch14_fib",
  "vsaq": "ch14_vsaq",
  "tf": "ch14_tf",
  "mtf": "ch14_mtf",
  "laq": "ch14_laq",
  "jtf": "ch14_jtf",
  "ctt": "ch14_ctt",
  "snc": "ch14_snc",
  "grade": "Grade 10",
  "gowf": "ch14_gowf",
  "afow": "ch14_afow",
  "cs": "ch14_cs",
  "ctco": "ch14_ctco",
  "map": "ch14_map",
  "dtf": "ch14_dtf",
  "grf": "ch14_grf",
  "afq": "ch14_afq",
  "pbq": "ch14_pbq",
  "yn": "ch14_yn",
  "un": "ch14_un"
},

{
  "subject": "Mathematics",
  "chapter": "ch15",
  "chapterName": "Chapter 15 - Probability",
  "all": [
    [
			{
				"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",
				"ansimg": {
				"image": "ch15a3.jpg",
				"width": "45",
				"height": "39"
				},
				"options": [
					"ch15a1.jpg",
					"ch15a2.jpg",
					"ch15a3.jpg",	
					"ch15a4.jpg"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following can’t be the probability of an event?",
				"ans": "(a) 1.5",
				"code": "MCQ",
				"options": [
					"(a) 1.5",
					"ch15a5.jpg",
					"(c) 25%",	
					"(d) 0.3"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Two dice are thrown together. The probability of getting the same number on both dice is",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch15a8.jpg",
				"width": "44",
				"height": "37"
				},
				"options": [
					"ch15a6.jpg",
					"ch15a7.jpg",
					"ch15a8.jpg",	
					"ch15a9.jpg"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Cards bearing numbers 2, 3, 4, ... 11 are kept in a bag. A card is drawn at random from the bag. The probability of getting a card with a prime number is",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch15a10.jpg",
				"width": "46",
				"height": "32"
				},
				"options": [
					"ch15a10.jpg",
					"ch15a11.jpg",
					"ch15a12.jpg",	
					"ch15a13.jpg"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The probability of getting an even number, when a die is thrown once, is",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch15a14.jpg",
				"width": "44",
				"height": "30"
				},
				"options": [
					"ch15a14.jpg",
					"ch15a15.jpg",
					"ch15a16.jpg",	
					"ch15a17.jpg"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A box contains 90 discs, numbered from 2 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23 is",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch15a20.jpg",
				"width": "53",
				"height": "37"
				},
				"options": [
					"ch15a18.jpg",
					"ch15a19.jpg",
					"ch15a20.jpg",	
					"ch15a21.jpg"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4 is",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch15a24.jpg",
				"width": "39",
				"height": "33"
				},
				"options": [
					"ch15a22.jpg",
					"ch15a23.jpg",
					"ch15a24.jpg",	
					"ch15a25.jpg"
				],
				"val": 7
			},
			{
				"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",
				"ansimg": {
				"image": "ch15a28.jpg",
				"width": "41",
				"height": "40"
				},
				"options": [
					"ch15a26.jpg",
					"ch15a27.jpg",
					"ch15a28.jpg",	
					"ch15a29.jpg"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In a family of 3 children, the probability of having at least one boy is",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch15a30.jpg",
				"width": "43",
				"height": "32"
				},
				"options": [
					"ch15a30.jpg",
					"ch15a31.jpg",
					"ch15a32.jpg",	
					"ch15a33.jpg"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If two different dice are rolled together, the probability of getting an even number on both dice is",
				"ans": null,
				"code": "MCQ",
				"ansimg": {
				"image": "ch15a37.jpg",
				"width": "45",
				"height": "36"
				},
				"options": [
					"ch15a34.jpg",
					"ch15a35.jpg",
					"ch15a36.jpg",	
					"ch15a37.jpg"
				],
				"val": 10
			}
			
	],
    [],
    [],
    [],
    [],
    [],
    [
		{
        "heading": "Answer the following questions in short.",
        "qus": "Two dice are rolled once. Find the probability of getting such numbers on the two dice whose product is 12.",
        "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": "ch15a53.jpg",
          "width": "299",
          "height": "149"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.",
        "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": "ch15a54.jpg",
          "width": "502",
          "height": "217"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Two dice are rolled once. Find the probability of getting such numbers on two dice whose product is a perfect square.",
        "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": "ch15a55.jpg",
          "width": "331",
          "height": "236"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.",
        "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": "ch15a56.jpg",
          "width": "386",
          "height": "331"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be <br/> (i) a blue card <br/> (ii) not a yellow card <br/> (iii) neither yellow nor a blue card.",
        "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": "ch15a57.jpg",
          "width": "389",
          "height": "442"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting <br/> (i) a king of red colour, (ii) a face card, (iii) the queen of diamonds.",
        "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": "ch15a58.jpg",
          "width": "344",
          "height": "449"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": null,
        "ans": null,
        "code": "SATQ",
        "options": null,
        "val": 7,
        "option1": [],
        "option2": [],
        "option3": [],
        "option4": [],
        "aoption1": [],
        "aoption2": [],
        "aoption3": [],
        "aoption4": null,
        "pic": {
          "image": "ch15a59.jpg",
          "width": "576",
          "height": "77"
        },
        "ansimg": {
          "image": "ch15a60.jpg",
          "width": "295",
          "height": "600"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Three different coins are tossed together. Find the probability of getting <br/> (i) exactly two heads <br/> (ii) at least two heads <br/> (iii) at least two tails.",
        "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": "ch15a61.jpg",
          "width": "402",
          "height": "344"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.",
        "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": "ch15a62.jpg",
          "width": "205",
          "height": "332"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Two different dice are thrown together. Find the probability that numbers obtained. <br/> (i) have a sum less than 7. <br/> (ii) have a product less than 16. <br/> (iii) is a doublet of odd numbers.",
        "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": "ch15a63.jpg",
          "width": "550",
          "height": "525"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "All the red face cards are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is: <br/> (i) of red colour, (ii) a queen, (iii) an ace, (iv) face card.",
        "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": "ch15a64.jpg",
          "width": "528",
          "height": "503"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A piggy bank contains hundred 50 p coins, seventy ₹ 1 coins, fifty ₹ 2 coins, and thirty ₹ 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin <br/> (i) will be a ₹ 1 coin <br/> (ii) will not be a ₹ 5 coin <br/> (iii) will be a 50 p or a ₹ 2 coin?",
        "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": "ch15a65.jpg",
          "width": "365",
          "height": "326"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A card is drawn at random from a well-shuffled deck of playing cards. Find the porbability that the card drawn is <br/> (i) a card of spade or an ace. <br/> (ii) a black king <br/> (iii) neither a jack nor a king <br/> (iv) either a king or a queen",
        "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": "ch15a66.jpg",
          "width": "560",
          "height": "800"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.",
        "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": "ch15a67.jpg",
          "width": "368",
          "height": "271"
        }
      },
	  {
        "heading": "Answer the following questions in short.",
        "qus": "Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained who has the better chance to get the number 25.",
        "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": "ch15a68.jpg",
          "width": "522",
          "height": "569"
        }
      }
	],
    [
		{
        "heading": "Very short answer type questions.",
        "qus": "Two different dice are tossed together. Find the probability that the product of two numbers on the top of the dice is 6.",
        "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": "ch15a38.jpg",
          "width": "196",
          "height": "147"
        },
        "val": 1
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.",
        "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": "ch15a39.jpg",
          "width": "427",
          "height": "94"
        },
        "val": 2
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.",
        "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": "ch15a40.jpg",
          "width": "429",
          "height": "135"
        },
        "val": 3
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A card is drawn at random from a well-shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.",
        "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": "ch15a41.jpg",
          "width": "510",
          "height": "158"
        },
        "val": 4
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?",
        "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": "ch15a42.jpg",
          "width": "264",
          "height": "131"
        },
        "val": 5
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less than or equal to 1?",
        "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": "ch15a43.jpg",
          "width": "326",
          "height": "109"
        },
        "val": 6
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Out of 200 bulbs in a box, 12 bulbs are defective. One bulb is taken out at random from the box. What is the probability that the drawn bulb is not defective?",
        "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": "ch15a44.jpg",
          "width": "273",
          "height": "200"
        },
        "val": 7
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A number is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less than or equal to 1?",
        "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": "ch15a45.jpg",
          "width": "308",
          "height": "135"
        },
        "val": 8
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Card bearing numbers 1, 3, 5, ..., 35 are kept in a bag. A card is drawn at random from bag. Find the probability of getting a card bearing. <br/> (i) a prime number less than 15. <br/> (ii) a number divisible by 3 and 5.",
        "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": "ch15a46.jpg",
          "width": "336",
          "height": "264"
        },
        "val": 9
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A coin is tossed two times. Find the probability of getting at least one head.",
        "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": "ch15a47.jpg",
          "width": "253",
          "height": "157"
        },
        "val": 10
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.",
        "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": "ch15a48.jpg",
          "width": "351",
          "height": "214"
        },
        "val": 11
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting (a) a red king (b) a queen or a jack.",
        "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": "ch15a49.jpg",
          "width": "303",
          "height": "269"
        },
        "val": 12
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "Two different dice are tossed together. Find the probability <br/> (i) that the number on each die is even. <br/> (ii) that the sum of numbers appearing on the two dice is 5.",
        "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": "ch15a50.jpg",
          "width": "387",
          "height": "243"
        },
        "val": 13
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "An integer is chosen at random between 1 and 100. Find the probability that it is: <br/> (i) divisible by 8. <br/> (ii) not divisible by 8",
        "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": "ch15a51.jpg",
          "width": "449",
          "height": "159"
        },
        "val": 14
      },
	  {
        "heading": "Very short answer type questions.",
        "qus": "A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. Find the probability that the selected ticket has a number which is multiple of 5.",
        "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": "ch15a52.jpg",
          "width": "557",
          "height": "158"
        },
        "val": 15
      }
	],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    [],
    []
  ],
  "mcq": "ch15_mcq",
  "co": "ch15_co",
  "nf": "ch15_nf",
  "saq": "ch15_saq",
  "fib": "ch15_fib",
  "vsaq": "ch15_vsaq",
  "tf": "ch15_tf",
  "mtf": "ch15_mtf",
  "laq": "ch15_laq",
  "jtf": "ch15_jtf",
  "ctt": "ch15_ctt",
  "snc": "ch15_snc",
  "grade": "Grade 10",
  "gowf": "ch15_gowf",
  "afow": "ch15_afow",
  "cs": "ch15_cs",
  "ctco": "ch15_ctco",
  "map": "ch15_map",
  "dtf": "ch15_dtf",
  "grf": "ch15_grf",
  "afq": "ch15_afq",
  "pbq": "ch15_pbq",
  "yn": "ch15_yn",
  "un": "ch15_un"
}

]

Youez - 2016 - github.com/yon3zu
LinuXploit