����JFIFXX�����    $.' ",#(7),01444'9=82<.342  2!!22222222222222222222222222222222222222222222222222����"��4�� ���,�PG"Z_�4�˷����kjز�Z�,F+��_z�,�© �����zh6�٨�ic�fu���#ډb���_�N�?��wQ���5-�~�I���8����TK<5o�Iv-�����k�_U_�����~b�M��d����Ӝ�U�Hh��?]��E�w��Q���k�{��_}qFW7HTՑ��Y��F�?_�'ϔ��_�Ջt��=||I ��6�έ"�����D���/[�k�9���Y�8ds|\���Ҿp6�Ҵ���]��.����6�z<�v��@]�i%��$j��~�g��J>��no����pM[me�i$[����s�o�ᘨ�˸ nɜG-�ĨU�ycP�3.DB�li�;��hj���x7Z^�N�h������N3u{�:j�x�힞��#M&��jL P@_���� P��&��o8������9�����@Sz6�t7#O�ߋ �s}Yf�T���lmr����Z)'N��k�۞p����w\�Tȯ?�8`�O��i{wﭹW�[�r�� ��Q4F�׊���3m&L�=��h3����z~��#�\�l :�F,j@�� ʱ�wQT����8�"kJO���6�֚l����}���R�>ډK���]��y����&����p�}b��;N�1�m�r$�|��7�>e�@B�TM*-iH��g�D�)� E�m�|�ؘbҗ�a��Ҿ����t4���o���G��*oCN�rP���Q��@z,|?W[0�����:�n,jWiE��W��$~/�hp\��?��{(�0���+�Y8rΟ�+����>S-S����VN;�}�s?.����� w�9��˟<���Mq4�Wv'��{)0�1mB��V����W[�����8�/<� �%���wT^�5���b��)iM� pg�N�&ݝ��VO~�q���u���9� ����!��J27����$O-���! �:�%H��� ـ����y�ΠM=t{!S�� oK8������t<����è:a������[�����ա�H���~��w��Qz`�po�^ ����Q��n� �,uu�C�$ ^���,������8�#��:�6��e�|~���!�3�3.�\0��q��o�4`.|� ����y�Q�`~;�d�ׯ,��O�Zw�������`73�v�܋�<���Ȏ�� ـ4k��5�K�a�u�=9Yd��$>x�A�&�� j0� ���vF��� Y�|�y��� ~�6�@c��1vOp�Ig����4��l�OD���L����� R���c���j�_�uX6��3?nk��Wy�f;^*B� ��@�~a�`��Eu������+���6�L��.ü>��}y���}_�O�6�͐�:�YrG�X��kG�����l^w���~㒶sy��Iu�!� W ��X��N�7BV��O��!X�2����wvG�R�f�T#�����t�/?���%8�^�W�aT��G�cL�M���I��(J����1~�8�?aT ���]����AS�E��(��*E}� 2��#I/�׍qz��^t�̔���b�Yz4x���t�){ OH��+(E��A&�N�������XT��o��"�XC��'���)}�J�z�p� ��~5�}�^����+�6����w��c��Q�|Lp�d�H��}�(�.|����k��c4^�"�����Z?ȕ ��a<�L�!039C� �Eu�C�F�Ew�ç ;�n?�*o���B�8�bʝ���'#Rqf���M}7����]����s2tcS{�\icTx;�\��7K���P���ʇ Z O-��~��c>"��?�������P��E��O�8��@�8��G��Q�g�a�Վ���󁶠�䧘��_%#r�>�1�z�a��eb��qcPѵ��n���#L��� =��׀t� L�7�`��V���A{�C:�g���e@�w1 Xp3�c3�ġ����p��M"'-�@n4���fG��B3�DJ�8[Jo�ߐ���gK)ƛ��$���� ���8�3�����+���� �����6�ʻ���� ���S�kI�*KZlT _`���?��K����QK�d����B`�s}�>���`��*�>��,*@J�d�oF*����弝��O}�k��s��]��y�ߘ��c1G�V���<=�7��7����6�q�PT��tXԀ�!9*4�4Tހ3XΛex�46���Y��D ����� �BdemDa����\�_l,��G�/���֌7���Y�](�xTt^%�GE�����4�}bT���ڹ�����;Y)���B�Q��u��>J/J �⮶.�XԄ��j�ݳ�+E��d ��r�5�_D�1 ��o�� �B�x�΢�#���<��W�����8���R6�@g�M�.��� dr�D��>(otU��@x=��~v���2� ӣ�d�oBd��3�eO�6�㣷�����ݜ6��6Y��Qz`��S��{���\P�~z m5{J/L��1������<�e�ͅPu�b�]�ϔ���'������f�b� Zpw��c`"��i���BD@:)ִ�:�]��hv�E�w���T�l��P���"Ju�}��وV J��G6��. J/�Qgl߭�e�����@�z�Zev2u�)]կ�����7x���s�M�-<ɯ�c��r�v�����@��$�ޮ}lk���a���'����>x��O\�ZFu>�����ck#��&:��`�$�ai�>2Δ����l���oF[h��lE�ܺ�Πk:)���`�� $[6�����9�����kOw�\|���8}������ބ:��񶐕��I�A1/�=�2[�,�!��.}gN#�u����b��� ~��݊��}34q����d�E��Lc��$��"�[q�U�硬g^��%B �z���r�pJ�ru%v\h1Y�ne`ǥ:g���pQM~�^�Xi� ��`S�:V29.�P���V�?B�k�� AEvw%�_�9C�Q����wKekPؠ�\�;Io d�{ ߞo�c1eP����\� `����E=���@K<�Y���eڼ�J���w����{av�F�'�M�@/J��+9p���|]�����Iw &`��8���&M�hg��[�{��Xj��%��Ӓ�$��(����ʹN���<>�I���RY���K2�NPlL�ɀ)��&e����B+ь����( � �JTx���_?EZ� }@ 6�U���뙢ط�z��dWI�n` D����噥�[��uV��"�G&Ú����2g�}&m��?ċ�"����Om#��������� ��{�ON��"S�X��Ne��ysQ���@Fn��Vg���dX�~nj�]J�<�K]:��FW��b�������62�=��5f����JKw��bf�X�55��~J �%^����:�-�QIE��P��v�nZum� z � ~ə ���� ���ة����;�f��\v���g�8�1��f24;�V���ǔ�)����9���1\��c��v�/'Ƞ�w�������$�4�R-��t���� e�6�/�ġ �̕Ecy�J���u�B���<�W�ַ~�w[B1L۲�-JS΂�{���΃������A��20�c#��@ 0!1@AP"#2Q`$3V�%45a6�FRUq��� ����^7ׅ,$n�������+��F�`��2X'��0vM��p�L=������5��8������u�p~���.�`r�����\���O��,ư�0oS ��_�M�����l���4�kv\JSd���x���SW�<��Ae�IX����������$I���w�:S���y���›R��9�Q[���,�5�;�@]�%���u�@ *ro�lbI �� ��+���%m:�͇ZV�����u�̉����θau<�fc�.����{�4Ա� �Q����*�Sm��8\ujqs]{kN���)qO�y�_*dJ�b�7���yQqI&9�ԌK!�M}�R�;������S�T���1���i[U�ɵz�]��U)V�S6���3$K{�ߊ<�(� E]Զ[ǼENg�����'�\?#)Dkf��J���o��v���'�%ƞ�&K�u�!��b�35LX�Ϸ��63$K�a�;�9>,R��W��3�3� d�JeTYE.Mϧ��-�o�j3+y��y^�c�������VO�9NV\nd�1 ��!͕_)a�v;����թ�M�lWR1��)El��P;��yوÏ�u 3�k�5Pr6<�⒲l�!˞*��u־�n�!�l:����UNW ��%��Chx8vL'��X�@��*��)���̮��ˍ��� ���D-M�+J�U�kvK����+�x8��cY������?�Ԡ��~3mo��|�u@[XeY�C�\Kp�x8�oC�C�&����N�~3-H���� ��MX�s�u<`���~"WL��$8ξ��3���a�)|:@�m�\���^�`�@ҷ)�5p+��6���p�%i)P M���ngc�����#0Aruz���RL+xSS?���ʮ}()#�t��mˇ!��0}}y����<�e� �-ή�Ԩ��X������ MF���ԙ~l L.3���}�V뽺�v�����멬��Nl�)�2����^�Iq��a��M��qG��T�����c3#������3U�Ǎ���}��לS�|qa��ڃ�+���-��2�f����/��bz��ڐ�� �ݼ[2�ç����k�X�2�* �Z�d���J�G����M*9W���s{��w���T��x��y,�in�O�v��]���n����P�$�JB@=4�OTI�n��e�22a\����q�d���%�$��(���:���: /*�K[PR�fr\nڙdN���F�n�$�4�[�� U�zƶ����� �mʋ���,�ao�u 3�z� �x��Kn����\[��VFmbE;�_U��&V�Gg�]L�۪&#n%�$ɯ�dG���D�TI=�%+AB�Ru#��b4�1�»x�cs�YzڙJG��f��Il��d�eF'T� iA��T���uC�$����Y��H?����[!G`}���ͪ� �纤Hv\������j�Ex�K���!���OiƸ�Yj�+u-<���'q����uN�*�r\��+�]���<�wOZ.fp�ێ��,-*)V?j-kÊ#�`�r��dV����(�ݽBk�����G�ƛk�QmUڗe��Z���f}|����8�8��a���i��3'J�����~G_�^���d�8w������ R�`(�~�.��u���l�s+g�bv���W���lGc}��u���afE~1�Ue������Z�0�8�=e�� f@/�jqEKQQ�J��oN��J���W5~M>$6�Lt�;$ʳ{���^��6�{����v6���ķܰg�V�cnn �~z�x�«�,2�u�?cE+Ș�H؎�%�Za�)���X>uW�Tz�Nyo����s���FQƤ��$��*�&�LLXL)�1�" L��eO��ɟ�9=���:t��Z���c��Ž���Y?�ӭV�wv�~,Y��r�ۗ�|�y��GaF�����C�����.�+� ���v1���fήJ�����]�S��T��B��n5sW}y�$��~z�'�c ��8 ��� ,! �p��VN�S��N�N�q��y8z˱�A��4��*��'������2n<�s���^ǧ˭P�Jޮɏ�U�G�L�J�*#��<�V��t7�8����TĜ>��i}K%,���)[��z�21z ?�N�i�n1?T�I�R#��m-�����������������1����lA�`��fT5+��ܐ�c�q՝��ʐ��,���3�f2U�եmab��#ŠdQ�y>\��)�SLY����w#��.���ʑ�f��� ,"+�w�~�N�'�c�O�3F�������N<���)j��&��,-� �љ���֊�_�zS���TǦ����w�>��?�������n��U仆�V���e�����0���$�C�d���rP �m�׈e�Xm�Vu� �L��.�bֹ��� �[Դaզ���*��\y�8�Է:�Ez\�0�Kq�C b��̘��cө���Q��=0Y��s�N��S.���3.���O�o:���#���v7�[#߫ ��5�܎�L���Er4���9n��COWlG�^��0k�%<���ZB���aB_���������'=��{i�v�l�$�uC���mƎҝ{�c㱼�y]���W�i ��ߧc��m�H� m�"�"�����;Y�ߝ�Z�Ǔ�����:S#��|}�y�,/k�Ld� TA�(�AI$+I3��;Y*���Z��}|��ӧO��d�v��..#:n��f>�>���ȶI�TX��� 8��y����"d�R�|�)0���=���n4��6ⲑ�+��r<�O�܂~zh�z����7ܓ�HH�Ga롏���nCo�>������a ���~]���R���̲c?�6(�q�;5%� |�uj�~z8R=X��I�V=�|{v�Gj\gc��q����z�؋%M�ߍ����1y��#��@f^���^�>N�����#x#۹��6�Y~�?�dfPO��{��P�4��V��u1E1J �*|���%���JN��`eWu�zk M6���q t[�� ��g�G���v��WIG��u_ft����5�j�"�Y�:T��ɐ���*�;� e5���4����q$C��2d�}���� _S�L#m�Yp��O�.�C�;��c����Hi#֩%+) �Ӎ��ƲV���SYź��g |���tj��3�8���r|���V��1#;.SQ�A[���S������#���`n�+���$��$I �P\[�@�s��(�ED�z���P��])8�G#��0B��[ى��X�II�q<��9�~[Z멜�Z�⊔IWU&A>�P~�#��dp<�?����7���c��'~���5 ��+$���lx@�M�dm��n<=e�dyX��?{�|Aef ,|n3�<~z�ƃ�uۧ�����P��Y,�ӥQ�*g�#먙R�\���;T��i,��[9Qi歉����c>]9�� ��"�c��P�� �Md?٥��If�ت�u��k��/����F��9�c*9��Ǎ:�ØF���z�n*�@|I�ށ9����N3{'��[�'ͬ�Ҳ4��#}��!�V� Fu��,�,mTIk���v C�7v���B�6k�T9��1�*l� '~��ƞF��lU��'�M ����][ΩũJ_�{�i�I�n��$���L�� j��O�dx�����kza۪��#�E��Cl����x˘�o�����V���ɞ�ljr��)�/,�߬h�L��#��^��L�ф�,íMƁe�̩�NB�L�����iL����q�}��(��q��6IçJ$�W�E$��:������=#����(�K�B����zђ <��K(�N�۫K�w��^O{!����)�H���>x�������lx�?>Պ�+�>�W���,Ly!_�D���Ō�l���Q�!�[ �S����J��1��Ɛ�Y}��b,+�Lo�x�ɓ)����=�y�oh�@�꥟/��I��ѭ=��P�y9��� �ۍYӘ�e+�p�Jnϱ?V\SO%�(�t� ���=?MR�[Ș�����d�/ ��n�l��B�7j� ��!�;ӥ�/�[-���A�>�dN�sLj ��,ɪv��=1c�.SQ�O3�U���ƀ�ܽ�E����������̻��9G�ϷD�7(�}��Ävӌ\�y�_0[w ���<΍>����a_��[0+�L��F.�޺��f�>oN�T����q;���y\��bՃ��y�jH�<|q-eɏ�_?_9+P���Hp$�����[ux�K w�Mw��N�ی'$Y2�=��q���KB��P��~������Yul:�[<����F1�2�O���5=d����]Y�sw:���Ϯ���E��j,_Q��X��z`H1,#II ��d�wr��P˂@�ZJV����y$�\y�{}��^~���[:N����ߌ�U�������O��d�����ؾe��${p>G��3c���Ė�lʌ�� ת��[��`ϱ�-W����dg�I��ig2��� ��}s ��ؤ(%#sS@���~���3�X�nRG�~\jc3�v��ӍL��M[JB�T��s3}��j�Nʖ��W����;7��ç?=X�F=-�=����q�ߚ���#���='�c��7���ڑW�I(O+=:uxq�������������e2�zi+�kuG�R��������0�&e�n���iT^J����~\jy���p'dtG��s����O��3����9* �b#Ɋ�� p������[Bws�T�>d4�ۧs���nv�n���U���_�~,�v����ƜJ1��s�� �QIz��)�(lv8M���U=�;����56��G���s#�K���MP�=��LvyGd��}�VwWBF�'�à �?MH�U�g2�� ����!�p�7Q��j��ڴ����=��j�u��� Jn�A s���uM������e��Ɔ�Ҕ�!)'��8Ϣ�ٔ��ޝ(��Vp���צ֖d=�IC�J�Ǡ{q������kԭ�߸���i��@K����u�|�p=..�*+����x�����z[Aqġ#s2a�Ɗ���RR�)*HRsi�~�a &f��M��P����-K�L@��Z��Xy�'x�{}��Zm+���:�)�) IJ�-i�u���� ���ܒH��'�L(7�y�GӜq���� j��� 6ߌg1�g�o���,kر���tY�?W,���p���e���f�OQS��!K�۟cҒA�|ս�j�>��=⬒��˧L[�� �߿2JaB~R��u�:��Q�] �0H~���]�7��Ƽ�I���(}��cq '�ήET���q�?f�ab���ӥvr� �)o��-Q��_'����ᴎo��K������;��V���o��%���~OK ����*��b�f:���-ťIR��`B�5!RB@���ï�� �u �̯e\�_U�_������� g�ES��3�������QT��a����x����U<~�c?�*�#]�MW,[8O�a�x��]�1bC|踤�P��lw5V%�)�{t�<��d��5���0i�XSU��m:��Z�┵�i�"��1�^B�-��P�hJ��&)O��*�D��c�W��vM��)����}���P��ܗ-q����\mmζZ-l@�}��a��E�6��F�@��&Sg@���ݚ�M����� ȹ 4����#p�\H����dYDo�H���"��\��..R�B�H�z_�/5˘����6��KhJR��P�mƶi�m���3�,#c�co��q�a)*Pt����R�m�k�7x�D�E�\Y�閣_X�<���~�)���c[[�BP����6�Yq���S��0����%_����;��Àv�~�| VS؇ ��'O0��F0��\���U�-�d@�����7�SJ*z��3n��y��P����O���������m�~�P�3|Y��ʉr#�C�<�G~�.,! ���bqx���h~0=��!ǫ�jy����l�O,�[B��~��|9��ٱ����Xly�#�i�B��g%�S��������tˋ���e���ې��\[d�t)��.+u�|1 ������#�~Oj����hS�%��i.�~X���I�H�m��0n���c�1uE�q��cF�RF�o���7� �O�ꮧ� ���ۛ{��ʛi5�rw?׌#Qn�TW��~?y$��m\�\o����%W� ?=>S�N@�� �Ʈ���R����N�)�r"C�:��:����� �����#��qb��Y�. �6[��2K����2u�Ǧ�HYR��Q�MV��� �G�$��Q+.>�����nNH��q�^��� ����q��mM��V��D�+�-�#*�U�̒ ���p욳��u:�������IB���m���PV@O���r[b= �� ��1U�E��_Nm�yKbN�O���U�}�the�`�|6֮P>�\2�P�V���I�D�i�P�O;�9�r�mAHG�W�S]��J*�_�G��+kP�2����Ka�Z���H�'K�x�W�MZ%�O�YD�Rc+o��?�q��Ghm��d�S�oh�\�D�|:W������UA�Qc yT�q������~^�H��/��#p�CZ���T�I�1�ӏT����4��"�ČZ�����}��`w�#�*,ʹ�� ��0�i��課�Om�*�da��^gJ݅{���l�e9uF#T�ֲ��̲�ٞC"�q���ߍ ոޑ�o#�XZTp����@ o�8��(jd��xw�]�,f���`~�|,s��^����f�1���t��|��m�򸄭/ctr��5s��7�9Q�4�H1꠲BB@l9@���C�����+�wp�xu�£Yc�9��?`@#�o�mH�s2��)�=��2�.�l����jg�9$�Y�S�%*L������R�Y������7Z���,*=�䷘$�������arm�o�ϰ���UW.|�r�uf����IGw�t����Zwo��~5 ��YյhO+=8fF�)�W�7�L9lM�̘·Y���֘YLf�큹�pRF���99.A �"wz��=E\Z���'a� 2��Ǚ�#;�'}�G���*��l��^"q��+2FQ� hj��kŦ��${���ޮ-�T�٭cf�|�3#~�RJ����t��$b�(R��(����r���dx� >U b�&9,>���%E\� Ά�e�$��'�q't��*�א���ެ�b��-|d���SB�O�O��$�R+�H�)�܎�K��1m`;�J�2�Y~9��O�g8=vqD`K[�F)k�[���1m޼c��n���]s�k�z$@��)!I �x՝"v��9=�ZA=`Ɠi �:�E��)`7��vI��}d�YI�_ �o�:ob���o ���3Q��&D&�2=�� �Ά��;>�h����y.*ⅥS������Ӭ�+q&����j|UƧ����}���J0��WW< ۋS�)jQR�j���Ư��rN)�Gű�4Ѷ(�S)Ǣ�8��i��W52���No˓� ۍ%�5brOn�L�;�n��\G����=�^U�dI���8$�&���h��'���+�(������cȁ߫k�l��S^���cƗjԌE�ꭔ��gF���Ȓ��@���}O���*;e�v�WV���YJ\�]X'5��ղ�k�F��b 6R�o՜m��i N�i����>J����?��lPm�U��}>_Z&�KK��q�r��I�D�Չ~�q�3fL�:S�e>���E���-G���{L�6p�e,8��������QI��h��a�Xa��U�A'���ʂ���s�+טIjP�-��y�8ۈZ?J$��W�P� ��R�s�]��|�l(�ԓ��sƊi��o(��S0��Y� 8�T97.�����WiL��c�~�dxc�E|�2!�X�K�Ƙਫ਼�$((�6�~|d9u+�qd�^3�89��Y�6L�.I�����?���iI�q���9�)O/뚅����O���X��X�V��ZF[�یgQ�L��K1���RҖr@v�#��X�l��F���Нy�S�8�7�kF!A��sM���^rkp�jP�DyS$N���q��nxҍ!U�f�!eh�i�2�m���`�Y�I�9r�6� �TF���C}/�y�^���Η���5d�'��9A-��J��>{�_l+�`��A���[�'��յ�ϛ#w:݅�%��X�}�&�PSt�Q�"�-��\縵�/����$Ɨh�Xb�*�y��BS����;W�ջ_mc�����vt?2}1�;qS�d�d~u:2k5�2�R�~�z+|HE!)�Ǟl��7`��0�<�,�2*���Hl-��x�^����'_TV�gZA�'j� ^�2Ϊ��N7t�����?w�� �x1��f��Iz�C-Ȗ��K�^q�;���-W�DvT�7��8�Z�������� hK�(P:��Q- �8�n�Z���܃e貾�<�1�YT<�,�����"�6{/ �?�͟��|1�:�#g��W�>$����d��J��d�B��=��jf[��%rE^��il:��B���x���Sּ�1հ��,�=��*�7 fcG��#q� �eh?��2�7�����,�!7x��6�n�LC�4x��},Geǝ�tC.��vS �F�43��zz\��;QYC,6����~;RYS/6���|2���5���v��T��i����������mlv��������&� �nRh^ejR�LG�f���? �ۉҬܦƩ��|��Ȱ����>3����!v��i�ʯ�>�v��オ�X3e���_1z�Kȗ\<������!�8���V��]��?b�k41�Re��T�q��mz��TiOʦ�Z��Xq���L������q"+���2ۨ��8}�&N7XU7Ap�d�X��~�׿��&4e�o�F��� �H����O���č�c�� 懴�6���͉��+)��v;j��ݷ�� �UV�� i��� j���Y9GdÒJ1��詞�����V?h��l����l�cGs�ځ�������y�Ac�����\V3�? �� ܙg�>qH�S,�E�W�[�㺨�uch�⍸�O�}���a��>�q�6�n6����N6�q������N ! 1AQaq�0@����"2BRb�#Pr���3C`��Scst���$4D���%Td�� ?���N����a��3��m���C���w��������xA�m�q�m���m������$����4n淿t'��C"w��zU=D�\R+w�p+Y�T�&�պ@��ƃ��3ޯ?�Aﶂ��aŘ���@-�����Q�=���9D��ռ�ѻ@��M�V��P��܅�G5�f�Y<�u=,EC)�<�Fy'�"�&�չ�X~f��l�KԆV��?�� �W�N����=(� �;���{�r����ٌ�Y���h{�١������jW����P���Tc�����X�K�r��}���w�R��%��?���E��m�� �Y�q|����\lEE4���r���}�lsI�Y������f�$�=�d�yO����p�����yBj8jU�o�/�S��?�U��*������ˍ�0������u�q�m [�?f����a�� )Q�>����6#������� ?����0UQ����,IX���(6ڵ[�DI�MNލ�c&���υ�j\��X�R|,4��� j������T�hA�e��^���d���b<����n�� �즇�=!���3�^�`j�h�ȓr��jẕ�c�,ٞX����-����a�ﶔ���#�$��]w�O��Ӫ�1y%��L�Y<�wg#�ǝ�̗`�x�xa�t�w��»1���o7o5��>�m뭛C���Uƃߜ}�C���y1Xνm�F8�jI���]����H���ۺиE@I�i;r�8ӭ����V�F�Շ| ��&?�3|x�B�MuS�Ge�=Ӕ�#BE5G�����Y!z��_e��q�р/W>|-�Ci߇�t�1ޯќd�R3�u��g�=0 5��[?�#͏��q�cf���H��{ ?u�=?�?ǯ���}Z��z���hmΔ�BFTW�����<�q�(v� ��!��z���iW]*�J�V�z��gX֧A�q�&��/w���u�gYӘa���; �i=����g:��?2�dž6�ى�k�4�>�Pxs����}������G�9��3 ���)gG�R<>r h�$��'nc�h�P��Bj��J�ҧH� -��N1���N��?��~��}-q!=��_2hc�M��l�vY%UE�@|�v����M2�.Y[|y�"Eï��K�ZF,�ɯ?,q�?v�M 80jx�"�;�9vk�����+ ֧�� �ȺU��?�%�vcV��mA�6��Qg^M����A}�3�nl� QRN�l8�kkn�'�����(��M�7m9و�q���%ޟ���*h$Zk"��$�9��: �?U8�Sl��,,|ɒ��xH(ѷ����Gn�/Q�4�P��G�%��Ա8�N��!� �&�7�;���eKM7�4��9R/%����l�c>�x;������>��C�:�����t��h?aKX�bhe�ᜋ^�$�Iհ �hr7%F$�E��Fd���t��5���+�(M6�t����Ü�UU|zW�=a�Ts�Tg������dqP�Q����b'�m���1{|Y����X�N��b �P~��F^F:����k6�"�j!�� �I�r�`��1&�-$�Bevk:y���#yw��I0��x��=D�4��tU���P�ZH��ڠ底taP��6����b>�xa����Q�#� WeF��ŮNj�p�J* mQ�N����*I�-*�ȩ�F�g�3 �5��V�ʊ�ɮ�a��5F���O@{���NX��?����H�]3��1�Ri_u��������ѕ�� ����0��� F��~��:60�p�͈�S��qX#a�5>���`�o&+�<2�D����: �������ڝ�$�nP���*)�N�|y�Ej�F�5ټ�e���ihy�Z �>���k�bH�a�v��h�-#���!�Po=@k̆IEN��@��}Ll?j�O������߭�ʞ���Q|A07x���wt!xf���I2?Z��<ץ�T���cU�j��]��陎Ltl �}5�ϓ��$�,��O�mˊ�;�@O��jE��j(�ا,��LX���LO���Ц�90�O �.����a��nA���7������j4 ��W��_ٓ���zW�jcB������y՗+EM�)d���N�g6�y1_x��p�$Lv:��9�"z��p���ʙ$��^��JԼ*�ϭ����o���=x�Lj�6�J��u82�A�H�3$�ٕ@�=Vv�]�'�qEz�;I˼��)��=��ɯ���x �/�W(V���p�����$ �m�������u�����񶤑Oqˎ�T����r��㠚x�sr�GC��byp�G��1ߠ�w e�8�$⿄����/�M{*}��W�]˷.�CK\�ުx���/$�WPw���r� |i���&�}�{�X� �>��$-��l���?-z���g����lΆ���(F���h�vS*���b���߲ڡn,|)mrH[���a�3�ר�[1��3o_�U�3�TC�$��(�=�)0�kgP���� ��u�^=��4 �WYCҸ:��vQ�ר�X�à��tk�m,�t*��^�,�}D*� �"(�I��9R����>`�`��[~Q]�#af��i6l��8���6�:,s�s�N6�j"�A4���IuQ��6E,�GnH��zS�HO�uk�5$�I�4��ؤ�Q9�@��C����wp�BGv[]�u�Ov���0I4���\��y�����Q�Ѹ��~>Z��8�T��a��q�ޣ;z��a���/��S��I:�ܫ_�|������>=Z����8:�S��U�I�J��"IY���8%b8���H��:�QO�6�;7�I�S��J��ҌAά3��>c���E+&jf$eC+�z�;��V����� �r���ʺ������my�e���aQ�f&��6�ND��.:��NT�vm�<- u���ǝ\MvZY�N�NT��-A�>jr!S��n�O 1�3�Ns�%�3D@���`������ܟ 1�^c<���� �a�ɽ�̲�Xë#�w�|y�cW�=�9I*H8�p�^(4���՗�k��arOcW�tO�\�ƍR��8����'�K���I�Q�����?5�>[�}��yU�ײ -h��=��% q�ThG�2�)���"ו3]�!kB��*p�FDl�A���,�eEi�H�f�Ps�����5�H:�Փ~�H�0Dت�D�I����h�F3�������c��2���E��9�H��5�zԑ�ʚ�i�X�=:m�xg�hd(�v����׊�9iS��O��d@0ڽ���:�p�5�h-��t�&���X�q�ӕ,��ie�|���7A�2���O%P��E��htj��Y1��w�Ѓ!����  ���� ࢽ��My�7�\�a�@�ţ�J �4�Ȼ�F�@o�̒?4�wx��)��]�P��~�����u�����5�����7X ��9��^ܩ�U;Iꭆ 5 �������eK2�7(�{|��Y׎ �V��\"���Z�1� Z�����}��(�Ǝ"�1S���_�vE30>���p;� ΝD��%x�W�?W?v����o�^V�i�d��r[��/&>�~`�9Wh��y�;���R��� ;;ɮT��?����r$�g1�K����A��C��c��K��l:�'��3 c�ﳯ*"t8�~l��)���m��+U,z��`(�>yJ�?����h>��]��v��ЍG*�{`��;y]��I�T� ;c��NU�fo¾h���/$���|NS���1�S�"�H��V���T���4��uhǜ�]�v;���5�͠x��'C\�SBpl���h}�N����� A�Bx���%��ޭ�l��/����T��w�ʽ]D�=����K���ž�r㻠l4�S�O?=�k �M:� ��c�C�a�#ha���)�ѐxc�s���gP�iG��{+���x���Q���I= �� z��ԫ+ �8"�k�ñ�j=|����c ��y��CF��/��*9ж�h{ �?4�o� ��k�m�Q�N�x��;�Y��4膚�a�w?�6�>e]�����Q�r�:����g�,i"�����ԩA�*M�<�G��b�if��l^M��5� �Ҩ�{����6J��ZJ�����P�*�����Y���ݛu�_4�9�I8�7���������,^ToR���m4�H��?�N�S�ѕw��/S��甍�@�9H�S�T��t�ƻ���ʒU��*{Xs�@����f�����֒Li�K{H�w^���������Ϥm�tq���s� ���ք��f:��o~s��g�r��ט� �S�ѱC�e]�x���a��) ���(b-$(�j>�7q�B?ӕ�F��hV25r[7 Y� }L�R��}����*sg+��x�r�2�U=�*'WS��ZDW]�WǞ�<��叓���{�$�9Ou4��y�90-�1�'*D`�c�^o?(�9��u���ݐ��'PI&� f�Jݮ�������:wS����jfP1F:X �H�9dԯ���˝[�_54 �}*;@�ܨ�� ð�yn�T���?�ןd�#���4rG�ͨ��H�1�|-#���Mr�S3��G�3�����)�.᧏3v�z֑��r����$G"�`j �1t��x0<Ɔ�Wh6�y�6��,œ�Ga��gA����y��b��)��h�D��ß�_�m��ü �gG;��e�v��ݝ�nQ� ��C����-�*��o���y�a��M��I�>�<���]obD��"�:���G�A��-\%LT�8���c�)��+y76���o�Q�#*{�(F�⽕�y����=���rW�\p���۩�c���A���^e6��K������ʐ�cVf5$�'->���ՉN"���F�"�UQ@�f��Gb~��#�&�M=��8�ט�JNu9��D��[̤�s�o�~������ G��9T�tW^g5y$b��Y'��س�Ǵ�=��U-2 #�MC�t(�i� �lj�@Q 5�̣i�*�O����s�x�K�f��}\��M{E�V�{�υ��Ƈ�����);�H����I��fe�Lȣr�2��>��W�I�Ȃ6������i��k�� �5�YOxȺ����>��Y�f5'��|��H+��98pj�n�.O�y�������jY��~��i�w'������l�;�s�2��Y��:'lg�ꥴ)o#'Sa�a�K��Z� �m��}�`169�n���"���x��I ��*+� }F<��cГ���F�P�������ֹ*�PqX�x۩��,� ��N�� �4<-����%����:��7����W���u�`����� $�?�I��&����o��o��`v�>��P��"��l���4��5'�Z�gE���8���?��[�X�7(��.Q�-��*���ތL@̲����v��.5���[��=�t\+�CNܛ��,g�SQnH����}*F�G16���&:�t��4ُ"A��̣��$�b �|����#rs��a�����T�� ]�<�j��BS�('$�ɻ� �wP;�/�n��?�ݜ��x�F��yUn�~mL*-�������Xf�wd^�a�}��f�,=t�׵i�.2/wpN�Ep8�OР���•��R�FJ� 55TZ��T �ɭ�<��]��/�0�r�@�f��V��V����Nz�G��^���7hZi����k��3�,kN�e|�vg�1{9]_i��X5y7� 8e]�U����'�-2,���e"����]ot�I��Y_��n�(JҼ��1�O ]bXc���Nu�No��pS���Q_���_�?i�~�x h5d'�(qw52] ��'ޤ�q��o1�R!���`ywy�A4u���h<קy���\[~�4�\ X�Wt/� 6�����n�F�a8��f���z �3$�t(���q��q�x��^�XWeN'p<-v�!�{�(>ӽDP7��ո0�y)�e$ٕv�Ih'Q�EA�m*�H��RI��=:��� ���4牢) �%_iN�ݧ�l]� �Nt���G��H�L��� ɱ�g<���1V�,�J~�ٹ�"K��Q�� 9�HS�9�?@��k����r�;we݁�]I�!{ �@�G�[�"��`���J:�n]�{�cA�E����V��ʆ���#��U9�6����j�#Y�m\��q�e4h�B�7��C�������d<�?J����1g:ٳ���=Y���D�p�ц� ׈ǔ��1�]26؜oS�'��9�V�FVu�P�h�9�xc�oq�X��p�o�5��Ա5$�9W�V(�[Ak�aY錎qf;�'�[�|���b�6�Ck��)��#a#a˙��8���=äh�4��2��C��4tm^ �n'c���]GQ$[Wҿ��i���vN�{Fu ��1�gx��1┷���N�m��{j-,��x�� Ūm�ЧS�[�s���Gna���䑴�� x�p 8<������97�Q���ϴ�v�aϚG��Rt�Һ׈�f^\r��WH�JU�7Z���y)�vg=����n��4�_)y��D'y�6�]�c�5̪�\� �PF�k����&�c;��cq�$~T�7j ���nç]�<�g ":�to�t}�159�<�/�8������m�b�K#g'I'.W�����6��I/��>v��\�MN��g���m�A�yQL�4u�Lj�j9��#44�t��l^�}L����n��R��!��t��±]��r��h6ٍ>�yҏ�N��fU�� ���� Fm@�8}�/u��jb9������he:A�y�ծw��GpΧh�5����l}�3p468��)U��d��c����;Us/�֔�YX�1�O2��uq�s��`hwg�r~�{ R��mhN��؎*q 42�*th��>�#���E����#��Hv�O����q�}�����6�e��\�,Wk�#���X��b>��p}�դ��3���T5��†��6��[��@�P�y*n��|'f�֧>�lư΂�̺����SU�'*�q�p�_S�����M�� '��c�6�����m�� ySʨ;M��r���Ƌ�m�Kxo,���Gm�P��A�G�:��i��w�9�}M(�^�V��$ǒ�ѽ�9���|���� �a����J�SQ�a���r�B;����}���ٻ֢�2�%U���c�#�g���N�a�ݕ�'�v�[�OY'��3L�3�;,p�]@�S��{ls��X�'���c�jw�k'a�.��}�}&�� �dP�*�bK=ɍ!����;3n�gΊU�ߴmt�'*{,=SzfD� A��ko~�G�aoq�_mi}#�m�������P�Xhύ����mxǍ�΂���巿zf��Q���c���|kc�����?���W��Y�$���_Lv����l߶��c���`?����l�j�ݲˏ!V��6����U�Ђ(A���4y)H���p�Z_�x��>���e��R��$�/�`^'3qˏ�-&Q�=?��CFVR �D�fV�9��{�8g�������n�h�(P"��6�[�D���< E�����~0<@�`�G�6����Hг�cc�� �c�K.5��D��d�B���`?�XQ��2��ٿyqo&+�1^� DW�0�ꊩ���G�#��Q�nL3��c���������/��x ��1�1[y�x�პCW��C�c�UĨ80�m�e�4.{�m��u���I=��f�����0QRls9���f���������9���~f�����Ǩ��a�"@�8���ȁ�Q����#c�ic������G��$���G���r/$W�(��W���V�"��m�7�[m�A�m����bo��D� j����۳� l���^�k�h׽����� ��#� iXn�v��eT�k�a�^Y�4�BN��ĕ��0 !01@Q"2AaPq3BR������?���@4�Q�����T3,���㺠�W�[=JK�Ϟ���2�r^7��vc�:�9 �E�ߴ�w�S#d���Ix��u��:��Hp��9E!�� V 2;73|F��9Y���*ʬ�F��D����u&���y؟��^EA��A��(ɩ���^��GV:ݜDy�`��Jr29ܾ�㝉��[���E;Fzx��YG��U�e�Y�C���� ����v-tx����I�sם�Ę�q��Eb�+P\ :>�i�C'�;�����k|z�رn�y]�#ǿb��Q��������w�����(�r|ӹs��[�D��2v-%��@;�8<a���[\o[ϧw��I!��*0�krs)�[�J9^��ʜ��p1)� "��/_>��o��<1����A�E�y^�C��`�x1'ܣn�p��s`l���fQ��):�l����b>�Me�jH^?�kl3(�z:���1ŠK&?Q�~�{�ٺ�h�y���/�[��V�|6��}�KbX����mn[-��7�5q�94�������dm���c^���h� X��5��<�eޘ>G���-�}�دB�ޟ� ��|�rt�M��V+�]�c?�-#ڛ��^ǂ}���Lkr���O��u�>�-D�ry� D?:ޞ�U��ǜ�7�V��?瓮�"�#���r��չģVR;�n���/_� ؉v�ݶe5d�b9��/O��009�G���5n�W����JpA�*�r9�>�1��.[t���s�F���nQ� V 77R�]�ɫ8����_0<՜�IF�u(v��4��F�k�3��E)��N:��yڮe��P�`�1}�$WS��J�SQ�N�j�ٺ��޵�#l���ј(�5=��5�lǏmoW�v-�1����v,W�mn��߀$x�<����v�j(����c]��@#��1������Ǔ���o'��u+����;G�#�޸��v-lη��/(`i⣍Pm^���ԯ̾9Z��F��������n��1��� ��]�[��)�'������:�֪�W��FC����� �B9،!?���]��V��A�Վ�M��b�w��G F>_DȬ0¤�#�QR�[V��kz���m�w�"��9ZG�7'[��=�Q����j8R?�zf�\a�=��O�U����*oB�A�|G���2�54 �p��.w7� �� ��&������ξxGHp� B%��$g�����t�Џ򤵍z���HN�u�Я�-�'4��0��;_��3 !01"@AQa2Pq#3BR������?��ʩca��en��^��8���<�u#��m*08r��y�N"�<�Ѳ0��@\�p��� �����Kv�D��J8�Fҽ� �f�Y��-m�ybX�NP����}�!*8t(�OqѢ��Q�wW�K��ZD��Δ^e��!� ��B�K��p~�����e*l}z#9ң�k���q#�Ft�o��S�R����-�w�!�S���Ӥß|M�l޶V��!eˈ�8Y���c�ЮM2��tk���� ������J�fS����Ö*i/2�����n]�k�\���|4yX�8��U�P.���Ы[���l��@"�t�<������5�lF���vU�����W��W��;�b�cД^6[#7@vU�xgZv��F�6��Q,K�v��� �+Ъ��n��Ǣ��Ft���8��0��c�@�!�Zq s�v�t�;#](B��-�nῃ~���3g������5�J�%���O������n�kB�ĺ�.r��+���#�N$?�q�/�s�6��p��a����a��J/��M�8��6�ܰ"�*������ɗud"\w���aT(����[��F��U՛����RT�b���n�*��6���O��SJ�.�ij<�v�MT��R\c��5l�sZB>F��<7�;EA��{��E���Ö��1U/�#��d1�a�n.1ě����0�ʾR�h��|�R��Ao�3�m3 ��%�� ���28Q� ��y��φ���H�To�7�lW>����#i`�q���c����a��� �m,B�-j����݋�'mR1Ήt�>��V��p���s�0IbI�C.���1R�ea�����]H�6����������4B>��o��](��$B���m�����a�!=��?�B� K�Ǿ+�Ծ"�n���K��*��+��[T#�{E�J�S����Q�����s�5�:�U�\wĐ�f�3����܆&�)����I���Ԇw��E T�lrTf6Q|R�h:��[K�� �z��c֧�G�C��%\��_�a�84��HcO�bi��ؖV��7H �)*ģK~Xhչ0��4?�0��� �E<���}3���#���u�?�� ��|g�S�6ꊤ�|�I#Hڛ� �ա��w�X��9��7���Ŀ%�SL��y6č��|�F�a 8���b��$�sק�h���b9RAu7�˨p�Č�_\*w��묦��F ����4D~�f����|(�"m���NK��i�S�>�$d7SlA��/�²����SL��|6N�}���S�˯���g��]6��; �#�.��<���q'Q�1|KQ$�����񛩶"�$r�b:���N8�w@��8$�� �AjfG|~�9F ���Y��ʺ��Bwؒ������M:I岎�G��`s�YV5����6��A �b:�W���G�q%l�����F��H���7�������Fsv7��k�� 403WebShell
403Webshell
Server IP : 54.89.25.11  /  Your IP : 216.73.216.255
Web Server : Apache/2.4.7 (Ubuntu)
System : Linux ip-172-31-88-18 3.13.0-74-generic #118-Ubuntu SMP Thu Dec 17 22:52:10 UTC 2015 x86_64
User : www-data ( 33)
PHP Version : 5.5.9-1ubuntu4.24
Disable Function : pcntl_alarm,pcntl_fork,pcntl_waitpid,pcntl_wait,pcntl_wifexited,pcntl_wifstopped,pcntl_wifsignaled,pcntl_wexitstatus,pcntl_wtermsig,pcntl_wstopsig,pcntl_signal,pcntl_signal_dispatch,pcntl_get_last_error,pcntl_strerror,pcntl_sigprocmask,pcntl_sigwaitinfo,pcntl_sigtimedwait,pcntl_exec,pcntl_getpriority,pcntl_setpriority,
MySQL : ON  |  cURL : ON  |  WGET : ON  |  Perl : ON  |  Python : ON  |  Sudo : ON  |  Pkexec : ON
Directory :  /var/www/html/kalemon/public/hfit/TG/Class-8/Math/assets/DataJS/

Upload File :
current_dir [ Writeable ] document_root [ Writeable ]

 

Command :

[ Back ]     

Current File : /var/www/html/kalemon/public/hfit/TG/Class-8/Math/assets/DataJS/ch1 - Copy.js
var chpdata=[

{
	"subject": "Mathematics",
	"chapter": "ch1",
	"chapterName": "Chapter 1 - Rational Numbers",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "For any two rational numbers a and b, ______________ is also a rational number.",
				"ans": "(d) All of these",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) a + b",
					"(b) a – b",
					"(c) a × b",
					"(d) All of these"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "a × b = for any two rational numbers a and b.",
				"ans": "(b) b × a",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) b + a",
					"(b) b × a",
					"(c) b – a",
					"(d) None"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"ch1a3.jpg",
					"ch1a4.jpg",
					"ch1a5.jpg",
					"(d) None"
				],
				"pic": {
					"image": "ch1a2.jpg",
					"width": "195",
					"height": "40"
				},
				"ansimg": {
					"image": "ch1a5.jpg",
					"width": "68",
					"height": "36"
				},
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "1 is the ______________ identity for rational numbers.",
				"ans": "(d) All of these",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) multiplicative",
					"(b) additive",
					"(c) Both",
					"(d) None"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "C + 0 = 0 + C = ______________, where C is a rational number.",
				"ans": "(a) C",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) C",
					"(b) 0",
					"(c) 1",
					"(d) –1"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": null,
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"ch1a61.jpg",
					"ch1a62.jpg",
					"ch1a63.jpg",
					"ch1a64.jpg"
				],
				"pic": {
					"image": "ch1a60.jpg",
					"width": "312",
					"height": "36"
				},
				"ansimg": {
					"image": "ch1a62.jpg",
					"width": "57",
					"height": "39"
				},
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "– (– x) is same as",
				"ans": "(b) x",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) –x",
					"(b) x",
					"ch1a65.jpg",
					"ch1a66.jpg"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The reciprocal of –1 is",
				"ans": "(a) –1",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) –1",
					"(b) 1",
					"(c) 0",
					"(d) Not defined"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If x is any rational number, then x+0 is equal to",
				"ans": "(c) x",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 0",
					"(b) – x",
					"(c) x",
					"(d) Not defined"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Multiplicative inverse of a negative rational number is",
				"ans": "(d) a negative rational number",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) a positive rational number",
					"(b) 0",
					"(c) 1",
					"(d) a negative rational number"
				],
				"val": 10
			}
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tFor any two rational numbers a and b, a – b is also a rational number.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tSubtraction is commutative for rational numbers.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tFor any three rational numbers a, b and c, a × (b × c) = (a × b) × c.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tZero has no reciprocal.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 4
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tWhen you use distributivity, you split a product as a sum or difference of two products.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 5
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tBetween any two given numbers, we need not  ecessarily get an integer but there will always lie a rational number.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 6
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tUnlike natural numbers and integers, the number of rational numbers between two rational numbers is not definite.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 7
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tWe can use the idea of median also to find rational numbers between any two given rational numbers.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 8
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tWe can use the idea of mean also to find rational numbers between any two given rational numbers.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 9
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "False",
				"code": "TF",
				"pic": {
					"image": "ch1a56.jpg",
					"width": "522",
					"height": "80"
				},
				"val": 10
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "True",
				"code": "TF",
				"pic": {
					"image": "ch1a57.jpg",
					"width": "174",
					"height": "45"
				},
				"val": 11
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "True",
				"code": "TF",
				"pic": {
					"image": "ch1a58.jpg",
					"width": "294",
					"height": "48"
				},
				"val": 12
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "False",
				"code": "TF",
				"pic": {
					"image": "ch1a59.jpg",
					"width": "326",
					"height": "106"
				},
				"val": 13
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe negative of 0 does not exist.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 14
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": null,
				"ans": "rational number",
				"code": "FIB",
				"pic": {
					"image": "ch1a1.jpg",
					"width": "680",
					"height": "56"
				},
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Rational numbers are ______________ under addition.",
				"ans": "closed",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "For any rational number a, a ÷ ______________ is not defined.",
				"ans": "0",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "For any two rational numbers a and b, a + b =  ______________.",
				"ans": "b + a",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "______________ is called the identity for the addition of rational numbers.",
				"ans": "Zero",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "______________ is the multiplicative identity for rational numbers.",
				"ans": "1",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "______________ has no reciprocal.",
				"ans": "Zero",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The number 1 and –1 are their own ______________.",
				"ans": "reciprocals",
				"code": "FIB",
				"val": 8
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The number 1 and –1 are their own ______________.",
				"ans": "-5",
				"code": "FIB",
				"pic": {
					"image": "ch1a25.jpg",
					"width": "239",
					"height": "98"
				},
				"val": 9
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The number 1 and –1 are their own ______________.",
				"ans": "0",
				"code": "FIB",
				"pic": {
					"image": "ch1a26.jpg",
					"width": "258",
					"height": "37"
				},
				"val": 10
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The product of ______________ rational numbers is always a  ______________.",
				"ans": "two, rational number",
				"code": "FIB",
				"val": 11
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The reciprocal of a ______________ rational number is positive rational number.",
				"ans": "positive",
				"code": "FIB",
				"val": 12
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "In a rational number, the ______________ tells the number of equal parts into which the first unit has been divided.",
				"ans": "denominator",
				"code": "FIB",
				"val": 13
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "There are ______________ rational numbers between any two given rational numbers.",
				"ans": "countless",
				"code": "FIB",
				"val": 14
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Zero has ______________ reciprocal.",
				"ans": "no",
				"code": "FIB",
				"val": 15
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The numbers ______________ and ______________ are their own reciprocal.",
				"ans": "1, –1",
				"code": "FIB",
				"val": 16
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "There are ______________ rational numbers between any two rational numbers.",
				"ans": "infinite",
				"code": "FIB",
				"val": 17
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The negative of a negative rational number is always a ______________ rational number.",
				"ans": "positive",
				"code": "FIB",
				"val": 18
			},
			{
				"heading": "Fill in the blanks.",
				"qus": null,
				"ans": "positive",
				"code": "FIB",
				"pic": {
					"image": "ch1a54.jpg",
					"width": "297",
					"height": "54"
				},
				"ansimg": {
					"image": "ch1a55.jpg",
					"width": "20",
					"height": "44"
				},
				"val": 19
			},
		],
		[
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Using appropriate properties find:",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 1,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch1a6.jpg",
					"width": "176",
					"height": "47"
				},
				"ansimg": {
					"image": "ch1a8.jpg",
					"width": "346",
					"height": "277"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Using appropriate properties find:",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 1,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch1a7.jpg",
					"width": "239",
					"height": "46"
				},
				"ansimg": {
					"image": "ch1a9.jpg",
					"width": "346",
					"height": "277"
				}
			},
		],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "Write the additive inverse of each of the following.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 1,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch1a10.jpg",
					"width": "157",
					"height": "112"
				},
				"ansimg": {
					"image": "ch1a11.jpg",
					"width": "343",
					"height": "112"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Verify that – (–x) = x for",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 2,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch1a12.jpg",
					"width": "173",
					"height": "43"
				},
				"ansimg": {
					"image": "ch1a13.jpg",
					"width": "550",
					"height": "137"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the multiplicative inverse of the following:",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 3,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch1a14.jpg",
					"width": "202",
					"height": "125"
				},
				"ansimg": {
					"image": "ch1a15.jpg",
					"width": "412",
					"height": "125"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Name the property under multiplication used in each of the following:",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 4,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch1a16.jpg",
					"width": "486",
					"height": "38"
				},
				"ansimg": {
					"image": "ch1a17.jpg",
					"width": "506",
					"height": "35"
				}
			},
			{
				"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": "ch1a18.jpg",
					"width": "219",
					"height": "35"
				},
				"ansimg": {
					"image": "ch1a19.jpg",
					"width": "365",
					"height": "49"
				}
			},
			{
				"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": "ch1a18.jpg",
					"width": "219",
					"height": "35"
				},
				"ansimg": {
					"image": "ch1a19.jpg",
					"width": "365",
					"height": "49"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": null,
				"ans": "Associativity.",
				"code": "SATQ",
				"options": null,
				"val": 7,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch1a20.jpg",
					"width": "436",
					"height": "36"
				}
			},
			{
				"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": "ch1a21.jpg",
					"width": "343",
					"height": "32"
				},
				"ansimg": {
					"image": "ch1a22.jpg",
					"width": "371",
					"height": "87"
				}
			},
			{
				"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": "ch1a21.jpg",
					"width": "343",
					"height": "32"
				},
				"ansimg": {
					"image": "ch1a22.jpg",
					"width": "371",
					"height": "87"
				}
			},
			{
				"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": "ch1a23.jpg",
					"width": "350",
					"height": "29"
				},
				"ansimg": {
					"image": "ch1a24.jpg",
					"width": "430",
					"height": "96"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Write, (i) The rational number that does not have a reciprocal.",
				"ans": "0 is rational number but its reciprocal is not defined.",
				"code": "SATQ",
				"options": null,
				"val": 9,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Write, (ii) The rational numbers that are equal to their reciprocals.",
				"ans": "1 and –1 are the rational numbers that are equal to their reciprocals.",
				"code": "SATQ",
				"options": null,
				"val": 10,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Write, (iii) The rational number that is equal to its negative.",
				"ans": "0 is the rational number that is equal to its negative.",
				"code": "SATQ",
				"options": null,
				"val": 11,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
			},
		],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": "Represent these numbers on the number line:",
				"ans": "Gills",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch1a27.jpg",
					"width": "108",
					"height": "38"
				},
				"ansimg": {
					"image": "ch1a28.jpg",
					"width": "518",
					"height": "172"
				},
				"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": "ch1a46.jpg",
					"width": "295",
					"height": "41"
				},
				"ansimg": {
					"image": "ch1a47.jpg",
					"width": "525",
					"height": "95"
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Write five rational numbers which are smaller than 3.",
				"ans": null,
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"ansimg": {
					"image": "ch1a48.jpg",
					"width": "341",
					"height": "105"
				},
				"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": "ch1a49.jpg",
					"width": "340",
					"height": "48"
				},
				"ansimg": {
					"image": "ch1a50.jpg",
					"width": "380",
					"height": "142"
				},
				"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": "ch1a51.jpg",
					"width": "302",
					"height": "38"
				},
				"ansimg": {
					"image": "ch1a52.jpg",
					"width": "319",
					"height": "108"
				},
				"val": 5
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Write five rational numbers greater than –2.",
				"ans": null,
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"ansimg": {
					"image": "ch1a53.jpg",
					"width": "282",
					"height": "108"
				},
				"val": 6
			},
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch1_un",
	"map": "ch1_map",
	"afq": "ch1_afq",
	"snc": "ch1_snc",
	"gowf": "ch1_gowf",
	"pbq": "ch1_pbq",
	"mtf": "ch1_mtf",
	"tf": "ch1_tf",
	"afow": "ch1_afow",
	"cs": "ch1_cs",
	"ctco": "ch1_ctco",
	"vsaq": "ch1_vsaq",
	"grade": "Grade 8",
	"mcq": "ch1_mcq",
	"dtf": "ch1_dtf",
	"grf": "ch1_grf",
	"fib": "ch1_fib",
	"saq": "ch1_saq",
	"laq": "ch1_laq",
	"nf": "ch1_nf",
	"co": "ch1_co",
	"jtf": "ch1_jtf",
	"yn": "ch1_yn",
	"ctt": "ch1_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch2",
	"chapterName": "Chapter 2 - Linear Equations in One Variable",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "For any two rational numbers a and b, ______________ is also a rational number.",
				"ans": "(d) All of these",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) a + b",
					"(b) a – b",
					"(c) a × b",
					"(d) All of these"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 2x – 3 = x + 5, then x =",
				"ans": "(b) 8",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 2",
					"(b) 8",
					"(c) 5",
					"(d) 3"
				],
				"val": 2
			},
			
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe difference between two whole numbers is 25, the ratio of the two numbers is 3:4, the numbers are –75 and –100.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tDevanshi has 2 times as many two rupee coins as he has five-rupee coins. If she has in all a sum of ₹63, She has 7 coins of ₹5 and 14 coins of ₹2.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe sum of three consecutive multiples of 11 is 363, the multiples are 121, 132 and 143.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe equations may have expressions with variable on both sides.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 3
			},
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "An ______________ equation is an equality involving variables.",
				"ans": "algebraic",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "An algebraic equation has an ______________ sign.",
				"ans": "equality",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The expression on the right of the equality sign is the ______________.",
				"ans": "Right Hand Side (RHS)",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Sum of two numbers is 55. One of the numbers is 5 more than other. The numbers are ______________ and ______________.",
				"ans": "25, 30",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": null,
				"ans": "1",
				"code": "FIB",
				"pic": {
					"image": "ch2a14.jpg",
					"width": "485",
					"height": "46"
				},
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The perimeter of a rectangle is 20 cm and its width is 5 cm, the length will be ______________.",
				"ans": "5 cm",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The present age of Salman’s father is three times the present age of Salman, the total of their present ages is 40, the equation will be formed as ______________.",
				"ans": "x + 3x = 40",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "An equation is the ______________ of the values of two expressions.",
				"ans": "equality",
				"code": "FIB",
				"val": 8
			},

			
		],
		[],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "If you subtract 2 from a number and multiply the result by 2 you get 4. What is the number?",
				"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": "ch2a15.jpg",
					"width": "687",
					"height": "158"
				}
			},
			
			{
				"heading": "Answer the following questions in short.",
				"qus": "The perimeter of a rectangular swimming pool is 164 m. Its length is 2m more than twice its breadth. What are the length and the breadth of the pool?",
				"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": "ch2a16.jpg",
					"width": "706",
					"height": "255"
				}
			},
			
			{
				"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": "ch2a31.jpg",
					"width": "702",
					"height": "66"
				},
				"ansimg": {
					"image": "ch2a17.jpg",
					"width": "625",
					"height": "247"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Sum of two numbers is 85. If one exceeds the other by 10, find the numbers.",
				"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": "ch2a18.jpg",
					"width": "570",
					"height": "192"
				}
			},
			
			{
				"heading": "Answer the following questions in short.",
				"qus": "Two numbers are in the ratio 4:2. If they differ by 16, what are the numbers?",
				"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": "ch2a19.jpg",
					"width": "634",
					"height": "164"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Three consecutive integers add upto 45. What are these integers?",
				"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": "ch2a20.jpg",
					"width": "679",
					"height": "191"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The sum of two consecutive multiples of 8 is 888. Find the multiples.",
				"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": "ch2a21.jpg",
					"width": "665",
					"height": "281"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3, and 4 respectively, they add upto 56. Find these numbers.",
				"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": "ch2a22.jpg",
					"width": "641",
					"height": "224"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The ages of Reema and Mehul are in the ratio 6:6. Four years later the sum of their ages will be 44 years. What are their present ages?",
				"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": "ch2a23.jpg",
					"width": "667",
					"height": "423"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The number of boys and girls in a class are in the ratio 7:5. The number of boys is 10 more than the number of girls. What is the total class strength?",
				"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": "ch2a24.jpg",
					"width": "616",
					"height": "318"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Dhruvi’s father is 28 years younger than Dhruvi’s grandfather and 30 years older than Dhruvi. The sum of the ages of all the three is 142 years. What is the age of each one of them?",
				"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": "ch2a25.jpg",
					"width": "710",
					"height": "315"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Eighteen years from now Parthiv’s age will be four times his present age. What is Parthiv’s present age?",
				"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": "ch2a26.jpg",
					"width": "560",
					"height": "186"
				}
			},
			{
				"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": "ch2a32.jpg",
					"width": "705",
					"height": "63"
				},
				"ansimg": {
					"image": "ch2a27.jpg",
					"width": "589",
					"height": "210"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Geeta is a cashier in a bank. She has currency notes of denominations ₹ 100, ₹ 50, ₹ 10 respectively. The ratio of the number of these notes is 2:3:5. The total cash with Geeta is ₹ 500,000. How many notes of each denomination does she have?",
				"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": "ch2a28.jpg",
					"width": "706",
					"height": "313"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "I have a total of ₹ 300 in coins of denomination ₹ 1, ₹ 2 and ₹ 5. The number ₹ 2 coins is 3 times the number of ₹ 5 coins. The total number of coins is 160. How many coins of each denomination are with me?",
				"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": "ch2a29.jpg",
					"width": "441",
					"height": "633"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The organizers of an essay competition decide that a winner in the competition gets a prize of ₹ 200 and a participant who does not win gets a prize of ₹ 40. The total prize money distributed is ₹ 4000. Find the number of winners, if the total number of participants is 80.",
				"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": "ch2a30.jpg",
					"width": "457",
					"height": "439"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 4x = 3x + 10",
				"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": "ch2a37.jpg",
					"width": "369",
					"height": "296"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 5x + 8 = 5 + 4x",
				"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": "ch2a38.jpg",
					"width": "304",
					"height": "286"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 4t – 2 = 2t – 4",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 19,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a39.jpg",
					"width": "308",
					"height": "470"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 6z + 3 = 2 + 3z",
				"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": "ch2a41.jpg",
					"width": "302",
					"height": "774"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 7x – 2 = 14 – x",
				"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": "ch2a42.jpg",
					"width": "309",
					"height": "514"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 9x + 3 = 3(x – 1) + 6",
				"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": "ch2a43.jpg",
					"width": "334",
					"height": "407"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: x = 3/6 (x + 9)",
				"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": "ch2a44.jpg",
					"width": "336",
					"height": "446"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 2x/2+1 = 8/16+ 2",
				"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": "ch2a45.jpg",
					"width": "312",
					"height": "898"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 2y + 5/3 = 26/3– y",
				"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": "ch2a46.jpg",
					"width": "345",
					"height": "353"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Solve and check result: 3m = 6m – 9/5",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 26,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a47.jpg",
					"width": "289",
					"height": "351"
				}
			},
			{
				"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": "ch2a48.jpg",
					"width": "693",
					"height": "61"
				},
				"ansimg": {
					"image": "ch2a49.jpg",
					"width": "517",
					"height": "217"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "A positive number is 3 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice to other new number. What are the numbers?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 27,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a50.jpg",
					"width": "648",
					"height": "251"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Sum of the digits of two digit number is 9. When we interchange the digits it is found that the resulting new number is greater than the original number by 27. What is the two digit number?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 28,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a51.jpg",
					"width": "641",
					"height": "532"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "One of the two digits of a two digit number is two times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 99. What is the original number?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 29,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a52.jpg",
					"width": "643",
					"height": "446"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Shikha’s mother’s present age is eight times Shikha’s present age. Shikha’s age, four years from now, will be one fourth of her mother’s present age. What are their present ages?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 29,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a53.jpg",
					"width": "644",
					"height": "324"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "There is a narrow rectangular plot, reserved for a school in Ratanpura village. The length and breadth of the plot are in the ratio 14:2. At the rate ₹ 100 per metre it will cost the village panchayat ₹ 80,000 to fence the plot. What are the dimensions of the plot?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 30,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a54.jpg",
					"width": "705",
					"height": "403"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ₹ 100 per metre and trouser material that costs him ₹ 80 per metre. For every 2 meters of the shirt material he buys 4 metres of the trouser material. He sells the materials at 14% and 4% profit respectively. His total sale is ₹40,000. How much trouser material did he buy?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 31,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a55.jpg",
					"width": "502",
					"height": "468"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Half of a herd of cow are grazing in the field and one-fourth of the remaining are sitting nearby. The rest 9 are drinking water from the pond. Find the number of cows in the herd.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 32,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a56.jpg",
					"width": "426",
					"height": "447"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "A grand mother is twelve times older than her grand daughter. She is also 55 years older than her. Find their present ages.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 33,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a57.jpg",
					"width": "704",
					"height": "196"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Salman’s age is two times his brother’s age. 9 years ago, he was one half times his brother’s age. Find their present ages.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 34,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a58.jpg",
					"width": "472",
					"height": "379"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": null,
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 35,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch2a59.jpg",
					"width": "288",
					"height": "38"
				},
				"ansimg": {
					"image": "ch2a60.jpg",
					"width": "331",
					"height": "233"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": null,
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 36,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch2a61.jpg",
					"width": "291",
					"height": "35"
				},
				"ansimg": {
					"image": "ch2a62.jpg",
					"width": "510",
					"height": "199"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": null,
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 37,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch2a63.jpg",
					"width": "339",
					"height": "36"
				},
				"ansimg": {
					"image": "ch2a64.jpg",
					"width": "534",
					"height": "162"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": null,
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 38,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch2a65.jpg",
					"width": "269",
					"height": "37"
				},
				"ansimg": {
					"image": "ch2a66.jpg",
					"width": "703",
					"height": "226"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": null,
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 39,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch2a67.jpg",
					"width": "347",
					"height": "32"
				},
				"ansimg": {
					"image": "ch2a68.jpg",
					"width": "698",
					"height": "231"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": null,
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 40,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch2a69.jpg",
					"width": "323",
					"height": "37"
				},
				"ansimg": {
					"image": "ch2a70.jpg",
					"width": "537",
					"height": "201"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Simplify and solve the linear equation 3(k – 3) = 5(2k + 1)",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 41,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a71.jpg",
					"width": "469",
					"height": "159"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Simplify and solve the linear equation 16(y – 5) – 2(y – 9) + 5(y + 6) = 0.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 42,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a72.jpg",
					"width": "436",
					"height": "134"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Simplify and solve the linear equation 3(5t – 7) – 2(9t – 11) = 4(8t – 13) – 17",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 42,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a73.jpg",
					"width": "518",
					"height": "162"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Simplify and solve the linear equation: 0.25(4F – 3) = 0.05(10F – 9)",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 43,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch2a74.jpg",
					"width": "489",
					"height": "249"
				}
			},
			
			
		],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": "Solve x – 3 =6",
				"ans": "x – 3 = 6 <br> Transposing 3 to R.H.S., we obtain <br> x = 6 + 3 = 9",
				"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": "ch2a1.jpg",
					"width": "132",
					"height": "40"
				},
				"ansimg": {
					"image": "ch2a2.jpg",
					"width": "241",
					"height": "141"
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Solve 6 = z + 3",
				"ans": "6 = z + 3 <br> Transposing 3 to L.H.S., we obtain <br> 6 – 3 = z <br> ∴ z = 3",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 3
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Solve 4x = 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": "ch2a3.jpg",
					"width": "243",
					"height": "127"
				},
				"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": "ch2a4.jpg",
					"width": "101",
					"height": "36"
				},
				"ansimg": {
					"image": "ch2a5.jpg",
					"width": "154",
					"height": "99"
				},
				"val": 5
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Solve 18 + 6p = 9",
				"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": "ch2a6.jpg",
					"width": "248",
					"height": "261"
				},
				"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": "ch2a7.jpg",
					"width": "115",
					"height": "40"
				},
				"ansimg": {
					"image": "ch2a8.jpg",
					"width": "263",
					"height": "133"
				},
				"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": "ch2a9.jpg",
					"width": "123",
					"height": "38"
				},
				"ansimg": {
					"image": "ch2a10.jpg",
					"width": "268",
					"height": "126"
				},
				"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": "ch2a11.jpg",
					"width": "136",
					"height": "39"
				},
				"ansimg": {
					"image": "ch2a12.jpg",
					"width": "264",
					"height": "326"
				},
				"val": 9
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Solve 6x – 5 = 15",
				"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": "ch2a13.jpg",
					"width": "248",
					"height": "272"
				},
				"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": "ch2a75.jpg",
					"width": "129",
					"height": "38"
				},
				"ansimg": {
					"image": "ch2a76.jpg",
					"width": "285",
					"height": "208"
				},
				"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": "ch2a77.jpg",
					"width": "135",
					"height": "42"
				},
				"ansimg": {
					"image": "ch2a78.jpg",
					"width": "309",
					"height": "241"
				},
				"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": "ch2a79.jpg",
					"width": "143",
					"height": "44"
				},
				"ansimg": {
					"image": "ch2a80.jpg",
					"width": "339",
					"height": "227"
				},
				"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": "ch2a81.jpg",
					"width": "146",
					"height": "42"
				},
				"ansimg": {
					"image": "ch2a82.jpg",
					"width": "328",
					"height": "166"
				},
				"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": "ch2a83.jpg",
					"width": "148",
					"height": "46"
				},
				"ansimg": {
					"image": "ch2a84.jpg",
					"width": "332",
					"height": "215"
				},
				"val": 14
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The ages of Tom and Jerry are in the ratio of 2 : 5. Three years from now, the ratio of their ages will be 2 : 4. Find their present ages.",
				"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": "ch2a85.jpg",
					"width": "708",
					"height": "378"
				},
				"val": 15
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The ages of Tom and Jerry are in the ratio of 2 : 5. Three years from now, the ratio of their ages will be 2 : 4. Find their present ages.",
				"ans": null,
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch2a86.jpg",
					"width": "707",
					"height": "67"
				},
				"ansimg": {
					"image": "ch2a87.jpg",
					"width": "426",
					"height": "421"
				},
				"val": 16
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch2_un",
	"map": "ch2_map",
	"afq": "ch2_afq",
	"snc": "ch2_snc",
	"gowf": "ch2_gowf",
	"pbq": "ch2_pbq",
	"mtf": "ch2_mtf",
	"tf": "ch2_tf",
	"afow": "ch2_afow",
	"cs": "ch2_cs",
	"ctco": "ch2_ctco",
	"vsaq": "ch2_vsaq",
	"grade": "Grade 8",
	"mcq": "ch2_mcq",
	"dtf": "ch2_dtf",
	"grf": "ch2_grf",
	"fib": "ch2_fib",
	"saq": "ch2_saq",
	"laq": "ch2_laq",
	"nf": "ch2_nf",
	"co": "ch2_co",
	"jtf": "ch2_jtf",
	"yn": "ch2_yn",
	"ctt": "ch2_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch3",
	"chapterName": "Chapter 3 - Understanding Quadrilaterals",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following can never be the measure of exterior angle of a regular polygon?",
				"ans": "(a) 22°",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 22°",
					"(b) 36°",
					"(c) 45°",
					"(d) 30°"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is not true for an exterior angle of a regular polygon with n sides?",
				"ans": null,
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"ch3a23.jpg",
					"(b) Exterior angle = 180° – interior angle.",
					"ch3a24.jpg",
					"ch3a25.jpg"
				],
				"ansimg": {
					"image": "ch3a25.jpg",
					"width": "271",
					"height": "46"
				},
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The number of sides of a regular polygon whose each interior angle is of 135° is",
				"ans": "(c) 8",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 6",
					"(b) 7",
					"(c) 8",
					"(d) 9"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "What is the measure of each exterior angle of a regular pentagon?",
				"ans": "(b) 72º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 180º",
					"(b) 72º",
					"(c) 75º",
					"(d) 360º"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "What is the measure of each exterior angle of a regular polygon of 18 sides?",
				"ans": "(a) 20º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 20º",
					"(b) 80º",
					"(c) 180º",
					"(d) 360º"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "What is the number of sides of a regular polygon, where each exterior angle has a measure of 36º?",
				"ans": "(b) 10",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 18",
					"(b) 10",
					"(c) 20",
					"(d) 5"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is a property of a parallelogram?",
				"ans": "(a) Opposite sides are parallel",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) Opposite sides are parallel",
					"(b) The diagonals bisect each other at right angles.",
					"(c) The diagonals are perpendicular to each other",
					"(d) All angles are equal"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If two adjacent angles of a parallelogram are (5x – 5) and (10x + 35), then the ratio of these angles is",
				"ans": "(a) 1 : 3",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 1 : 3",
					"(b) 2 : 3",
					"(c) 1 : 4",
					"(d) 1 : 2"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a",
				"ans": "(b) rectangle",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) rhombus",
					"(b) rectangle",
					"(c) square",
					"(d) parallelogram"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which one has all the properties of a kite and a parallelogram?",
				"ans": "(b) Rhombus",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) Trapezium",
					"(b) Rhombus",
					"(c) rectangle",
					"(d) parallelogram"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "PQRS is a trapezium in which PQ || SR and ∠Q = 110º then ∠R is equal to",
				"ans": "(a) 70º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 70º",
					"(b) 50º",
					"(c) 65º",
					"(d) 55º"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If a diagonal of a quadrilateral bisects both the angles then it is a",
				"ans": "(c) rhombus",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) kite",
					"(b) parallelogram",
					"(c) rhombus",
					"(d) rectangle"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If PQRS is a parallelogram then ∠P – ∠R is equal to",
				"ans": "(d) 0º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 60º",
					"(b) 90º",
					"(c) 80º",
					"(d) 0º"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "For which of the following figures, diagonals are equal?",
				"ans": "(d) Rectangle",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) Trapezium",
					"(b) Rhombus",
					"(c) Parallelogram",
					"(d) Rectangle"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "What is the sum of all the angles of a pentagon?",
				"ans": "(c) 540º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 180º",
					"(b) 360º",
					"(c) 540º",
					"(d) 720º"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In the trapezium ABCD, the measure of ∠D is",
				"ans": "(d) 125º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 55º",
					"(b) 115º",
					"(c) 135º",
					"(d) 125º"
				],
				"pic": {
					"image": "ch3a53.jpg",
					"width": "129",
					"height": "108"
				},
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The sum of adjacent angles of a parallelogram is",
				"ans": "(a) 180º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 180º",
					"(b) 120º",
					"(c) 360º",
					"(d) 90º"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The closed curve which is also a polygon, is",
				"ans": null,
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"ch3a54.jpg",
					"ch3a55.jpg",
					"ch3a56.jpg",
					"ch3a57.jpg"
				],
				"ansimg": {
					"image": "ch3a57.jpg",
					"width": "113",
					"height": "49"
				},
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90º. Then, PQRS is a",
				"ans": "(b) rectangle",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) square",
					"(b) rectangle",
					"(c) rhombus",
					"(d) trapezium"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the figures satisfy the following property that only one pair of sides are parallel.",
				"ans": "(a) P",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) P",
					"(b) Q",
					"(c) R",
					"(d) S"
				],
				"pic": {
					"image": "ch3a58.jpg",
					"width": "282",
					"height": "64"
				},
				"val": 20
			},
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA simple closed curve made up of only line segments is called a polygon.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "false",
				"code": "TF",
				"pic": {
					"image": "ch3a1.jpg",
					"width": "212",
					"height": "46"
				},
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tDecagon has hundred vertices.\n\t\t_________\n\t",
				"ans": "false",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA diagonal is a line segment connecting consecutive vertices of a polygon.\n\t\t_________\n\t",
				"ans": "false",
				"code": "TF",
				"val": 4
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "false",
				"code": "TF",
				"pic": {
					"image": "ch3a2.jpg",
					"width": "209",
					"height": "34"
				},
				"val": 5
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "True",
				"code": "TF",
				"pic": {
					"image": "ch3a3.jpg",
					"width": "211",
					"height": "45"
				},
				"val": 6
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tSum of measures of a triangle is 180°.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 7
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe adjacent angles in a parallelogram are supplementary.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 8
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe diagonals of a parallelogram bisect each other.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 9
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tBEST is a parallelogram, ∠B + ∠E = 360.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 10
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tPQRS is a parallelogram m ∠P = m ∠R.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 11
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA parallelogram is a quadrilateral whose opposite sides are parallel.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 12
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA rectangle whose adjacent sides are equal becomes a square.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 13
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIn trapezium ABCD with AB || CD if ∠A = 100º then ∠D = 100º\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 14
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll angles of a trapezium are equal.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 15
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll kites are square.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 16
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll rectangles are parallelograms.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 17
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll rhombus are square.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 18
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tRectangle is a regular quadrilateral.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 19
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tDiagonals of a rectangle are of equal length.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 20
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tDiagonals of rectangle bisect each other at right angles.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 21
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll rectangles are squares.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 22
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll rhombuses are parallelograms.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 23
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll squares are rhombuses and also rectangles.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 24
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll squares are not parallelograms.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 25
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll kites are rhombuses.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 26
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll rhombuses are kites.\n\t\t_________\n\t",
				"ans": "True.",
				"code": "TF",
				"val": 27
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll parallelograms are trapeziums.\n\t\t_________\n\t",
				"ans": "True.",
				"code": "TF",
				"val": 28
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll squares are trapeziums.\n\t\t_________\n\t",
				"ans": "True.",
				"code": "TF",
				"val": 29
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll angles of a trapezium are equal.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 30
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAll rhombuses are square.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 31
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA quadrilateral has two diagonals.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 32
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA polygon is regular, if all of its sides are equal.\n\t\t_________\n\t",
				"ans": "False.",
				"code": "TF",
				"val": 33
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tEvery trapezium is a rectangle.\n\t\t_________\n\t",
				"ans": "False.",
				"code": "TF",
				"val": 33
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "Paper is a model for a ______________ surface.",
				"ans": "plane",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Number of sides of Heptagon ______________.",
				"ans": "7",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A rectangle has ______________ diagonals.",
				"ans": "2",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A square is a ______________ polygon.",
				"ans": "regular",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The sum of measures of the three angles of a triangle is ______________.",
				"ans": "180°",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Trapezium is a quadrilateral with a pair of ______________ sides.",
				"ans": "parallel",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A quadrilateral that is not a parallelogram but has two opposite angles of equal measure is ______________.",
				"ans": "Kite",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "In a parallelogram ______________ sides are parallel.",
				"ans": "opposite",
				"code": "FIB",
				"val": 8
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The opposite angles of a parallelogram are of ______________ measure.",
				"ans": "equal",
				"code": "FIB",
				"val": 9
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A ______________ is a regular quadrilateral.",
				"ans": "Square",
				"code": "FIB",
				"val": 10
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A quadrilateral in which pair of opposite sides is parallel is ______________.",
				"ans": "Trapezium",
				"code": "FIB",
				"val": 11
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "If all sides of a qaudrilateral are equal it is a ______________.",
				"ans": "Rhombus",
				"code": "FIB",
				"val": 12
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "In a rhombus, diagonals intersect at ______________ angles.",
				"ans": "right",
				"code": "FIB",
				"val": 13
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Diagonals of a rectangle are of ______________ length.",
				"ans": "equal",
				"code": "FIB",
				"val": 14
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A rhombus is a parallelogram in which ______________ sides are equal.",
				"ans": "all",
				"code": "FIB",
				"val": 15
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "______________ is a regular quadrilateral.",
				"ans": "Square",
				"code": "FIB",
				"val": 16
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The sum of all exterior angles of a polygon is ______________.",
				"ans": "360º",
				"code": "FIB",
				"val": 17
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures is ______________.",
				"ans": "kite",
				"code": "FIB",
				"val": 18
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Sum of the angles of a hexagon is ______________.",
				"ans": "720º",
				"code": "FIB",
				"val": 19
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "If the diagonals of a quadrilateral bisect each other, it is a  ______________.",
				"ans": "parallelogram",
				"code": "FIB",
				"val": 20
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Adjacent angles of a parallelogram are ______________.",
				"ans": "Supplementary",
				"code": "FIB",
				"val": 21
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A quadrilateral has ______________ diagonals.",
				"ans": "two",
				"code": "FIB",
				"val": 22
			}
		],
		[],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find x in the following figures:",
				"ans": "The things that have life in them are called living things. For example, human beings, plants and animals",
				"code": "SATQ",
				"options": null,
				"val": 1,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch3a10.jpg",
					"width": "359",
					"height": "161"
				},
				"ansimg": {
					"image": "ch3a11.jpg",
					"width": "447",
					"height": "475"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the measure of each exterior angle of a regular polygon of <br> (a) 12 sides <br> (b) 16 sides",
				"ans": "The things that have life in them are called living things. For example, human beings, plants and animals",
				"code": "SATQ",
				"options": null,
				"val": 2,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch3a12.jpg",
					"width": "456",
					"height": "296"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "How many sides does a regular polygon have, if the measure of an exterior angle is 36º?",
				"ans": "The things that have life in them are called living things. For example, human beings, plants and animals",
				"code": "SATQ",
				"options": null,
				"val": 3,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch3a13.jpg",
					"width": "500",
					"height": "86"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "How many sides does a regular polygon have, if each of its interior angles is 156º?",
				"ans": "The things that have life in them are called living things. For example, human beings, plants and animals",
				"code": "SATQ",
				"options": null,
				"val": 4,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch3a14.jpg",
					"width": "453",
					"height": "169"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "(a) Is it possible to have a regular polygon with measure of each exterior angle as 26º? <br> (b) Can it be an interior angle of a regular polygon? Why?",
				"ans": "(a) No. (Since 26º is not a divisor of 360º) <br> (b) No. (Becuase each exterior angle is 180º – 26º = 154º. Which is not a divisor of 360º)",
				"code": "SATQ",
				"options": null,
				"val": 5,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "(a) What is the minimum interior angle possible for a regular polygon? Why? <br> (b) What is the maximum exterior angle possible for a regular polygon?",
				"ans": "(a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle of 60º. <br> (∵ Sum of all the angles of a triangle = 180º) <br> ∴ x + x + x = 180º) ⇒ 3x = 180º <br> x = 60º <br> <br/> (b) By (a), we can observe that the greatest exterior angle is 180º – 60º = 120º.",
				"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": "Given a parallelogram ABCD. Complete each statement along with the definition or property used. <br> (i) AD = _____ <br> (ii) ∠DCB = _____ <br> (iii) OC = ____ <br> (iv) m∠DAB + m∠CDA = _____",
				"ans": "(i) AD = BC <br> (ii) ∠DCB = ∠DAB <br> (iii) OC = OA <br> (iv) m∠DAB + m∠CDA = 180º",
				"code": "SATQ",
				"options": null,
				"val": 7,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch3a15.jpg",
					"width": "145",
					"height": "94"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Consider the following parallelograms. Find the values of the unknowns p, q, r.",
				"ans": "(i) ∠B + ∠C = 180º [∵ Adjacent angles in a parallelogram are supplementary] <br> 160º + p = 180º <br> ∴ p = 180º – 160º = 20º <br> p = r = 20º [Since opposite angles of a parallelogram are equal] <br> also q = 160º [Since opposite angles of a parallelogram are equal <br> <br/> (ii) p + 46º = 180º [Adjacent angles in a || gm are supplementary] <br> p = 180º – 46º = 134º <br> p = r = 134º [Corresponding angles] <br> q = p = 134º (opp. ∠'s of a || gm) <br> <br/>  (iii) p = 90º [Vertically opposite angles] <br> q + p + 75º = 180º [Angles sum property of a triangle] <br> q + 90º + 75º = 180º <br> q + 165º = 180º <br> ∴ q = 180º – 165º = 15º <br> ∴ q = r = 15º [Alternate angles] <br> <br/> (iv) r = 85º [Corresponding angles] <br> p + 85º = 180º, p = 95º [Adjacent angles in a ||gm are supplementary] <br> and q = 85º [Opposite angles are equal in a ||gm] <br> <br/> (v) q = 111º [Opposite angles are equal in a ||gm] <br> 40º + 111º + p = 180º (∵ q = 111º) <br> ∴ 151º + p = 180º <br> ∴ p = 180º – 151º = 29º <br> and p = r = 29º [Alternate angles]",
				"code": "SATQ",
				"options": null,
				"val": 8,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch3a16.jpg",
					"width": "504",
					"height": "256"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Can a quadrilateral ABCD be a parallelogram if <br> (i) ∠D + ∠B = 180º? <br> (ii) AB = DC = 9 cm, AD = 4 cm and BC = 5.5 cm? <br> (iii) ∠A = 72º and ∠C = 65º?",
				"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": "ch3a17.jpg",
					"width": "550",
					"height": "272"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.",
				"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": "ch3a18.jpg",
					"width": "399",
					"height": "100"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The measures of two adjacent angles of a parallelogram are in the ratio 4 : 6. Find the measure of each of the angles of the parallelogram.",
				"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": "ch3a19.jpg",
					"width": "434",
					"height": "125"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.",
				"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": "ch3a20.jpg",
					"width": "465",
					"height": "173"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The adjacent figure, KLMN is a parallelogram. Find the angle measures x, l and s. State the properties you use to find them.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 13,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch3a21.jpg",
					"width": "151",
					"height": "101"
				},
				"ansimg": {
					"image": "ch3a26.jpg",
					"width": "427",
					"height": "321"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The following figures FUNT and WUNT are parallelogarms. Find d and f. (Lengths are in cm)",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 14,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch3a27.jpg",
					"width": "291",
					"height": "107"
				},
				"ansimg": {
					"image": "ch3a28.jpg",
					"width": "533",
					"height": "531"
				}
			},
			{
				"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": "ch3a29.jpg",
					"width": "505",
					"height": "152"
				},
				"ansimg": {
					"image": "ch3a30.jpg",
					"width": "550",
					"height": "347"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Explain how this figure is a trapezium. Which of its two sides are parallel?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 16,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch3a31.jpg",
					"width": "181",
					"height": "120"
				},
				"ansimg": {
					"image": "ch3a32.jpg",
					"width": "441",
					"height": "80"
				}
			},
		],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": null,
				"ans": "Gills",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch3a61.jpg",
					"width": "550",
					"height": "175"
				},
				"ansimg": {
					"image": "ch3a62.jpg",
					"width": "550",
					"height": "499"
				},
				"val": 1
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "How many diagonals does each of the following have? <br> (a) A convex quadrilateral <br> (b) A regular hexagon <br> (c) A triangle",
				"ans": "Gills",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch3a63.jpg",
					"width": "550",
					"height": "124"
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try.)",
				"ans": "Gills",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch3a4.jpg",
					"width": "550",
					"height": "449"
				},
				"val": 3
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)",
				"ans": "Gills",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch3a5.jpg",
					"width": "485",
					"height": "198"
				},
				"ansimg": {
					"image": "ch3a6.jpg",
					"width": "485",
					"height": "248"
				},
				"val": 4
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What is a regular polygon? State the name of a regular polygon of <br> (a) 3 sides <br> (b) 4 sides <br> (c) 6 sides",
				"ans": "A regular polygon: A polygon having all sides of equal length and the interior angles of equal size is known as regular polygon <br> (i) 3 sides. Polygon having three sides is called a triangle. <br> (ii) 4 sides. Polygon having four sides is called a quadrilateral. <br> (iii) 6 sides. Polygon having six sides is called a hexagon.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"val": 5
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the angle measure x in the following figures.",
				"ans": "(a) Using angle sum property of a quadrilateral, <br> 36º + 60º + 120º + x = 360º <br> ∴ 216º + x = 360º <br> x = 360º – 216º = 144º <br><br/> (b) Using angle sum property of a quadrilateral, 90º + 80º + 45º + x = 360º <br> ∴ 215º + x = 360º <br> ∴ x = 360º – 215º = 145º <br><br/> (c) First base interior angle = 180º – 65º = 115º <br> Second base interior angle = 180º – 100º = 80º <br> There are 5 sides, n = 5 <br> ∴ Angle sum of a polygon = (n – 2) × 180º <br> = (5 – 2) × 180º <br> = 3 × 180º = 540º <br> ∴ 30º + x + 115º + 80º + x = 540º <br> ∴ 225º + 2x = 540º <br> ∴ 2x = 540º – 225º = 315º <br> ∴ x = 157.5º <br><br/> (d) Angle sum of a polygon = (n – 2) × 180º <br> = (6 – 2) × 180º <br> = 4 × 180º = 720º <br> ∴ x + x + x + x + x + x = 720º <br> ∴ 6x = 720º ∴ x = 120º <br> Hence each interior angle is 120º",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch3a7.jpg",
					"width": "550",
					"height": "85"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null,
				},
				"val": 6
			},
			{
				"heading": "Very short answer type questions.",
				"qus": null,
				"ans": "(a) Since sum of linear pair angles is 180º. <br> ∴ 92º + x = 180º <br> ∴ x = 180º – 92º = 88º <br> And z + 36º = 180º <br> ∴ z = 180º – 36º = 144º <br> Also y = 92º + 36º = 128º [Exterior angle property] <br> ∴ x + y + z = 88º + 128º + 144º = 360º <br><br/> (b) Using angle sum property of a quadrilateral, <br> ∴ 50º + 70º + 130º + n = 360º <br> ∴ 250º + n = 360º <br> ∴ n = 360º – 250º <br> ∴ n = 110º <br> Since sum of linear pair angles is 180º. <br> ∴ w + 110º = 180º ...(i) <br> ∴ x + 130º = 180º ...(ii) <br> y + 70º = 180º ...(iii) <br> z + 50º = 180º ...(iv) <br> Adding eqs. (i), (ii), (iii), (iv), <br> x + y + z + w + 110º + 130º + 70º + 50º = 180º + 180º + 180º + 180º <br> ∴ x + y + z + w + 360º = 720º <br> ∴ x + y + z + w = 720º – 360º <br> ∴ x + y + z + w = 360º",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch3a8.jpg",
					"width": "429",
					"height": "166"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null,
				},
				"val": 7
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Identify all the quadrilaterals that have: <br> (a) Four right angles. <br> (b) Four sides of equal lengths.",
				"ans": "(a) Square and rectangle have four right angles. <br> (b) Rhombus and square have sides of equal lengths.",
				"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": "Explain how a square is <br> (i) a quadrilateral <br> (ii) a parallelogram <br> (iii) a rhombus <br> (iv) a rectangle.",
				"ans": "(i) A square is a quadrilateral, since it has four sides. <br> (ii) A square is a parallelogram, since its opposite sides are parallel to each other. <br> (iii) A square is a rhombus, since it is a parallelogram with all four sides equal. <br> (iv) A square is a rectangle, since having each adjacent angle a right angle and opposite sides are equal.",
				"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": "Name the quadrilateral whose diagonals: <br> (i) bisect each other <br> (ii) are equal <br> (iii) are perpendicular bisectors of each other.",
				"ans": "(i) If diagonals of a quadrilateral bisect each other the it is a rhombus or parallelogram or rectangle or square. <br> (ii) If diagonals are equal, then it is a square or rectangle. <br> (iii) If diagonals of a quadrilateral are perpendicular bisector of each other, then it is a rhombus or square.",
				"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": "Explain why a rectangle is a convex quadrilateral.",
				"ans": "A rectangle is a convex quadrilateral since its vertex are raised and both of its diagonals lie in its interior.",
				"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": "ABC is right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The doted lines are drawn additionally to help you.)",
				"ans": "Since, two right triangles make a rectangle where O is equidistant point from A, B, C and D because O is the mid-point of the two diagonals of a rectangle. Since AC and BD are equal diagonals and intersect at mid-point. So, O is the equidistant from A, B, C and D.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch3a33.jpg",
					"width": "145",
					"height": "110",
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null,
				},
				"val": 12
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "In parallelogram ABCD, find ∠B, ∠C and ∠D",
				"ans": "In a parallelogram, the opposite angles are equal, <br> therefore ∠C = ∠A = 80º. Also, adjacent angles are supplementary. <br> ∴ ∠A + ∠B = 180º <br> 80º + ∠B = 180º <br> ∠B = 180º – 80º ⇒ B = 100º <br> Now ∠B = ∠D <br> ∴ ∠D = 100º",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch3a59.jpg",
					"width": "120",
					"height": "87",
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null,
				},
				"val": 13
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the values of x and y in the following kite.",
				"ans": "The given figure is a kite. <br> In a kite, one pair of opposite angles are equal <br> ∴ y = 110º <br> Now, by the angle sum property of a quadrilateral, we have <br> 110º + 60º + 110º + x = 360º <br> ∴ x = 360º – 280º ⇒ x = 80º",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch3a60.jpg",
					"width": "102",
					"height": "155",
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null,
				},
				"val": 14
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch3_un",
	"map": "ch3_map",
	"afq": "ch3_afq",
	"snc": "ch3_snc",
	"gowf": "ch3_gowf",
	"pbq": "ch3_pbq",
	"mtf": "ch3_mtf",
	"tf": "ch3_tf",
	"afow": "ch3_afow",
	"cs": "ch3_cs",
	"ctco": "ch3_ctco",
	"vsaq": "ch3_vsaq",
	"grade": "Grade 8",
	"mcq": "ch3_mcq",
	"dtf": "ch3_dtf",
	"grf": "ch3_grf",
	"fib": "ch3_fib",
	"saq": "ch3_saq",
	"laq": "ch3_laq",
	"nf": "ch3_nf",
	"co": "ch3_co",
	"jtf": "ch3_jtf",
	"yn": "ch3_yn",
	"ctt": "ch3_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch4",
	"chapterName": "Chapter 4 - Practical Geometry",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "If three angles of a quadrilateral are each equal to 75º, then, the fourth angle is",
				"ans": "(b) 135º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 150º",
					"(b) 135º",
					"(c) 45º",
					"(d) 75º"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A quadrilateral whose opposite sides and all the angles are equal is a",
				"ans": "(a) rectangle",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) rectangle",
					"(b) parallelogram",
					"(c) square",
					"(d) rhombus"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The sum of adjacent angle of a parallelogram is",
				"ans": "(a) 180º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 180º",
					"(b) 120º",
					"(c) 360º",
					"(d) 90º"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "To construct a unique parallelogram, the minimum number of measurements required is",
				"ans": "(b) 3",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 2",
					"(b) 3",
					"(c) 4",
					"(d) 5"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "To construct a unique rectangle, the minimum number of measurements required is",
				"ans": "(c) 2",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 4",
					"(b) 3",
					"(c) 2",
					"(d) 1"
				],
				"val": 5
			}
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tSum of all the angles of a quadrilateral is 180º.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIf opposite angles of a quadrilateral are equal, it must be a parallelogram.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA quadrilateral can be drawn if only measures of four sides are given.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA quadrilateral can have all four angles as obtuse.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 4
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA quadrilateral can be drawn if three sides and two diagonals are given.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 5
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "A polygon is a simple closed curve made up of only ______________.",
				"ans": "line segments",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "In a rhombus, diagonals intersect at ______________ angles.",
				"ans": "right",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A quadrilateral can be constructed uniquely, if its three sides and ______________ angles are given.",
				"ans": "two included",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A rhombus is a parallelogram in which ______________ sides are equal.",
				"ans": "all",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "If the diagonals of a quadrilateral bisect each other, it is a ______________.",
				"ans": "parallelogram",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Adjacent angles of a parallelogram are supplementary ______________.",
				"ans": "supplementary",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A regular polygon is a polygon whose all sides are equal and all ______________ are equal.",
				"ans": "angles",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "______________ is a regular quadrilateral.",
				"ans": "Square",
				"code": "FIB",
				"val": 8
			}
		],
		[],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral ABCD. <br> AB = 5.5 cm, BC = 5.9 cm, <br> CD = 4.8 cm, AD = 6.2 cm, AC = 8.7 cm",
				"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": "ch4a1.jpg",
					"width": "460",
					"height": "391"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral TROG <br> TR = 3.7 cm, RO = 4.2 cm, OG = 5.2 cm <br> GT = 4.7 cm, GR = 6.7 cm",
				"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": "ch4a2.jpg",
					"width": "526",
					"height": "357"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Parallelogram CORE <br> OR = 6.5 cm, RE = 5 cm, EO = 8 cm.",
				"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": "ch4a3.jpg",
					"width": "517",
					"height": "330"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Rhombus BEST. <br> BE = 6.5 cm, ET = 7 cm.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 4,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch4a4.jpg",
					"width": "499",
					"height": "294"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral LIZA <br> LI = 4.7 cm, IZ = 3.8 cm, AZ = 2.8 cm, IA = 4 cm, LZ = 5 cm",
				"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": "ch4a5.jpg",
					"width": "454",
					"height": "277"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral LOFT. <br> OF = 7.8 cm, LF = 7.4 cm, LT = 6.3 cm, FT = 5.1 cm, OT = 9.8 cm",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 6,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch4a6.jpg",
					"width": "445",
					"height": "316"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Rhombus SEND. <br> SN = 6.4 cm, DE = 7.6 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": "ch4a7.jpg",
					"width": "417",
					"height": "230"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral TURN. <br> TU = 6.7 cm, UR = 4.3 cm, ∠T = 60º, ∠U = 105º, ∠R = 105º.",
				"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": "ch4a8.jpg",
					"width": "451",
					"height": "267"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral CAMP. <br> CA = 4.3 cm, AM = 5.5 cm, ∠C = 90º, ∠M = 70º, ∠P = 125º.",
				"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": "ch4a9.jpg",
					"width": "468",
					"height": "272"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Parallelogram THOR. <br> TH = 5 cm, HO = 7 cm, ∠R = 85º",
				"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": "ch4a10.jpg",
					"width": "548",
					"height": "342"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Rectangle THIN. <br> TH = 7.5 cm, HI = 5.2 cm.",
				"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": "ch4a11.jpg",
					"width": "486",
					"height": "218"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral GATE. <br> GA = 4 cm, AT = 6 cm, TE = 4.8 cm, ∠A = 60º, ∠T = 90º.",
				"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": "ch4a12.jpg",
					"width": "550",
					"height": "259"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct the following quadrilaterals. <br> Quadrilateral DONE. <br> DO = 4.5 cm, ON = 4 cm, NE = 5 cm, ∠O = 75º, ∠N = 120º.",
				"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": "ch4a13.jpg",
					"width": "550",
					"height": "292"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw the following: <br> The square PECK with PE = 5.3 cm",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 14,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch4a14.jpg",
					"width": "550",
					"height": "242"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw the following: <br> A rhombus whose diagonals are 5.4 and 6.8 cm",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 14,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch4a15.jpg",
					"width": "550",
					"height": "255"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw the following: <br> A rectangle with adjacent sides of length 7 cm and 4 cm.",
				"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": "ch4a16.jpg",
					"width": "550",
					"height": "224"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw the following: <br> A parallelogram LOCK where LO = 5.8 cm and OC = 4.4 cm.",
				"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": "ch4a17.jpg",
					"width": "550",
					"height": "245"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct a rhombus whose side is 5 cm and an angle is of 60º.",
				"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": "ch4a18.jpg",
					"width": "447",
					"height": "388"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct a square of side 4 cm.",
				"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": "ch4a19.jpg",
					"width": "550",
					"height": "237"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Construct a quadrilateral BEAR in which BE = 6 cm, EA = 7 cm, RB = RE = 5 cm and BA = 9 cm. Measure its fourth side.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 19,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch4a20.jpg",
					"width": "550",
					"height": "229"
				}
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch4_un",
	"map": "ch4_map",
	"afq": "ch4_afq",
	"snc": "ch4_snc",
	"gowf": "ch4_gowf",
	"pbq": "ch4_pbq",
	"mtf": "ch4_mtf",
	"tf": "ch4_tf",
	"afow": "ch4_afow",
	"cs": "ch4_cs",
	"ctco": "ch4_ctco",
	"vsaq": "ch4_vsaq",
	"grade": "Grade 8",
	"mcq": "ch4_mcq",
	"dtf": "ch4_dtf",
	"grf": "ch4_grf",
	"fib": "ch4_fib",
	"saq": "ch4_saq",
	"laq": "ch4_laq",
	"nf": "ch4_nf",
	"co": "ch4_co",
	"jtf": "ch4_jtf",
	"yn": "ch4_yn",
	"ctt": "ch4_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch5",
	"chapterName": "Chapter 5 - Data Handling",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "The height of a rectangle in a histogram shows the",
				"ans": "(d) frequency of the class",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) width of the class",
					"(b) upper limit of the class",
					"(c) lower limit of the class",
					"(d) frequency of the class"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A geometric representation showing the relationship between a whole and its part is a",
				"ans": "(a) pie chart",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) pie chart",
					"(b) histogram",
					"(c) bargraph",
					"(d) pictograph"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In a pie chart, the total angle at the centre of the circle is",
				"ans": "(b) 360º",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 180º",
					"(b) 360º",
					"(c) 270º",
					"(d) 90º"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The Range of the data 30, 61, 55, 56, 60, 20, 26, 46, 28, 56 is",
				"ans": "(d) 61",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 26",
					"(b) 30",
					"(c) 41",
					"(d) 61"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is not a random experiment?",
				"ans": "(b) Rolling a die",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) Tossing a coin",
					"(b) Rolling a die",
					"(c) Choosing a card from a deck fo 52 cards",
					"(d) Throwing a stone from roof of a building"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "What is the probability of choosing a vowel from the alphabets?",
				"ans": "(b) 5/26",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 21/26",
					"(b) 5/26",
					"(c) 1/26",
					"(d) 3/26"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A graph showing two sets of data simultaneously is known as",
				"ans": "(d) double bar graph",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) pictograph",
					"(b) histogram",
					"(c) pie chart",
					"(d) double bar graph"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Tally marks are used to find",
				"ans": "(c) frequency",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) class intervals",
					"(b) range",
					"(c) frequency",
					"(d) upper limit"
				],
				"val": 8
			}
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tDouble bar graph is useful for the comparison of the data.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tUsually, data available to us in an organised form.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tFrequency gives the number of times that a particular entry occurs.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tTo draw meaningful inferences, data should be grouped.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 4
			},			
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIn a pie chart, a whole circle is divided into sectors.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 5
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe central angle of a sector in a pie chart cannot be more than 180º.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 6
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tSum of all the central angles in a pie chart is 360º.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 7
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIn a pie chart, two central angles can be of 180º.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 8
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tGetting a prime number on throwing a die is an event.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 9
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIf a pair of coins is tossed, then the number of outcomes are 2.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 10
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tOn throwing a die once, the probability of occurrence of an even number is 1/2\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 11
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tOne or more outcomes of an experiment make an event.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 12
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "_______________ is usually collected in the context of a situation that we want to study.",
				"ans": "Data",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Data may be represented _______________ to give a clear idea of what it represents.",
				"ans": "graphically",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A _______________ shows two sets of data simultaneously.",
				"ans": "bar graph",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Data available to us in an unorganised form is called _______________.",
				"ans": "raw data",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A _______________ shows the relationship between a whole and its parts.",
				"ans": "circle graph",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A circle graph is also called a _______________.",
				"ans": "pie chart",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The total angle at the centre of a circle is _______________.",
				"ans": "360º",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Experiments whose results have an equal chance of occuring are called _______________.",
				"ans": "random experiments",
				"code": "FIB",
				"val": 8
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Outcome of an experiment or a collection of outcomes make an _______________.",
				"ans": "event",
				"code": "FIB",
				"val": 9
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Data available in an unorganised form is called _______________ data.",
				"ans": "raw",
				"code": "FIB",
				"val": 10
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "In the class interval 26 – 33, 33 is known as _______________.",
				"ans": "upper class limit",
				"code": "FIB",
				"val": 11
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A pie chart is used to compare _______________ to a whole.",
				"ans": "a part",
				"code": "FIB",
				"val": 12
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "In the experiment of tossing a coin one time, the outcome is either _______________ or _______________.",
				"ans": "head, tail",
				"code": "FIB",
				"val": 13
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "When a die is rolled, the six possible outcomes are _______________.",
				"ans": "1, 2, 3, 4, 5, 6",
				"code": "FIB",
				"val": 14
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Each outcome or a collection of outcomes in an experiment makes an _______________.",
				"ans": "event",
				"code": "FIB",
				"val": 15
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The difference between the upper and lower limits of class interval is called _______________ of the class interval.",
				"ans": "size",
				"code": "FIB",
				"val": 16
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The total number of outcomes when a coin is tossed is _______________.",
				"ans": "2",
				"code": "FIB",
				"val": 17
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "When a die is thrown, outcomes 1, 2, 3, 4, 5, 6 are equally _______________.",
				"ans": "likely",
				"code": "FIB",
				"val": 18
			}
			
		],
		[],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "For which of these would you use a Bar graph to show the data? <br> A. A bar graph makes it easy to compare sets of data between groups at a glance. <br> B. The number of letters for different areas in a postman’s bag. <br> C. The height of competitors in an athletics meet. <br> D. Bar graph can also show big changes in data over time. <br> Give reasons for each.",
				"ans": "In Case of the data given in alternative (A) and (D), we will use Bar graph because it presents categorical data with rectangular bars with heights or lengths proportional to the values. In case of alternatives (B) and (C), we do not know number of letters for different areas and height of competitors in an athletics. So we can’t use both option for bar graph.",
				"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 customer who came to a departmental store are marked as: Boy (B) or Girl (G). The following list gives the customer who came during the first hour in the morning:",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 2,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch5a18.jpg",
					"width": "550",
					"height": "123"
				},
				"ansimg": {
					"image": "ch5a1.jpg",
					"width": "500",
					"height": "264"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The weekly wages (in ₹) of 20 workers in a factory is: <br/> 930, 935, 900, 910 <br/>915, 920, 936, 940<br/>945, 960, 961, 982<br/>999, 952, 932, 918<br/>901, 905, 977, 948<br/>Using tally marks make a frequency table with intervals as 900 – 910, 910 – 920 and so on.",
				"ans": "A frequency distribution table by using tally marks for the above data is as follows.",
				"code": "SATQ",
				"options": null,
				"val": 3,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [
					{
						"image": "Interval",
						"width": null,
						"height": null
					},
					{
						"image": "900 – 910",
						"width": null,
						"height": null
					},
					{
						"image": "910 – 920",
						"width": null,
						"height": null
					},
					{
						"image": "920 – 930",
						"width": null,
						"height": null
					},
					{
						"image": "930 – 940",
						"width": null,
						"height": null
					},
					{
						"image": "940 – 950",
						"width": null,
						"height": null
					},
					{
						"image": "950 – 960",
						"width": null,
						"height": null
					},
					{
						"image": "960 – 970",
						"width": null,
						"height": null
					},
					{
						"image": "970 – 980",
						"width": null,
						"height": null
					},
					{
						"image": "980 – 990",
						"width": null,
						"height": null
					},
					{
						"image": "990 – 1000",
						"width": null,
						"height": null
					}
				],
				"aoption2": [
					{
						"image": "Tally Marks",
						"width": null,
						"height": null
					},
					{
						"image": "|||",
						"width": null,
						"height": null
					},
					{
						"image": "|||",
						"width": null,
						"height": null
					},
					{
						"image": "|",
						"width": null,
						"height": null
					},
					{
						"image": "||||",
						"width": null,
						"height": null
					},
					{
						"image": "|||",
						"width": null,
						"height": null
					},
					{
						"image": "|",
						"width": null,
						"height": null
					},
					{
						"image": "||",
						"width": null,
						"height": null
					},
					{
						"image": "|",
						"width": null,
						"height": null
					},
					{
						"image": "|",
						"width": null,
						"height": null
					},
					{
						"image": "|",
						"width": null,
						"height": null
					}
				],
				"aoption3": [
					{
						"image": "Frequency",
						"width": null,
						"height": null
					},
					{
						"image": "3",
						"width": null,
						"height": null
					},
					{
						"image": "3",
						"width": null,
						"height": null
					},
					{
						"image": "1",
						"width": null,
						"height": null
					},
					{
						"image": "4",
						"width": null,
						"height": null
					},
					{
						"image": "3",
						"width": null,
						"height": null
					},
					{
						"image": "1",
						"width": null,
						"height": null
					},
					{
						"image": "2",
						"width": null,
						"height": null
					},
					{
						"image": "1",
						"width": null,
						"height": null
					},
					{
						"image": "1",
						"width": null,
						"height": null
					},
					{
						"image": "1",
						"width": null,
						"height": null
					}
				],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw a Histogram for the frequency table made for the data in Question 3 and answer the following question. <br> (i) Which group has the maximum number of workers? <br> (ii) How many workers earn ₹ 950 and more? <br> (iii) How many workers earn less than 950?",
				"ans": "(i) 930 – 940 is the group which has the maximum number of workers. <br> (ii) The workers who earn more than ₹ 950 are the number of workers who fall in the group of 950 – 960 or 960 – 970 or 970 – 980 or 980 – 990 or 990 – 1000. Hence the total number of workers earning more than 950 will be the sum of the numbers of all these workers i.e. 1 + 2 + 1 + 1 + 1 = 06. <br> (iii) The workers who earn less than ₹ 950 are the number of workers who fall in the group 900–910 or 910 – 920 or 920 – 930, 930 – 940 or 940 – 950. Hence the total will be the sum of the numbers of all these workers i.e., 3 + 3 + 1 + 4 + 3 = 14.",
				"code": "SATQ",
				"options": null,
				"val": 4,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch5a3.jpg",
					"width": "502",
					"height": "274"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The number of hours for which students of a particular class play games in mobile during holiday is shown through the given graph. <br> Answer the following: <br> (i) For how many hours, did the maximum number of students play games in mobile? <br> (ii) How many students play games in mobile for less than 4 hours? <br> (iii) How many students spent more than 5 hours in playing games in mobile?",
				"ans": "(i) From the graph, it can be observed that the maximum number of students (i.e. 32) play games in mobile for 4 – 5 hours. <br> (ii) The students who play games in mobile for less than 4 hours are the students who play games in mobile for 1 – 2 hours or 2 – 3 hours or 3 – 4 hours. Hence, total number of students = 4 + 8 + 22 = 34. <br> (iii) The students who play games in mobile for more than 5 hours are the students who play games in mobile for 5 – 6 hours or 6 – 7 hours. Hence, required no. of students = 8 + 6 = 14.",
				"code": "SATQ",
				"options": null,
				"val": 5,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch5a4.jpg",
					"width": "252",
					"height": "255"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "A survey was made to find the type of fast food that a certain group of young people liked to eat in a city. Adjoining pie chart shows the findings of this survey. <br> From this pie chart answer the following.<br>(i) If 20 people liked vadapav to eat. How many young people were surveyed? <br> (ii) Which type of fast food is liked by the maximum number of people? <br> (iii) If karnavati fast food center makes 1000 items to eat, how many of each type would it make.",
				"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": "ch5a6.jpg",
					"width": "550",
					"height": "489"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "A group of 460 people were asked to vote for their favourite season from three seasons rainy, winter and summer. <br> (i) Which season got the most vote? <br> (ii) Find the central angle of each sector? <br> (iii) Draw a pie chart to show this information.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 7,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch5a7.jpg",
					"width": "374",
					"height": "86"
				},
				"ansimg": {
					"image": "ch5a8.jpg",
					"width": "550",
					"height": "376"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 8,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch5a9.jpg",
					"width": "487",
					"height": "136"
				},
				"ansimg": {
					"image": "ch5a10.jpg",
					"width": "550",
					"height": "363"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The adjoining pie chart gives the marks scored in an examination by a student in Gujarati, English, Mathematics, Social science and Science. If the total marks obtained by the students were 600, answer the following questions. <br> (i) In which subject did the student score 100 marks? <br> (Hint:) For 600 marks, the central angle = 360º (so for 100 marks, what is the central angle?) <br> (ii) How many more marks were obtained by the student in Mathematics than in Hindi? <br> (iii) Examine whether the sum of the marks obtained in Social science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles)",
				"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": "ch5a11.jpg",
					"width": "550",
					"height": "331"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Number 1 to 20 are written on twenty separate papers (one number on one paper) kept in a box and mixed well. One paper is chosen from the box without looking into it. What is the probability of <br> (i) getting a number 8? <br> (ii) getting a number less than 8. <br> (iii) getting a number greater than 12? <br> (iv) getting a 2 digit number?",
				"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": "ch5a15.jpg",
					"width": "550",
					"height": "280"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "If you have a spinning wheel with 1 green sectors, 3 blue sector and 1 red sector. What is the probability of getting a red sector? What is the probability of getting, a non green sector?",
				"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": "ch5a16.jpg",
					"width": "550",
					"height": "151"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the probabilities of the events given in Quesiton-2.",
				"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": "ch5a17.jpg",
					"width": "550",
					"height": "223"
				}
			},
		],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": "Answer the following questions based on the pie chart given <br> (i) Which type of programmes are viewed the most? <br> (ii) Which type of programmes are viewed the least? <br> (iii) Which two types of programmes have number of viewers equal to those watching sports channels?",
				"ans": "(i) Entertainment progammes are viewed the most. <br> (ii) Informative programmes are viewed the least. <br> (iii) News and informative programmes have number of viewers equal to those watching sports channels.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch5a5.jpg",
					"width": "208",
					"height": "229"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 1
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "List the outcomes you can see in these experiments. <br> (a) Spinning wheel. <br> (b) Tossing three coins together.",
				"ans": "(a) On spinning the given wheel, the possible outcomes are A, B, C, D <br> (b) By tossing three coins together, the possible outcomes are HHT, HTH, HHH, TTH, THT, TTT, THH,HTT where H and T represents Head and Tail of the coins respectively.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch5a12.jpg",
					"width": "129",
					"height": "122"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the <br> (a) Probability of the pointer stopping on C (in (Question 1 – (a))? <br> (b) Probability of getting an ace from a well shuffled deck of 52 playing cards? <br> (c) Probability of getting an Orange (see figure below) from red apples (R) and oranges (O).",
				"ans": "(a) On spinning the given wheel, the possible outcomes are A, B, C, D <br> (b) By tossing three coins together, the possible outcomes are HHT, HTH, HHH, TTH, THT, TTT, THH,HTT where H and T represents Head and Tail of the coins respectively.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch5a13.jpg",
					"width": "153",
					"height": "150"
				},
				"ansimg": {
					"image": "ch5a14.jpg",
					"width": "500",
					"height": "226"
				},
				"val": 3
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch5_un",
	"map": "ch5_map",
	"afq": "ch5_afq",
	"snc": "ch5_snc",
	"gowf": "ch5_gowf",
	"pbq": "ch5_pbq",
	"mtf": "ch5_mtf",
	"tf": "ch5_tf",
	"afow": "ch5_afow",
	"cs": "ch5_cs",
	"ctco": "ch5_ctco",
	"vsaq": "ch5_vsaq",
	"grade": "Grade 8",
	"mcq": "ch5_mcq",
	"dtf": "ch5_dtf",
	"grf": "ch5_grf",
	"fib": "ch5_fib",
	"saq": "ch5_saq",
	"laq": "ch5_laq",
	"nf": "ch5_nf",
	"co": "ch5_co",
	"jtf": "ch5_jtf",
	"yn": "ch5_yn",
	"ctt": "ch5_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch6",
	"chapterName": "Chapter 6 - Squares and Square Roots",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "225 is the square of",
				"ans": "(b) dog",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 15",
					"(b) 25",
					"(c) 35",
					"(d) 40"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is a square of an even number?",
				"ans": "(b) 196",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 289",
					"(b) 196",
					"(c) 225",
					"(d) 169"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A number ending in 9 will have the unit’s place of its square as",
				"ans": "(c) 1",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 3",
					"(b) 9",
					"(c) 1",
					"(d) 6"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following will have 9 at the unit’s place?",
				"ans": "(c) 27<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 14<sup>2</sup>",
					"(b) 62<sup>2</sup>",
					"(c) 27<sup>2</sup>",
					"(d) 35<sup>2</sup>"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "13<sup>2</sup> =",
				"ans": "(a) 169",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 169",
					"(b) 196",
					"(c) 13",
					"(d) 131"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "5, 12, 13 are",
				"ans": "(b) Pythagorean triplet",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) consecutive",
					"(b) Pythagorean triplet",
					"(c) even",
					"(d) odd"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Pythagorean triplet whose smallest number is 6",
				"ans": "(c) 6, 8, 10",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 6, 7, 8",
					"(b) 6, 8, 9",
					"(c) 6, 8, 10",
					"(d) 10, 13, 6"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "How many natural numbers lie between 8<sup>2</sup> and 9<sup>2</sup>?",
				"ans": "(b) 16",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 15",
					"(b) 16",
					"(c) 17",
					"(d) 10"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If one member of a Pythagorean triplet is 2m, then the other two members are",
				"ans": "(b) 16",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) m, m<sup>2</sup> + 1",
					"(b) m<sup>2</sup> + 1, m<sup>2</sup> – 1",
					"(c) m<sup>2</sup>, m<sup>2</sup> – 1",
					"(d) m2, m + 1"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A perfect square can never have the following digit in its one’s place",
				"ans": "(b) 8",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 1",
					"(b) 8",
					"(c) 4",
					"(d) 6"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A square board has an area of 144 sq. units. How long is each side of the board?",
				"ans": "(b) 12 units",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 11 units",
					"(b) 12 units",
					"(c) 13 units",
					"(d) 14 units"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which letter best represents the location of √36 on a number line?",
				"ans": "(c) C",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 0",
					"(b) A",
					"(c) C",
					"(d) B"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "To find square root by division method place a bar over every pair of digits starting from the _____ side.",
				"ans": "(b) right",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) left",
					"(b) right",
					"(c) middle",
					"(d) none"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "How many bars 4096 number has?",
				"ans": "(d) 2",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 4",
					"(b) 1",
					"(c) 3",
					"(d) 2"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "In 176341 first bar is over",
				"ans": "(c) 41",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 17",
					"(b) 34",
					"(c) 41",
					"(d) 63"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "√350 is approximately",
				"ans": "(b) 19",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 18",
					"(b) 19",
					"(c) 20",
					"(d) 10"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is a square of an even number?",
				"ans": "(a) 144",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 144",
					"(b) 169",
					"(c) 441",
					"(d) 625"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A number ending in 9 will have the unit’s place of its square as",
				"ans": "(c) 1",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 3",
					"(b) 9",
					"(c) 1",
					"(d) 6"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following will have 4 at the unit’s place?",
				"ans": "(c) 1",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 14<sup>2</sup>",
					"(b) 62<sup>2</sup>",
					"(c) 27<sup>2</sup>",
					"(d) 35<sup>2</sup>"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following cannot be a perfect square?",
				"ans": "(c) 1",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 841",
					"(b) 529",
					"(c) 198",
					"(d) All of these"
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If M is the square of a natural number n, then n is",
				"ans": "(d) √M",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) the square of M",
					"(b) greater than M",
					"(c) equal to M",
					"(d) √M"
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": null,
				"ans": "(d) 13",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 14",
					"(b) 12",
					"(c) 16",
					"(d) 13"
				],
				"pic": {
					"image": "ch6a22.jpg",
					"width": "231",
					"height": "29"
				},
				"val": 22
			},
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe square of 96 will have 6 at the unit’s place.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe sum of two perfect squares is a perfect square.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThere is no square number between 30 and 40.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe square of every natural number is always greater than the number itself.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 4
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t100 is a perfect square.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 5
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t10000 is a perfect square.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 6
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t75<sup>2</sup> = (7 × 8) hundreds + 25\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 7
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t5<sup>2</sup> + 7<sup>2</sup> = 12<sup>2</sup>\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 8
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t6<sup>2</sup> + 8<sup>2</sup> = 10<sup>2</sup>\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 9
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t14 × 16 = 15<sup>2</sup> – 1\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 10
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t105<sup>2</sup> = 11025\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 11
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t48 × 3 is a perfect square.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 12
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t40 is a perfect square.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 13
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThere are 200 natural numbers between 100<sup>2</sup> and 101<sup>2</sup>.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 14
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe sum of first n odd natural numbers is n<sup>2</sup>.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 15
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe sum of two perfect squares is a perfect square.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 16
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThere is no perfect square number between 50 and 60.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 17
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe square of 2.8 is 78.4.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 18
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe square of every natural number is always greater than the number itself.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 19
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t1000 is a perfect square.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 21
			},
			{
				"heading": "State True or False.",
				"qus": null,
				"ans": "False",
				"code": "TF",
				"pic": {
					"image": "ch6a21.jpg",
					"width": "450",
					"height": "33"
				},
				"val": 22
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "There are ______________ perfect squares between 1 and 50.",
				"ans": "6",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The unit’s digit in the square of 1384 is ______________.",
				"ans": "6",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The square of 4000 will have ______________ zeroes.",
				"ans": "6",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The square of 0.5 is ______________.",
				"ans": "0.25",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "1 km<sup>2</sup> = ______________ m<sup>2</sup>.",
				"ans": "1000000",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Square of 40<sup>2</sup> =______________.",
				"ans": "1600",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "625 is the square of ______________.",
				"ans": "25",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "(a + b)<sup>2</sup> = ______________.",
				"ans": "a<sup>2</sup> + 2ab + b<sup>2</sup>",
				"code": "FIB",
				"val": 8
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "When a square number ends in 6, the number whose square it is, will have either ______________ or ______________ in unit’s place.",
				"ans": "4, 6",
				"code": "FIB",
				"val": 9
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "(39)<sup>2</sup> = ______________.",
				"ans": "(30 + 9)<sup>2</sup>",
				"code": "FIB",
				"val": 10
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "If 6 = 2 × 3 then 6<sup>2</sup> = ______________.",
				"ans": "(2 × 3)<sup>2</sup>",
				"code": "FIB",
				"val": 11
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "5<sup>2</sup>  = x<sup>2</sup>  + 16, then x<sup>2</sup>  = ______________.",
				"ans": "9",
				"code": "FIB",
				"val": 12
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "14<sup>2</sup> = 196, then square root of 196 is ______________.",
				"ans": "14",
				"code": "FIB",
				"val": 13
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Positive square root of a number is denoted by the symbol ______________.",
				"ans": "√",
				"code": "FIB",
				"val": 14
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "There are ______________ perfect, squares between 1 and 100.",
				"ans": "eight",
				"code": "FIB",
				"val": 15
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The unit’s digit in the square of 1294 is ______________.",
				"ans": "6",
				"code": "FIB",
				"val": 16
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The square of 5.5 is ______________.",
				"ans": "30.25",
				"code": "FIB",
				"val": 17
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The square root of 5.3 × 5.3 is ______________.",
				"ans": "5.3",
				"code": "FIB",
				"val": 18
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The least number by which 125 be multiplied to make it a perfect square, is ______________.",
				"ans": "5",
				"code": "FIB",
				"val": 19
			},
		],
		[],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "Write a Pythagoras triplet whose one member is : <br> 20",
				"ans": "There are three numbers 2m, m<sup>2</sup> – 1 and m<sup>2</sup> + 1 in a Pythagorean Triplet. <br> Here, 2m = 20 <br>∴ m = 20/2 = 10 <br> Therefore, Second number (m<sup>2</sup> – 1) = (10)<sup>2</sup> – 1 = 100 – 1 = 99 <br> Third number (m<sup>2</sup> + 1) = (10)<sup>2</sup> + 1 = 100 + 1 = 101 <br> Hence, Pythagorean triplet is 20, 99, 101",
				"code": "SATQ",
				"options": null,
				"val": 1,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Write a Pythagoras triplet whose one member is : <br> 24",
				"ans": "There are three numbers 2m, m<sup>2</sup> – 1 and m<sup>2</sup> + 1 in a Pythagorean Triplet. <br> Here, 2m = 24 <br>∴ m = 24/2 = 12 <br> Therefore, Second number (m<sup>2</sup> – 1) = (12)<sup>2</sup> – 1 = 144 – 1 = 143 <br> Third number (m<sup>2</sup> + 1) = (12)<sup>2</sup> + 1 = 144 + 1 = 145 <br> Hence, Pythagorean triplet is 24, 143, 145",
				"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": "Write a Pythagoras triplet whose one member is : <br> 8",
				"ans": "There are three numbers 2m, m<sup>2</sup> – 1 and m<sup>2</sup> + 1 in a Pythagorean Triplet. <br> Here, 2m = 8 <br>∴ m = 8/2 = 4 <br> Therefore, Second number (m<sup>2</sup> – 1) = (4)<sup>2</sup> – 1 = 16 – 1 = 15 <br> Third number (m<sup>2</sup> + 1) = (4)<sup>2</sup> + 1 = 16 + 1 = 17 <br> Hence, Pythagorean triplet is 8, 15, 17",
				"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": "Write a Pythagoras triplet whose one member is : <br> 22",
				"ans": "There are three numbers 2m, m<sup>2</sup> – 1 and m<sup>2</sup> + 1 in a Pythagorean Triplet. <br> Here, 2m = 22 <br>∴ m = 22/2 = 11 <br> Therefore, Second number (m<sup>2</sup> – 1) = (11)<sup>2</sup> – 1 = 121 – 1 = 120 <br> Third number (m<sup>2</sup> + 1) = (11)<sup>2</sup> + 1 = 121 + 1 = 122 <br> Hence, Pythagorean triplet is 22, 120, 122",
				"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 the square roots of the following numbers by prime factorisation method: <br> (i) 625 <br> (ii) 1225 <br> (iii) 3844 <br> (iv) 5625 <br> (v) 2304",
				"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": "ch6a1.jpg",
					"width": "550",
					"height": "469"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square numbers. Also, find the square root of the square number so obtained: <br> (i) 432 <br> (ii) 1000 <br> (iii) 700",
				"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": "ch6a2.jpg",
					"width": "498",
					"height": "647"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained: <br> (i) 5445 <br> (ii) 3872",
				"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": "ch6a3.jpg",
					"width": "485",
					"height": "394"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained: <br> (iii) 3380 <br> (iv) 8092",
				"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": "ch6a4.jpg",
					"width": "508",
					"height": "371"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The students of class VIII of a school donated ₹ 3136 for flood base camp. Each student donated as many rupees as the number of students in the class. Find number of students in the class.",
				"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": "ch6a5.jpg",
					"width": "399",
					"height": "244"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "1936 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.",
				"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": "ch6a6.jpg",
					"width": "385",
					"height": "258"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the smallest square number that is divisible by each of the numbers 4, 6 and 15.",
				"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": "ch6a7.jpg",
					"width": "486",
					"height": "182"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the smallest square number that is divisible by each of the numbers 3, 18 and 21.",
				"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": "ch6a8.jpg",
					"width": "502",
					"height": "188"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the square roots of each of the following numbers by Division method. <br> 6889 <br> 4225 <br> 7921",
				"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": "ch6a9.jpg",
					"width": "371",
					"height": "472"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the number of digits in the square root of each of the following numbers. (without any calculation) <br> (i) 6561 <br> (ii) 676 <br> (iii) 12544",
				"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": "ch6a10.jpg",
					"width": "456",
					"height": "283"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the square root of the following decimal numbers: <br> 4.84 <br> 24.01 <br> 10.24",
				"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": "ch6a11.jpg",
					"width": "400",
					"height": "445"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained: <br> 531 <br> 24.01 <br> 2606",
				"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": "ch6a12.jpg",
					"width": "546",
					"height": "594"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained: <br> 3726 <br> 6244 <br> 2606",
				"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": "ch6a13.jpg",
					"width": "535",
					"height": "500"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the least number must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. <br> 3726 <br> 836 <br> 3013",
				"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": "ch6a14.jpg",
					"width": "423",
					"height": "493"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the least number must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. <br> 3726 <br> 475 <br> 1430",
				"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": "ch6a15.jpg",
					"width": "424",
					"height": "511"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the length of the side of a square whose area is 784 m<sup>2</sup>?",
				"ans": "Let the length of side of a square be x metre. <br> Area of square = (Side)<sup>2</sup> <br>∴ 784 = (x)<sup>2</sup> <br>∴ √784 = x <br>∴ √2 × 2 × 2 × 2 × 7 × 7 = x <br> ∴ 2 × 2 × 7 = x <br>∴ 28 = x ∴ x = 28",
				"code": "SATQ",
				"options": null,
				"val": 16,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch6a16.jpg",
					"width": "78",
					"height": "71"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "In a right triangle, ∠Q = 90º <br> (i) If PQ = 7 cm, QR = 24 cm, find PR. <br> (ii) If QR = 24 cm, PR = 26 cm, then find PQ",
				"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": "ch6a17.jpg",
					"width": "383",
					"height": "448"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Soham has 665 stones. He wants to keep these stones in such a way that the number of rows and number of columns remain same. Find the minimum number of stones be needed more for this.",
				"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": "ch6a19.jpg",
					"width": "412",
					"height": "180"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "There are 1035 chairs in a school. School staff have to arrange chairs in such a manner that the number of rows is equal to number of columns. How many chairs would be left out in this arrangement?",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 19,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch6a20.jpg",
					"width": "540",
					"height": "148"
				}
			},
		],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": "What will be the unit digit of the squares of the following numbers? <br> 69",
				"ans": "The number 69 contains its unit’s place digit 9. So, square of 9 is 81. <br> Hence, unit’s digit of square of 69 is 1.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 1
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What will be the unit digit of the squares of the following numbers? <br> 88770",
				"ans": "The number 88770 contains its unit’s place digit 0. So, square of 0 is 0. <br> Hence, units digit of square of 88770 is 0.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What will be the unit digit of the squares of the following numbers? <br> 461",
				"ans": "The number 461 contains its unit’s place digit 1. So, square of 1 is 1. <br> Hence, units digit of square of 461 is 1.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 3
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What will be the unit digit of the squares of the following numbers? <br> 12856",
				"ans": "The number 12856 contains its unit’s place digit 6. So, square of 6 is 36. <br> Hence, units digit of square of 12856 is 6.",
				"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": "What will be the unit digit of the squares of the following numbers? <br> 382",
				"ans": "The number 382 contains its unit’s place digit 2. So, square of 2 is 4. <br> Hence, units digit of square of 382 is 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": 5
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What will be the unit digit of the squares of the following numbers? <br> 70433",
				"ans": "The number 70433 contains its unit’s place digit 3. So, square of 3 is 9. <br> Hence, units digit of square of 70433 is 9.",
				"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": "What will be the unit digit of the squares of the following numbers? <br> 3205",
				"ans": "The number 3205 contains its unit’s place digit 5. So, square of 5 is 25. <br> Hence, units digit of square of 3205 is 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": 7
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What will be the unit digit of the squares of the following numbers? <br> 631",
				"ans": "The number 631 contains its unit’s place digit 1. So, square of 1 is 1. <br> Hence, units digit of square of 631 is 1.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 8
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What will be the unit digit of the squares of the following numbers? <br> 58927",
				"ans": "The number 58927 contains its unit’s place digit 7. So, square of 7 is 49. <br> Hence, units digit of square of 58927 is 9.",
				"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": "What will be the unit digit of the squares of the following numbers? <br> 70828",
				"ans": "The number 70828 contains its unit’s place digit 8. So, square of 8 is 64. <br> Hence, units digit of square of 70828 is 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": "The following numbers are obviously not perfect squares. Give reasons: <br> 3048",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0’s. <br> ∴ 3048 is not a perfect square number because its unit digit is 8.",
				"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": "The following numbers are obviously not perfect squares. Give reasons: <br> 38173",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0’s. <br> ∴ 38173 is not a perfect square number because its unit digit is 3.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 12
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The following numbers are obviously not perfect squares. Give reasons: <br> 5067",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0’s. <br> ∴ 5067 is not a perfect square number because its unit digit is 7.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 13
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The following numbers are obviously not perfect squares. Give reasons: <br> 808080",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0’s. <br> ∴ 808080 is not a perfect square number because it is not having even number of zeroes.",
				"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": "The following numbers are obviously not perfect squares. Give reasons: <br> 80122",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0’s. <br> ∴ 80122 is not a perfect square number because its unit digit is 2.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 15
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The following numbers are obviously not perfect squares. Give reasons: <br> 39260",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0’s. <br> ∴ 39260 is not a perfect square number because it is not having even number of zeroes.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 16
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The following numbers are obviously not perfect squares. Give reasons: <br> 90702",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0. <br> ∴ 90702 is not a perfect square number because its unit digit is 2.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 17
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The following numbers are obviously not perfect squares. Give reasons: <br> 56707",
				"ans": "Since perfect square numbers contain their unit’s digit 1, 4, 5, 6, 9 and even number of 0. <br> ∴ 56707 is not a perfect square number because its unit digit is 7.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 18
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The squares of which of the following would be odd number: <br> 3526",
				"ans": "Unit’s digit of given number is 6 and square of 6 is 36. Therefore, square of 3526 would not be an odd 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": 19
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The squares of which of the following would be odd number: <br> 38024",
				"ans": "Unit’s digit of given number is 4 and square of 4 is 16. Therefore, square of 38024 would not be an odd 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": 20
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The squares of which of the following would be odd number: <br> 681",
				"ans": "Unit’s digit of given number is 1 and square of 1 is 1. Therefore, square of 681 would be an odd 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": 21
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "The squares of which of the following would be odd number: <br> 2939",
				"ans": "Unit’s digit of given number is 9 and square of 9 is 81. Therefore, square of 2939 would be an odd 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": 22
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Observe the following pattern and find the missing digits",
				"ans": "1<sup>2</sup> = 1 <br> 11<sup>2</sup> = 121 <br> 111<sup>2</sup> = 12321 <br> 1111<sup>2</sup> = 1234321 <br> 11111<sup>2</sup> = ? <br> 111111<sup>2</sup> = ? <br> 1111111<sup>2</sup> = ? <br> 11111<sup>2</sup> = 123454321 <br> 111111<sup>2</sup> = 12345654321 <br> 1111111<sup>2</sup> = 1234567654321",
				"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": 23
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Observe the following pattern and find the missing digits",
				"ans": "7<sup>2</sup> = 49 <br> 67<sup>2</sup> = 4489 <br> 667<sup>2</sup> = 444889 <br> 6667<sup>2</sup> = 44448889 <br> 66667<sup>2</sup> = ? <br> 666667<sup>2</sup> = ? <br> 66667<sup>2</sup> = 4444488889 <br> 666667<sup>2</sup> = 444444888889",
				"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": "Without adding find the sum: <br> (i) 1 + 3 + 5 + 7 + 9 + 11 <br> (ii) 1 + 3 + 5 + 7 <br> (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15",
				"ans": "(i) Here, there are 6 odd numbers: 6<sup>2</sup> = 36 <br> 1 + 3 + 5 + 7 + 9 + 11 = 36 <br> <br/> (ii) Here there are 4 odd numbers: 4<sup>2</sup> = 16 <br> <br/> (ii) Here, there are 8 odd numbers: 8<sup>2</sup> = 64 <br> 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64",
				"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
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "(i) Express 81 as the sum of 9 odd numbers. <br> (ii) Express 169 as the sum of 13 odd numbers.",
				"ans": "(i) 81 is the square of 9. <br> Therefore, it has the sum of 9 odd numbers. <br> 81 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 <br> 169 is the square of 13. <br> Therefore, it has the sum of 13 odd numbers. <br> <br/> (ii) 169 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25",
				"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": 26
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "How many numbers lie between squares of the following numbers? <br> (i) 16 and 17 <br> (ii) 21 and 23 <br> (iii) 61 and 62",
				"ans": "(i) Since non-perfect square numbers between n<sup>2</sup> and (n + 1)<sup>2</sup> are 2n. <br> Here, n = 16 <br> ∴ non-perfect square numbers between 16 and 17 <br> = 2n = 2 × 16 = 32 <br> <br/> (ii) Since non-perfect squares number <br>  between n<sup>2</sup> and (n + 1)<sup>2</sup> are 2n. <br> Here, n = 21 <br> non-perfect square numbers between 21 and 23 <br> = 2n = 2 × 21 = 42 <br> <br/> (iii) Since non-perfect square numbers between n<sup>2</sup> and (n + 1)<sup>2</sup> are 2n. <br> Here, n = 61 <br> non-perfect square number between 61 and 62 = 2n = 2 × 61 = 122",
				"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": 27
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the squares of the following numbers: <br> 41",
				"ans": "(41)<sup>2</sup> = (40 + 1)<sup>2</sup> <br> = (40)<sup>2</sup>  + 2(40) (1) + (1)<sup>2</sup> <br> [∵ (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>] <br> = 1600 + 80 + 1 = 1681",
				"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": 28
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the squares of the following numbers: <br> 89",
				"ans": "(89)<sup>2</sup> = (80 + 9)<sup>2</sup> <br> = (80)<sup>2</sup>  + 2(80) (9) + (9)<sup>2</sup> <br> [∵ (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>] <br> = 6400 + 1440 + 81 = 7921",
				"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": 29
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the squares of the following numbers: <br> 75",
				"ans": "(75)<sup>2</sup> = (70 + 5)<sup>2</sup> <br> = (70)<sup>2</sup>  + 2(70) (5) + (5)<sup>2</sup> <br> [∵ (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>] <br> = 4900 + 700 + 25 = 5625",
				"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": 30
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the squares of the following numbers: <br> 91",
				"ans": "(91)<sup>2</sup> = (90 + 1)<sup>2</sup> <br> = (90)<sup>2</sup>  + 2(90) (1) + (1)<sup>2</sup> <br> [∵ (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>] <br> = 8100 + 180 + 1 = 8281",
				"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": 31
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the squares of the following numbers: <br> 66",
				"ans": "(66)<sup>2</sup> = (60 + 1)<sup>2</sup> <br> = (60)<sup>2</sup>  + 2(60) (6) + (6)<sup>2</sup> <br> [∵ (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>] <br> = 3600 + 720 + 36 = 4356",
				"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": 32
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the squares of the following numbers: <br> 54",
				"ans": "(54)<sup>2</sup> = (50 + 4)<sup>2</sup> <br> = (50)<sup>2</sup>  + 2(50) (4) + (4)<sup>2</sup> <br> [∵ (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>] <br> = 2500 + 400 + 16 = 2916",
				"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": 33
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "What could be possible one’s digits of the square root of each of the following numbers: <br> (i) 34596 (ii) 87778161 (iii) 97121025 (iv) 641456929",
				"ans": "Unit’s digit of the squares of numbers are 0, 1, 4, 5, 6 and 9. <br> Thus possible one’s digits of the given numbers are: <br> (i) 4 or 6 (ii) 1 or 9 (iii) 5 (iv) 3 or 7",
				"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": 34
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the square root of 81 and 225 by the method of repeated subtraction.",
				"ans": "By successive subtraction of odd natural numbers from 81, <br> 81 – 1 = 80 &nbsp;&nbsp; 80 – 3 = 77 &nbsp;&nbsp; 77 – 5 = 72 <br> 72 – 7 = 65 &nbsp;&nbsp; 65 – 9 = 56 &nbsp;&nbsp; 56 – 11 = 45 <br> 45 – 13 = 32 &nbsp;&nbsp; 32 – 15 = 17 &nbsp;&nbsp; 17 – 17 = 0 <br> The successive method is completed in 9 steps ∴ √81 = 9 <br> By successive subtraction of odd natural numbers from 225 <br> 225 – 1 = 224 &nbsp;&nbsp; 224 – 3 = 221 &nbsp;&nbsp; 221 – 5 = 216 <br> 216 – 7 = 209 &nbsp;&nbsp; 209 – 9 = 200 &nbsp;&nbsp; 200 – 11 = 189 <br> 189 – 13 = 176 &nbsp;&nbsp; 176 – 15 = 161 &nbsp;&nbsp; 161 – 17 = 144 <br> 144 – 19 = 125 &nbsp;&nbsp; 125 – 21 = 104 &nbsp;&nbsp; 104 – 23 = 81 <br> 81 – 25 = 56 &nbsp;&nbsp; 56 – 27 = 29 &nbsp;&nbsp; 29 – 29 = 0 <br> The successive method is completed in fifteen steps ∴ √225 = 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": 35
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Show that 500 is not a perfect square.",
				"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": "ch6a23.jpg",
					"width": "450",
					"height": "142"
				},
				"val": 36
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Is 176 a perfect square? If not; find the smallest number by which it should be multiplied to get a perfect square.",
				"ans": "Factorisation of 176 = <u>2 × 2</u> × <u>2 × 2</u> × 11 <br> Here, 11 has no pair. <br> So, it is not a perfect square and 11 is the smallest number by which 176 should be multiplied to get a perfect square. <br> Then, 176 × 11 = 2<sup>2</sup> × 2<sup>2</sup> × 11 × 11 <br> = 2<sup>2</sup> × 2<sup>2</sup> × 11<sup>2</sup> = 1936 <br> = (44)<sup>2</sup>, which is a perfect square of 44.",
				"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": 37
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch6_un",
	"map": "ch6_map",
	"afq": "ch6_afq",
	"snc": "ch6_snc",
	"gowf": "ch6_gowf",
	"pbq": "ch6_pbq",
	"mtf": "ch6_mtf",
	"tf": "ch6_tf",
	"afow": "ch6_afow",
	"cs": "ch6_cs",
	"ctco": "ch6_ctco",
	"vsaq": "ch6_vsaq",
	"grade": "Grade 8",
	"mcq": "ch6_mcq",
	"dtf": "ch6_dtf",
	"grf": "ch6_grf",
	"fib": "ch6_fib",
	"saq": "ch6_saq",
	"laq": "ch6_laq",
	"nf": "ch6_nf",
	"co": "ch6_co",
	"jtf": "ch6_jtf",
	"yn": "ch6_yn",
	"ctt": "ch6_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch7",
	"chapterName": "Chapter 7 - Cubes and Cube Roots",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "The smallest natural number which must be multiplied with 392 to make a perfect cube is ______.",
				"ans": "(c) 7",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 8",
					"(b) 6",
					"(c) 7",
					"(d) 5"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "By which smallest natural number should 1188 be divided to make it a perfect cube?",
				"ans": "(a) 44",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 44",
					"(b) 22",
					"(c) 33",
					"(d) 11"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The one’s digit of the cube of 23 is ________",
				"ans": "(b) 7",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 6",
					"(b) 7",
					"(c) 3",
					"(d) 9"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following numbers is a perfect cube?",
				"ans": "(b) 216",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 243",
					"(b) 216",
					"(c) 392",
					"(d) 8640"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following numbers is not a perfect cube?",
				"ans": "(b) 567",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 216",
					"(b) 567",
					"(c) 125",
					"(d) 343"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If m is the cube root of n then n is ________.",
				"ans": "(a) m<sup>3</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) m<sup>3</sup>",
					"(b) √m",
					"(c) m/3",
					"(d) 3√m"
				],
				"val": 6
			}
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\t9 is a perfect cube.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe cube of odd numbers are also odd.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tEach prime factor appears three time in its cubes.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tFor any integer M, M<sup>2</sup> < M<sup>3</sup>.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 4
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIf in the prime factorisation of any number each factor appears three times, then the number is a perfect cube.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 5
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCube of any even number is itself an even number.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 6
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA perfect cube ends with two zeroes.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 7
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIf square of a number ends with 2, then its cube ends with 8.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 8
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThere is no perfect cube which ends with 27.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 9
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe cube of a two digit number may be a four digit number.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 10
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe cube of a two digit number may have seven or more digits.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 11
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe cube of a single digit number may be a two digit number.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 12
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe cube root of 8000 is 200\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 13
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThere are five perfect cubes between 1 and 1000.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 14
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCube of an even number is odd.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 15
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCube of an even number is even.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 16
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCube of an odd number is odd.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 17
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThere is no cube root of a negative integer.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 18
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "A cube is a solid figure which has all its sides ____________.",
				"ans": "equal",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "1, 8, 27.... are called ____________ or cube numbers.",
				"ans": "perfect cubes",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A cube is obtained when a number is multiplied by itself ____________ times.",
				"ans": "three",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "There are only ____________ perfect cubes from 1 to 1000.",
				"ans": "ten",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The symbol ____________ denotes ‘cube-root’.",
				"ans": "√ 3",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Cube root of 8000 is ____________.",
				"ans": "20",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "There are ____________ perfect cubes between 1 and 1000.",
				"ans": "8",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The cube of 100 will have ____________ zeroes.",
				"ans": "6",
				"code": "FIB",
				"val": 8
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "One’s digit in the cube of 38 is ____________.",
				"ans": "2",
				"code": "FIB",
				"val": 9
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The cube of an odd number is always an ____________ number.",
				"ans": "odd",
				"code": "FIB",
				"val": 10
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The cube root of a number x is denoted by ____________.",
				"ans": "3√x or x1/3",
				"code": "FIB",
				"val": 11
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The least number by which 72 be multiplied to make it a perfect cube is ____________.",
				"ans": "3",
				"code": "FIB",
				"val": 12
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Cube of a number ending in 7 will end in the digit ____________.",
				"ans": "3",
				"code": "FIB",
				"val": 13
			}
		],
		[],
		[],
		[],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": "Which of the following numbers are not perfect cubes? <br> (i) 108 <br> (ii) 216 <br> (iii) 11664",
				"ans": "Gills",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch7a1.jpg",
					"width": "543",
					"height": "680"
				},
				"val": 1
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. <br> 32 ",
				"ans": "32 = <u>2 × 2 × 2</u> × 2 × 2 <br> Here, two 2s are left which are not in triplet. To make 32 a cube, one more 2 is required. <br> In that case 32 × 2 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> = 64 is a perfect cube. <br> Hence, the smallest natural number by which 32 should be multiplied to make it a perfect cube is 2.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. <br> 256",
				"ans": "256 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × 2 × 2 <br> Here, two 2s are left which are not in triplet. <br> To make 256 a cube, one more 2 is required. <br> Then, we obtain <br> 256 × 2 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> = 512 is a perfect cube. <br> Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 3
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. <br> 675",
				"ans": "675 = <u>3 × 3 × 3</u> × 5 × 5 <br> Here, two 5s are left which are not in a triplet. To make 675 a cube, one more 5 is required. <br> Then, we obtain <br> 675 × 5 = <u>3 × 3 × 3</u> × <u>5 × 5 × 5</u> = 3375 is a perfect cube. <br> Hence, the smallest natural number by which 675 should be multiplied to make it a perfect cube is 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": "Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. <br> 100",
				"ans": "100 = 2 × 2 × 5 × 5 <br> Here, two 2s and two 5s are left which are not in triplet. To make 100 a cube, we required one more 2 and one more 5. <br> Then, we obtain <br> 100 × 2 × 5 = <u>2 × 2 × 2</u> × <u>5 × 5 × 5</u> = 1000 is a perfect cube. <br> Hence, the smallest natural number by which 100 should be multiplied to make it a perfect cube is 2 × 5 = 10.",
				"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": "Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. <br> 648",
				"ans": "648 = <u>2 × 2 × 2</u> × <u>3 × 3 × 3</u> × 3 <br> Here, one 3 is left which is not in triplet. <br> If we divide 648 by 3, then it will become a perfect cube. <br> thus, 648 ÷ 3 = 216 = <u>2 × 2 × 2</u> × <u>3 × 3 × 3</u> is a perfect cube. <br> Hence, the smallest number by which 648 should be divided to make it a perfect cube is 3.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 6
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. <br> 625",
				"ans": "625 = <u>5 × 5 × 5</u> × 5 <br> Here, one 5 is left which is not in triplet. <br> If we divide 625 ÷ 5 = 125 = <u>5 × 5 × 5</u> is a perfect cube. <br> Hence, the smallest number by which 625 should be divided to make it a perfect cube is 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": 6
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. <br> 128",
				"ans": "128 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × 2 <br> Here, one 2 is left which is not in triplet. <br> If we divide 128 by 2, then it will become a perfect cube. <br> Thus, 128 ÷ 2 = 64 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> is a perfect cube. <br> Hence, the smallest number by which 128 should be divided to make it a perfect cube is 2.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 7
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. <br> 704",
				"ans": "704 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × 11 <br> Here, one 11 is left which is not in triplet. <br> If we divide 704 by 11, then it will become a perfect cube. <br> Thus, 704 ÷ 11 = 64 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> is a perfect cube. <br> Hence, the smallest number by which 704 should be divided to make it a perfect cube is 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": 8
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Parth makes a cuboid of plasticine of sides 4 cm, 2 cm, 4 cm. How many such cuboids will he need to form a cube?",
				"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": "ch7a2.jpg",
					"width": "550",
					"height": "414"
				},
				"val": 9
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the cube root of each of the following numbers by prime factorisation method. <br> 4096",
				"ans": "Prime factorisation of 4096 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> <br> ∴ 3 √4096 = 2 × 2 × 2 × 2 = 16",
				"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 cube root of each of the following numbers by prime factorisation method. <br> 1728",
				"ans": "Prime factorisation of 1728 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × <u>3 × 3 × 3</u> <br>∴ 3√1728 = 2 × 2 × 3 = 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": 11
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the cube root of each of the following numbers by prime factorisation method. <br> 729",
				"ans": "Prime factorisation of 729 = <u>3 × 3 × 3</u> × <u>3 × 3 × 3</u> <br> ∴3 √729 = 3 × 3 = 9",
				"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": "Find the cube root of each of the following numbers by prime factorisation method. <br> 3375",
				"ans": "Prime factorisation of 3375 = <u>3 × 3 × 3</u> × <u>5 × 5 × 5</u> <br> ∴ 3 √3375 = 3 × 5 = 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": 13
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the cube root of each of the following numbers by prime factorisation method. <br> 74088",
				"ans": "Prime factorisation of 74088 = <u>2 × 2 × 2</u> × <u>3 × 3 × 3</u> × <u>7 × 7 × 7</u> <br>∴ 3√74088 = 2 × 3 × 7 = 42",
				"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": "Find the cube root of each of the following numbers by prime factorisation method. <br> 6859",
				"ans": "Prime factorisation of 6859 = <u>19 × 19 × 19</u> <br>∴ 3√6859 = 19",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 15
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the cube root of each of the following numbers by prime factorisation method. <br> 110592",
				"ans": "Prime factorisation of 110592 = <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × <u>2 × 2 × 2</u> × <u>3 × 3 × 3</u> <br>∴ 3 √110592 = 2 × 2 × 2 × 2 × 3 = 48",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 16
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the cube root of each of the following numbers by prime factorisation method. <br> 10648",
				"ans": "Prime factorisation of 10648 = <u>2 × 2 × 2</u> × <u>11 × 11 × 11</u> <br> ∴ 3 √10648 = 2 × 11 = 22",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 17
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the cube root of each of the following numbers by prime factorisation method. <br> 15625",
				"ans": "Prime factorisation of 15625 = <u>5 × 5 × 5</u> × <u>5 × 5 × 5</u> <br> ∴ 3 √15625 = 5 × 5 = 25",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 18
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the cube root of each of the following numbers by prime factorisation method. <br> 54872",
				"ans": "Prime factorisation of 54872 = <u>2 × 2 × 2</u> × <u>19 × 19 × 19</u> <br> ∴ 3 √54872 = 2 × 19 = 38",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 19
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Write cubes of first three multiples of 3.",
				"ans": "Since the first three multiples of 3 are 3, 6, 9. <br> Hence, the cubes of first three multiples of 3 are (3)<sup>3</sup>; (6)<sup>3</sup> and (9)<sup>3</sup> i.e 27, 216 and 729.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 19
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Using prime factorisation, find which of the following are perfect cubes <br> (a) 128 <br> (b) 1331",
				"ans": "(a) We have 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 <br> Since 2 remains after grouping triplets. 128 is not a perfect cube. <br> (b) We have 1331 = 11 × 11 × 11 <br> Since the prime factors appear in triplets. 1331 is a perfect cube.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 20
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch7_un",
	"map": "ch7_map",
	"afq": "ch7_afq",
	"snc": "ch7_snc",
	"gowf": "ch7_gowf",
	"pbq": "ch7_pbq",
	"mtf": "ch7_mtf",
	"tf": "ch7_tf",
	"afow": "ch7_afow",
	"cs": "ch7_cs",
	"ctco": "ch7_ctco",
	"vsaq": "ch7_vsaq",
	"grade": "Grade 8",
	"mcq": "ch7_mcq",
	"dtf": "ch7_dtf",
	"grf": "ch7_grf",
	"fib": "ch7_fib",
	"saq": "ch7_saq",
	"laq": "ch7_laq",
	"nf": "ch7_nf",
	"co": "ch7_co",
	"jtf": "ch7_jtf",
	"yn": "ch7_yn",
	"ctt": "ch7_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch8",
	"chapterName": "Chapter 8 - Comparing Quantities",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "Ratio of 25 boys and 15 girls are",
				"ans": "(a) 5 : 3",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 5 : 3",
					"(b) 3 : 5",
					"(c) 25 : 15",
					"(d) 15 : 25"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Ratio of 121 students and 11 teachers",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 11 : 121",
					"(b) 121 : 11",
					"(c) 1 : 11",
					"(d) 11 : 1"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Ratio of 50 m to 15 km",
				"ans": "(b) 1 : 300",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 300 : 1",
					"(b) 1 : 300",
					"(c) 5 : 15",
					"(d) 1 : 3"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "3 : 4 convert into percentage",
				"ans": "(d) 75%",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 25%",
					"(b) 50%",
					"(c) 12%",
					"(d) 75%"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "7 : 5 convert into percentage",
				"ans": "(b) 140%",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 70%",
					"(b) 140%",
					"(c) 7%",
					"(d) 5%"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If market price of an article is ₹ 11,200 and the discount is 12%, then the selling price of the article is",
				"ans": "(a) ₹9856",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) ₹9856",
					"(b) ₹11344",
					"(c) ₹11212",
					"(d) ₹11188"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Kavya purchases a jupiter costing ₹ 56,840 and the Rate of Sales tax is 10% then the total amount paid by her is ₹ ________.",
				"ans": "(b) 62524",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 56840",
					"(b) 62524",
					"(c) 70000",
					"(d) 50000"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The market price of an article is ₹ 80 and it is sold at ₹ 76, then the discount is",
				"ans": "(b) 62524",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 5%",
					"(b) 95%",
					"(c) 10%",
					"(d) approx 11%"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Suppose a certain sum doubles in 2 yr at r% rate of simple interest per annum and R% rate of interest per annum compounded annually then",
				"ans": "(b) R < r",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) r < R",
					"(b) R < r",
					"(c) R = r",
					"(d) cannot be determined"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The compound interest on ₹ 50000 at 4% per annum for 2 yr compounded annually is",
				"ans": "(b) R < r",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) ₹ 4000",
					"(b) ₹ 4080",
					"(c) ₹ 4280",
					"(d) ₹ 4050"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A jacket was sold for ₹ 1120 after a discount of 20%. The market price of the jacket is",
				"ans": "(b) R < r",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) ₹ 1440",
					"(b) ₹ 1400",
					"(c) ₹ 960",
					"(d) ₹ 866.66"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The original price of a washing machine which was bought for ₹ 13500 including of 8% vat, is",
				"ans": "(c) ₹ 12500",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) ₹ 12420",
					"(b) ₹ 14580",
					"(c) ₹ 12500",
					"(d) ₹ 13492"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If 90% of x is 315 km, then the value of x is",
				"ans": "(b) 350 km",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 325 km",
					"(b) 350 km",
					"(c) 3500 km",
					"(d) 300 km"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The marked price of an article is ₹ 80 and it is sold at ₹ 76, then the discount rate is",
				"ans": "(a) 5%",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 5%",
					"(b) 95%",
					"(c) 10%",
					"(d) approx 11%"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "A Jacket was sold for ₹ 1120 after allowing a discount of 20%. The marked price of the jacket is",
				"ans": "(b) ₹1400",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) ₹1440",
					"(b) ₹1400",
					"(c) ₹960",
					"(d) ₹866.66"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The original price of a washing machine which was bought for ₹ 13500 including of 8% VAT, is",
				"ans": "(c) ₹12500",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) ₹12420",
					"(b) ₹14580",
					"(c) ₹12500",
					"(d) ₹13492"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The compound interest on ₹ 50000 at 4% per annum for 2 years compounded annually is",
				"ans": "(b) ₹ 4080",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) ₹ 4000",
					"(b) ₹ 4080",
					"(c) ₹ 4280",
					"(d) ₹ 4050"
				],
				"val": 17
			}
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAdditional Expenses made after buying an article are included in the cost price and are known as value Added Tax.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tDiscount is a reduction given on Cost price of an article.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCP = MP – discount.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA man purchased a bicycle for ₹ 1040 and sold it for ₹ 800. His loss percentage is 30%.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 4
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCompound interest is the interest calculated on the previous year’s amount.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 5
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA man purchased a bicycle for ₹ 1040 and sold it for ₹ 800. His loss percent is 30%.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 6
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tSimple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 7
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe cost of a book marked at ₹ 190 after paying a sales tax of 2% is ₹ 182.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 8
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tSales tax is always calculated on the cost price of an item and is added to the value of the bill.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 9
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tDiscount is a reduction given on cost price of an article.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 10
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCompound interest is the interest calculated on the previous year’s amount.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 11
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tIf the discount of ₹ y is available on the marked price of ₹ x, then the discount per cent is x/y × 100%.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 12
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "ST Means ____________.",
				"ans": "Sales Tax",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Fomula of Discount = _______________.",
				"ans": "Market price – Sale price",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Discount = Discount% of _______________.",
				"ans": "Market price",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "_______________ is charged on the sale of an item by the government and is added to the bill amount.",
				"ans": "Sales tax",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Sales Tax = Tax% of _______________.",
				"ans": "bill amount",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The discount on an item for sale is calculated on the _______________.",
				"ans": "Market price",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "_______________ expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.",
				"ans": "Overhead",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Percentages are fractions with _______________ equal to 100.",
				"ans": "denominator",
				"code": "FIB",
				"val": 8
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The cost price of 10 tables is equal to the sale price of 5 tables. The profit percentage in this transaction is _______________.",
				"ans": "100%",
				"code": "FIB",
				"val": 9
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "2500 is greater than 500 by _______________ %.",
				"ans": "400%",
				"code": "FIB",
				"val": 10
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The cost price of 10 tables is equal to the sale price of 5 tables. The profit percent in this transaction is _______________.",
				"ans": "100%",
				"code": "FIB",
				"val": 11
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The discount on an item for sale is calculated on the _______________.",
				"ans": "marked price",
				"code": "FIB",
				"val": 12
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Sales tax = Tax% of _______________.",
				"ans": "bill amount",
				"code": "FIB",
				"val": 13
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "_______________ is a reduction on the marked price of the article.",
				"ans": "Discount",
				"code": "FIB",
				"val": 14
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Increase of a number from 150 to 162 is equal to increase of _______________ per cent.",
				"ans": "8",
				"code": "FIB",
				"val": 15
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The marked price of an article when it is sold for ₹ 880 after a discount of 12%, is _______________.",
				"ans": "₹ 1000",
				"code": "FIB",
				"val": 16
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Four times a number is a _______________% increase in the number.",
				"ans": "300",
				"code": "FIB",
				"val": 17
			}
		],
		[
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Calculate the amount and compound interest on: <br> (a) ₹ 20,000 for 2 years at 6% per annum compounded annually.",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 1,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a17.jpg",
					"width": "375",
					"height": "352"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Calculate the amount and compound interest on: <br> (b) ₹75,000 for 2½ years at 10% per annum compounded annually.",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 2,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a18.jpg",
					"width": "489",
					"height": "306"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Calculate the amount and compound interest on: <br> (c) ₹10,000 for 1 year at 6% per annum compounded half-yearly.",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 3,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a19.jpg",
					"width": "396",
					"height": "324"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Calculate the amount and compound interest on: <br> (c) ₹ 22,000 for 1 year at 10% per annum compounded half yearly.",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 4,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a20.jpg",
					"width": "405",
					"height": "298"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Taniya borrowed ₹ 35,400 from a bank to buy a vehicle at a rate of 12% p.a. compounded annually. What amount will she pay at the end of 2 years 3 months to clear the loan?",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 5,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a21.jpg",
					"width": "499",
					"height": "259"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Zoya borrows ₹ 35,500 per annum for 2 years at simple interest of 15% and Krina borrows the same amount for the same time period at 11% per annum compounded annually. Who pays more interest and by how much?",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 6,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a22.jpg",
					"width": "534",
					"height": "449"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "I borrowed ₹ 24,000 from Neha at 8% per annum simple interest for 3 years. Had I borrowed this sum at 8% per annum compound interest, what extra amount would I have to pay?",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 7,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a23.jpg",
					"width": "539",
					"height": "293"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Sohan invested ₹ 40,000 at an interest rate of 10% per annum compounded half yearly. What amount would he get: <br> (a) after 6 months <br> (b) after 1 year?",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 8,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a24.jpg",
					"width": "482",
					"height": "406"
				}
			},
			{
				"heading": "Answer the following questions in detail.",
				"qus": "Paras takes a loan of ₹ 50,000 from a bank. If the rate of interest is 12% per annum, find the difference in the amount he would be paying after 1 1/2 years if the interest is <br> (a) Compounded annually <br> (b) Compounded half yearly",
				"ans": null,
				"code": "LATQ",
				"options": null,
				"val": 9,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": "ch8a25.jpg",
					"width": "443",
					"height": "586"
				}
			},
		],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "In Kankaria entry gate, price of ticket increases by 2%. If the price of its new ticket is ₹ 12, find the price of its original ticket.",
				"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": "ch8a7.jpg",
					"width": "271",
					"height": "84"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "On Monday, attendance of a school was 800 students. But on Tuesday, due to heavy rain only 100 students came. What is the percentage decrease in attendance?",
				"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": "ch8a8.jpg",
					"width": "309",
					"height": "65"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "A shopkeeper buys 60 Rakhis for ₹ 4200 and sells them at profit of 15%, find the selling price of the Rakhi.",
				"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": "ch8a9.jpg",
					"width": "320",
					"height": "73"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The cost of one bicycle is ₹ 1500 and ₹ 350 were spent for repairing. If it is sold at a profit of 12%, find the selling price.",
				"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": "ch8a10.jpg",
					"width": "295",
					"height": "104"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Ritika bought a gas stove and a chimney for ₹ 4000 each. She made a loss of 20% on gas stove and profit of 4% on chimney. Find the gain or loss on the whole transaction and its percentage.",
				"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": "ch8a11.jpg",
					"width": "399",
					"height": "240"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "On Independence, there was a special offer of discount of 15% on the marked price of all the items. What would a customer have to pay for a Rado Watch marked at ₹ 2025?",
				"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": "ch8a12.jpg",
					"width": "573",
					"height": "63"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "A milkman sold a buffalo and a cow for ₹ 15000 and ₹ 12000 respectively. For buffalo, he got 5% gain and for a cow, he got 10% loss. Find overall gain or loss. (Hint: find C.P.)",
				"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": "ch8a13.jpg",
					"width": "422",
					"height": "247"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The price of LED is ₹ 45000. The sales tax charged is at the rate of 15%. What is the amount Kashyap has to pay?",
				"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": "ch8a14.jpg",
					"width": "336",
					"height": "66"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Kajal bought a mixer to gift her friend at a discount of 15% on marked price. If she pays ₹ 21000, find the marked price.",
				"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": "ch8a15.jpg",
					"width": "391",
					"height": "71"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "I purchased a hair dryer for ₹ 2400 including 6% VAT. Find the price before VAT.",
				"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": "ch8a16.jpg",
					"width": "287",
					"height": "60"
				}
			},
		],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the ratio of the following <br> (a) 15 hours to 35 hours <br> (b) 3 m to 30 cm",
				"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": "ch8a1.jpg",
					"width": "364",
					"height": "181"
				},
				"val": 1
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Convert the following ratios to percentages <br> (a) 2 : 5 <br> (b) 5 : 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": "ch8a2.jpg",
					"width": "461",
					"height": "129"
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "16% of 50 students are gone to picnic. How many students are not gone to picnic?",
				"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": "ch8a3.jpg",
					"width": "385",
					"height": "98"
				},
				"val": 3
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "A cricket team won 5 matches out of the total number of matches they played. If their win percentage was 20. Then how many of matches they played in all?",
				"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": "ch8a4.jpg",
					"width": "140",
					"height": "117"
				},
				"val": 4
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "After shopping, I had ₹ 2100 left after spending 25% of my money. How much did I have in the beginning?",
				"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": "ch8a5.jpg",
					"width": "400",
					"height": "155"
				},
				"val": 5
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "If 20% children like video game, 40% children like cartoon, 10% like movie and the remaining children like to play outdoor games. If total children are 10000. Find the number of children liking video games, cartoon, movies and outdoor games.",
				"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": "ch8a6.jpg",
					"width": "518",
					"height": "276"
				},
				"val": 6
			},
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch8_un",
	"map": "ch8_map",
	"afq": "ch8_afq",
	"snc": "ch8_snc",
	"gowf": "ch8_gowf",
	"pbq": "ch8_pbq",
	"mtf": "ch8_mtf",
	"tf": "ch8_tf",
	"afow": "ch8_afow",
	"cs": "ch8_cs",
	"ctco": "ch8_ctco",
	"vsaq": "ch8_vsaq",
	"grade": "Grade 8",
	"mcq": "ch8_mcq",
	"dtf": "ch8_dtf",
	"grf": "ch8_grf",
	"fib": "ch8_fib",
	"saq": "ch8_saq",
	"laq": "ch8_laq",
	"nf": "ch8_nf",
	"co": "ch8_co",
	"jtf": "ch8_jtf",
	"yn": "ch8_yn",
	"ctt": "ch8_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch9",
	"chapterName": "Chapter 9 - Algebraic Expressions and Identities",
	"all": [
		[
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following expression is monomial?",
				"ans": "(a) 5 : 3",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) a + b",
					"(b) x<sup>2</sup>y – xy<sup>2</sup> + y<sup>2</sup>",
					"(c) ax<sup>2</sup> + bx<sup>2</sup> + cx + d",
					"(d) 3xy"
				],
				"val": 1
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following expression is binomial?",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 3",
					"(b) x<sup>2</sup> + 2x + 1",
					"(c) 4l + 5m",
					"(d) x<sup>3</sup> + x<sup>2</sup> + 6x + 1"
				],
				"val": 2
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following expression is trinomial?",
				"ans": "(b) 1 : 300",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) (x + 5)<sup>2</sup>",
					"(b) x<sup>2</sup>y + 5xy",
					"(c) xy",
					"(d) 7"
				],
				"val": 3
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following pairs of terms are like terms?",
				"ans": "(d) 75%",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 3, 5x",
					"(b) 7x, – 13x",
					"(c) 5a, 6b",
					"(d) 7, 11x<sup>2</sup>"
				],
				"val": 4
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following pairs of terms are unlike terms?",
				"ans": "(b) 140%",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) x<sup>2</sup>, 3x<sup>2</sup>",
					"(b) 5, 7",
					"(c) 7x, 9x<sup>2</sup>",
					"(d) 5a<sup>3</sup>, 7a<sup>3</sup>"
				],
				"val": 5
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Additive inverse of 6y<sup>2</sup> is",
				"ans": "(a) ₹9856",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 6y",
					"(b) –6y<sup>2</sup>",
					"(c) –6y",
					"(d) 0"
				],
				"val": 6
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The area of a rectangle with 2 cm length, 5 cm breadth is",
				"ans": "(c) 10 cm<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 2 cm<sup>2</sup>",
					"(b) 5 cm<sup>2</sup>",
					"(c) 10 cm<sup>2</sup>",
					"(d) 7 cm<sup>2</sup>"
				],
				"val": 7
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "The volume of a cuboid having 3 cm length, 11 cm breadth and 9 cm height is",
				"ans": "(b) 297 cm<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 33 cm<sup>2</sup>",
					"(b) 297 cm<sup>2</sup>",
					"(c) 99 cm<sup>2</sup>",
					"(d) 23 cm<sup>2</sup>"
				],
				"val": 8
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "5lm × 19x<sup>2</sup>yz = _________.",
				"ans": "(c) 95lmx<sup>2</sup>yz",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 24lmx<sup>2</sup>yz",
					"(b) 14lmx<sup>2</sup>yz",
					"(c) 95lmx<sup>2</sup>yz",
					"(d) 190lmx<sup>2</sup>yz"
				],
				"val": 9
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "3abc × 11lmn × 19xyz = _________.",
				"ans": "(c) 627abclmnxyz",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 33abclmnxyz",
					"(b) 209abclmnxyz",
					"(c) 627abclmnxyz",
					"(d) 57abclmnxyz"
				],
				"val": 10
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "3x(5x + 7xy) = _________.",
				"ans": "(b) 15x<sup>2</sup> + 21x<sup>2</sup>y",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 15x + 21x<sup>2</sup>y",
					"(b) 15x<sup>2</sup> + 21x<sup>2</sup>y",
					"(c) 15x<sup>2</sup> + 21xy",
					"(d) 15x<sup>2</sup> + 21xy<sup>2</sup>"
				],
				"val": 11
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "5a<sup>2</sup>(11ab – 7c) = _________.",
				"ans": "(c) 55a<sup>3</sup>b – 35a2c",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 55a<sup>2</sup>b – 35a2c",
					"(b) 55a<sup>3</sup>b – 35ac",
					"(c) 55a<sup>3</sup>b – 35a2c",
					"(d) 55a<sup>2</sup>b – 35ac"
				],
				"val": 12
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "5p × (3p<sup>2</sup> + 7p + 30) = _________.",
				"ans": "(a) 15p<sup>3</sup> + 35p<sup>2</sup> + 150p",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 15p<sup>3</sup> + 35p<sup>2</sup> + 150p",
					"(b) 15p<sup>2</sup> + 35p + 150",
					"(c) 15 + 35p + 150",
					"(d) 15p<sup>3</sup> + 35p + 150"
				],
				"val": 13
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "11m (7 – 5m) = _________.",
				"ans": "(d) 77m – 55m<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 77 – 55m<sup>2</sup>",
					"(b) 77m – 55",
					"(c) 77m + 55m<sup>2</sup>",
					"(d) 77m – 55m<sup>2</sup>"
				],
				"val": 14
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "8(4y<sup>2</sup> + 7y – 9) = _________.",
				"ans": "(c) 32y<sup>2</sup> + 56y – 72",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 32y + 56y<sup>2</sup> – 72",
					"(b) 32y<sup>2</sup> + 56 – 72y",
					"(c) 32y<sup>2</sup> + 56y – 72",
					"(d) 32y + 56y – 72"
				],
				"val": 15
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Multiplication of (3x – 8) and (4x + 9) is _________.",
				"ans": "(b) 12x<sup>2</sup> – 5x – 72",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 12x – 5x<sup>2</sup> – 72",
					"(b) 12x<sup>2</sup> – 5x – 72",
					"(c) 12x<sup>2</sup> – 72x – 5",
					"(d) –5x<sup>2</sup> – 72x – 12"
				],
				"val": 16
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Multiplication of (2x – 5y) and (6x + 7y) is _________.",
				"ans": "(a) 12x<sup>2</sup> – 16xy – 35y<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 12x<sup>2</sup> – 16xy – 35y<sup>2</sup>",
					"(b) 12x<sup>2</sup> – 16xy – 35y",
					"(c) 12x<sup>2</sup> – 16x2y<sup>2</sup> – 35y<sup>2</sup>",
					"(d) –16x2y<sup>2</sup> + 12xy – 35y<sup>2</sup>"
				],
				"val": 17
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Multiplication of (3a + 9) and (2b – 7) is _________.",
				"ans": "(d) 6ab – 21a + 18b – 63",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 6a<sup>2</sup>b<sup>2</sup> – 21a + 18b – 63",
					"(b) 6ab – 21 + 18b – 63",
					"(c) 6ab – 21a<sup>2</sup> + 18b – 63",
					"(d) 6ab – 21a + 18b – 63"
				],
				"val": 18
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Multiplication of (3a<sup>2</sup> + b<sup>2</sup>) and (3a – 5b) is _________.",
				"ans": "(d) 6ab – 21a + 18b – 63",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 9a<sup>3</sup> – 15ab<sup>2</sup> + 3a<sup>2</sup>b – 5b<sup>3</sup>",
					"(b) 9a<sup>3</sup> – 15ab + 3ab<sup>2</sup> – 5b<sup>3</sup>",
					"(c) 9a<sup>3</sup> – 15a<sup>2</sup>b + 3ab<sup>2</sup> – 5b<sup>3</sup>",
					"(d) 9a<sup>3</sup> + 15a<sup>2</sup>b + 3ab – 5b<sup>3</sup>"
				],
				"val": 19
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Multiplication of (3a + 2b) and (a – b + c) is _________.",
				"ans": "(d) 6ab – 21a + 18b – 63",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 3a – 2b<sup>2</sup> – ab + 2bc + 3ca",
					"(b) 3a<sup>2</sup> – 2b<sup>2</sup> – ab + 2bc + 3ca",
					"(c) 3a<sup>2</sup> – 2b – ab + 2bc + 3ca",
					"(d) 3a<sup>2</sup> – 2b2 – a + 2bc + 3ca"
				],
				"val": 20
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is correct?",
				"ans": "(b) (a – b)<sup>2</sup> = a<sup>2</sup> – 2ab + b<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) (a – b)<sup>2</sup> = a<sup>2</sup> + 2ab – b2",
					"(b) (a – b)<sup>2</sup> = a<sup>2</sup> – 2ab + b<sup>2</sup>",
					"(c) (a – b)<sup>2</sup> = a<sup>2</sup> – b<sup>2</sup>",
					"(d) (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab – b<sup>2</sup>"
				],
				"val": 21
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "If we subtract –3p<sup>2</sup>q<sup>2</sup> from p2q2, then we get",
				"ans": "(d) 4p<sup>2</sup>q<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) –4p<sup>2</sup>q<sup>2</sup>",
					"(b) –2p<sup>2</sup>q<sup>2</sup>",
					"(c) 2p<sup>2</sup>q<sup>2</sup>",
					"(d) 4p<sup>2</sup>q<sup>2</sup>"
				],
				"val": 22
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Like term as 6x<sup>3</sup>y<sup>2</sup> is",
				"ans": "(b) –4x<sup>3</sup>y<sup>2</sup>",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 4x<sup>2</sup>y<sup>2</sup>",
					"(b) –4x<sup>3</sup>y<sup>2</sup>",
					"(c) 6px<sup>3</sup>y<sup>2</sup>",
					"(d) 4x<sup>3</sup>y"
				],
				"val": 23
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Which of the following is binomial?",
				"ans": "(d) 6(x<sup>2</sup> + y)",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 5 × x + x",
					"(b) 4x<sup>2</sup> + 5y + 2z",
					"(c) 5x × 3y × 2z",
					"(d) 6(x<sup>2</sup> + y)"
				],
				"val": 24
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Sum of x –y + xy, y + z – yz & z – x – xz is",
				"ans": "(a) 2z + xy – xz – yz",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 2z + xy – xz – yz",
					"(b) 2z + xy – xz + yz",
					"(c) 2z + xy + xz + yz",
					"(d) 2z – xy + xz + yz"
				],
				"val": 25
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Product of the monomials 4a, –7b<sup>3</sup>, –7ab is",
				"ans": "(a) 2z + xy – xz – yz",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 196a<sup>2</sup>b<sup>4</sup>",
					"(b) 196ab<sup>4</sup>",
					"(c) –196 a<sup>2</sup>b<sup>4</sup>",
					"(d) 196 a<sup>2</sup>b<sup>3</sup>"
				],
				"val": 26
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Square of 3a – 4b is",
				"ans": "(d) 9a<sup>2</sup> + 16b<sup>2</sup> – 24ab",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) 9a<sup>2</sup> – 16b<sup>2</sup>",
					"(b) 6a<sup>2</sup> – 8b<sup>2</sup>",
					"(c) 9a<sup>2</sup> + 16b<sup>2</sup> + 24ab",
					"(d) 9a<sup>2</sup> + 16b<sup>2</sup> – 24ab"
				],
				"val": 27
			},
			{
				"heading": "Multiple Choice Question.",
				"qus": "Factorised form of x<sup>2</sup> – 10x + 21 is",
				"ans": "(b) (x – 7) (x – 3)",
				"code": "MCQ",
				"width": null,
				"height": null,
				"optn": null,
				"options": [
					"(a) (x – 1) (x – 4)",
					"(b) (x – 7) (x – 3)",
					"(c) (x – 7) (x + 3)",
					"(d) (x + 7) (x + 3)"
				],
				"val": 28
			}
		],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA constant term is not an expression.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tEvery constant term is monomial.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t3x + 5 is monomial.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 3
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tA polynomial with variable of highest exponent 0(zero) is monomial.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 4
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tTwo monomials with same variable and same exponent of variable are like terms.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 5
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tTwo monomials with different (distinct) variables are unlike terms.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 6
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAddition of two polynomials of same variable of same exponent is always polynomial of same exponent of same variable of given two polynomials.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 7
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAddition of two monomials of same variable with same exponent is monomial.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 8
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tAdditive inverse of a rational number is an irrational number.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 9
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tSubtraction of two binomials must be binomial.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 10
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tExponent of any variable is always natural number.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 11
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tTwo polynomials of same variable with different (distinct) exponents are unlike terms.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 12
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tPolynomial has variable with negative exponent.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 13
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe area of a rectangle with 5 cm length and 3 cm breadth is 30 cm<sup>2</sup>.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 14
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe volume of a cuboid with 5 cm length, 7 cm breadth and 11 cm height is 385 cm<sup>3</sup>.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 15
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t5xy + 11ab = 45abxy.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 15
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t3lm × 5 mn × 11xy = 165 lm<sup>2</sup>nxy.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 16
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\t(a + b) (a – b) = a<sup>2</sup> – b<sup>2</sup>\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 17
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe numerical coefficient of the term –5p<sup>2</sup>q<sup>2</sup> is –5\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 18
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tx<sup>2</sup>y + y<sup>2</sup>z + z<sup>2</sup>y is a binomial.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 19
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCommon factor of 11xy<sup>2</sup>, 121x<sup>3</sup>y<sup>3</sup>, 1331x2y is 11xy.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 20
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tFactorised form of x<sup>2</sup> + 30x + 216 is (x + 18) (x – 12)\n\t\t_________\n\t",
				"ans": "false",
				"code": "TF",
				"val": 21
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tThe value of (x + 1) (x – 1) (x<sup>2</sup> + 1) is x<sup>2</sup> – 1\n\t\t_________\n\t",
				"ans": "false",
				"code": "TF",
				"val": 22
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "The numerical factor of a term is called its _______________.",
				"ans": "coefficient",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "An expression containing one or more terms with non-zero coefficient (with variables having non negative exponents) is called a _______________.",
				"ans": "polynomial",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "An expression with only one term, only two terms and only three terms is called _______________ , _______________ and _______________ respectively.",
				"ans": "monomial, binomial, trinomial",
				"code": "FIB",
				"val": 3
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Subtraction of a number is the same as addition of its _______________.",
				"ans": "additive inverse",
				"code": "FIB",
				"val": 4
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The area of a rectangle = _______________ × _______________.",
				"ans": "length, breadth",
				"code": "FIB",
				"val": 5
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The volume of a rectangular box = _______________ × _______________ × _______________.",
				"ans": "length, breadth, height",
				"code": "FIB",
				"val": 6
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Multiplication of two monomials is a monomial . In general, multiplication of any number of monomials is _______________.",
				"ans": "monomial",
				"code": "FIB",
				"val": 7
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Multiplication of one non-zero monomial and one binomial must be _______________. (We must not consider given binomial as ax + b with a = 0, b = 0 or a ≠ 0, b = 0 or a = 0, b ≠ 0 in “1”. Also, assume that x is non-zero.)",
				"ans": "binomial",
				"code": "FIB",
				"val": 8
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Multiplication of one non-zero monomial and one non-zero trinomial must be  _______________. (We must not consider given trinomial as ax<sup>2</sup> + bx + c with a = b = c = 0 or a ≠ 0, b = c = 0 or a = c = 0, b ≠ 0 or a = b = 0, c ≠ 0 in “2”. Also, assume that x is non-zero.)",
				"ans": "trinomial",
				"code": "FIB",
				"val": 9
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Multiplication of two binomials contains _______________ terms. (Note: We must not consider given two binomials of the form ax + b with a = 0, b = 0 or a ≠ 0, b = 0 or a = 0, b ≠ 0. Also, assume that x is always non-zero.)",
				"ans": "four",
				"code": "FIB",
				"val": 10
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Multiplication of one binomial and one trinomial contains _______________ terms. (Note: We must not consider given binomial of the from ax + b with a = b = 0 or a ≠ 0, b = 0 or a = 0, b ≠ 0. Also, we must not consider given trinomial of the form ax<sup>2</sup> + bx + c with a = b = c = 0 or a ≠ 0, b = c = 0 or a = c = 0, b ≠ 0 or a = b = 0, c ≠ 0. Also, assume that x is always non-zero.)",
				"ans": "five",
				"code": "FIB",
				"val": 11
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "(a + b)<sup>2</sup> = _______________.",
				"ans": "a<sup>2</sup> + 2ab + b<sup>2</sup>",
				"code": "FIB",
				"val": 12
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "(a - b)<sup>2</sup> = _______________.",
				"ans": "a<sup>2</sup> - 2ab + b<sup>2</sup>",
				"code": "FIB",
				"val": 13
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "(a + b) (a – b) = _______________.",
				"ans": "a<sup>2</sup> - b<sup>2</sup>",
				"code": "FIB",
				"val": 14
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "(x + a) (x + b) = _______________.",
				"ans": "x<sup>2</sup> + (a + b)x + ab",
				"code": "FIB",
				"val": 15
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "The product of two polynomials is a _______________.",
				"ans": "Polynomial",
				"code": "FIB",
				"val": 16
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Common factor of px2 + qx is _______________.",
				"ans": "x",
				"code": "FIB",
				"val": 17
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Factorised form of 15 mn + 12mnp is _______________.",
				"ans": "3mn (5 + 4p)",
				"code": "FIB",
				"val": 18
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "Volume of rectangular box with length 3p, breadth 2q and height 5r is _______________.",
				"ans": "(3 × 2 × 5)pqr = 30 pqr",
				"code": "FIB",
				"val": 19
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "30x<sup>3</sup>y<sup>2</sup>z ÷ 15xy<sup>2</sup> is equal to _______________.",
				"ans": "2x<sup>2</sup>z",
				"code": "FIB",
				"val": 20
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "57<sup>2</sup> – 47<sup>2</sup> = (57 – 47) × = _______________.",
				"ans": "1040",
				"code": "FIB",
				"val": 21
			}
			
		],
		[],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "Complete the table.",
				"ans": "The things that have life in them are called living things. For example, human beings, plants and animals",
				"code": "SATQ",
				"options": null,
				"val": 1,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a3.jpg",
					"width": "550",
					"height": "171"
				},
				"ansimg": {
					"image": "ch9a4.jpg",
					"width": "550",
					"height": "171"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the product.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 2,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a5.jpg",
					"width": "179",
					"height": "138"
				},
				"ansimg": {
					"image": "ch9a6.jpg",
					"width": "574",
					"height": "207"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "(a) Simplify 11x<sup>2</sup>(9x<sup>3</sup> – 19) + 3 and find its values for",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 3,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a7.jpg",
					"width": "149",
					"height": "38"
				},
				"ansimg": {
					"image": "ch9a8.jpg",
					"width": "354",
					"height": "527"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "(b) Simplify a<sup>3</sup>(a<sup>4</sup> + a<sup>2</sup> + 1) + 5 and find its value for <br> (i) a = 2, <br> (ii) a = 3.",
				"ans": "(b) a<sup>3</sup>(a<sup>4</sup> + a<sup>2</sup> + 1) + 5 <br> = a<sup>7</sup> + a<sup>5</sup> + a<sup>3</sup> + 5 <br><br/> (i) Value of a<sup>3</sup> (a<sup>4</sup> + a<sup>2</sup> + 1) + 5 for (a = 2)<br/> = (2)<sup>3</sup> × {(2)<sup>4</sup> + (2)<sup>2</sup> + 1} + 5 <br/> = 8 × (16 + 4 + 1) + 5 <br/> = 8 × 21 + 5 = 168 + 5 <br/> = 173 <br><br/> (ii) Value of a<sup>3</sup>(a<sup>4</sup> + a<sup>2</sup> + 1) + 5 for (a = 3) <br/> = (3)<sup>3</sup> × {(3)<sup>4</sup> + (3)<sup>2</sup> + 1} + 5 <br/> = 27 × (81 + 9 + 1) + 5 <br/> = 27 × 91 + 5 <br/> = 2457 + 5 = 2462",
				"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": "Add: 3p(4p – 7q), 4q(7q – 9s) and 9s(7s – 2p) <br> Add: 4x(5z – 3x – 7y) and 5y (2z – 9y – 3x)",
				"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": "ch9a9.jpg",
					"width": "587",
					"height": "203"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Subtract: 9l(2l – 6m + 3n) from 3l(20n – 2m + 3l) <br> Subtract: 6a(2a + 5b + 3c) – 9b(3a – 2b + 5c) from 8c(–2a + 3b + 4c)",
				"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": "ch9a9.jpg",
					"width": "376",
					"height": "375"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Use a suitable identity to get each of the following products. <br> (i) (x + 9) (x + 9) <br> (ii) (3y + 9) (3y + 9) <br> (iii) (3a – 5) (3a – 5) <br> (iv) (3x – 5) (3x + 5) <br> (v) (–3a + 2c) (–3a + 2c)",
				"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": "ch9a11.jpg",
					"width": "550",
					"height": "322"
				}
			},
			{
				"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": "ch9a12.jpg",
					"width": "326",
					"height": "99"
				},
				"ansimg": {
					"image": "ch9a13.jpg",
					"width": "550",
					"height": "425"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Use the identity (x + a) (x + b) = x2 + (a + b)x + ab to find the following products. <br> (i) (x + 5) (x + 11) <br> (ii) (8x + 7) (8x + 3) <br> (iii) (8x – 7) (8x – 3) <br> (iv) (8x + 3) (8x – 1)",
				"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": "ch9a14.jpg",
					"width": "550",
					"height": "593"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Use the identity (x + a) (x + b) = x2 + (a + b)x + ab to find the following products. <br> (v) (3x + 7y) (3x + 5y) <br> (vi) (3a<sup>2</sup> + 7) (3a2 + 1) <br> (vii) (5xyz – 6) (5xyz – 4)",
				"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": "ch9a15.jpg",
					"width": "461",
					"height": "386"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Find the following squares by using the identities.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 10,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a16.jpg",
					"width": "104",
					"height": "151"
				},
				"ansimg": {
					"image": "ch9a17.jpg",
					"width": "500",
					"height": "297"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Show that",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 11,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a18.jpg",
					"width": "285",
					"height": "122"
				},
				"ansimg": {
					"image": "ch9a20.jpg",
					"width": "500",
					"height": "478"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Show that",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 12,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a19.jpg",
					"width": "497",
					"height": "61"
				},
				"ansimg": {
					"image": "ch9a21.jpg",
					"width": "450",
					"height": "293"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Using identities, evaluate <br> (i) 81<sup>2</sup> <br> (ii) 98<sup>2</sup> <br> (iii) 101<sup>2</sup> <br> (iv) 1002<sup>2</sup> <br> (v) 4.8<sup>2</sup> <br> (vi) 77 × 83 <br> (vii) 298 × 304 <br> (viii) 9.1<sup>2</sup>",
				"ans": "(i) 81<sup>2</sup> = (80 + 1)<sup>2</sup> <br> = (80)<sup>2</sup> + 2(80) (1) + (1)<sup>2</sup> <br> = 6400 + 160 + 1 = 6561 <br><br/> (ii) 98<sup>2</sup> = (100 – 2)<sup>2</sup> <br> = (100)<sup>2</sup> – 2(100) (2) + (2)<sup>2</sup> <br> = 10000 – 400 + 4 <br> = 10004 – 400 = 9604 <br><br/> (iii) 101<sup>2</sup> = (100 + 1)<sup>2</sup> <br> = (100)<sup>2</sup> + 2(100) (1) + (1)<sup>2</sup> <br> = 10000 + 200 + 1 = 10201 <br> (iv) 1002<sup>2</sup> = (1000 + 2)<sup>2</sup> <br> = 1000000 + 2(1000)(2) + 4 <br> = 1000000 + 4000 + 4= 1004004 <br><br/> (v) 4.8<sup>2</sup> = (5 – 0.2)<sup>2</sup> <br> = (5)<sup>2</sup> – 4(5) (0.2) + (0.2)<sup>2</sup> <br> = 25 – 4 + 0.04 = 21 + 0.04 = 21.04 <br><br/> (vi) 77 × 83 = (80 – 3) × (80 + 3) = (80)<sup>2</sup> – (3)<sup>2</sup> <br> [∵ (a – b) (a + b) = a<sup>2</sup> – b<sup>2</sup>] <br> = 6400 – 9 = 6391 <br><br/> (vii) 298 × 304 = (300 – 2) × (300 + 4) <br> = (300)<sup>2</sup> + (–2 + 4) (300) + (–2) (4) <br> [∵ (x + a) (x + b) = x2 + (a + b) x + ab] <br> = 90000 + 600 – 8 = 90600 – 8 = 90592 <br><br/> (viii) 9.1<sup>2</sup> = (9.0 + 0.1)<sup>2</sup> <br> = (9.0)<sup>2</sup> + 2(9.0) (0.1) + (0.1)<sup>2</sup> <br> = 81 + 1.8 + 0.01 <br> = 82.81",
				"code": "SATQ",
				"options": null,
				"val": 13,
				"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 a<sup>2</sup> – b<sup>2</sup> = (a + b) (a – b), find <br> (i) 52<sup>2</sup> – 48<sup>2</sup> <br> (ii) (1.01)<sup>2</sup> – (0.99)<sup>2</sup> <br> (iii) 154<sup>2</sup> – 146<sup>2</sup>",
				"ans": "(i) 52<sup>2</sup> – 48<sup>2</sup> = (52 – 48) (52 + 48) = 4 × 100 = 400 <br><br/> (ii) (1.01)<sup>2</sup> – (0.99)<sup>2</sup> = (1.00 + 0.01)<sup>2</sup> – (1.0 – 0.01)<sup>2</sup> <br><br/> = (1.00)<sup>2</sup> + 2 × (1.00) (0.01) + (0.01)<sup>2</sup> – {(1.0)<sup>2</sup> – 2 × (1.0) (0.01) + (0.01)<sup>2</sup>} <br> ∴ (1.01)<sup>2</sup> – (0.99)<sup>2</sup> = 1.00 + 0.02 + 0.0001 – (1.00 – 0.02 + 0.0001) <br> = 1.0201 – (1.0001 – 0.02) = 1.0201 – 0.9801 = 0.0400 <br><br/> (iii) 154<sup>2</sup> – 146<sup>2</sup> = (154 + 146)(154 – 146) <br> [a<sup>2</sup> – b<sup>2</sup> = (a + b)(a – b)] = 300 × 8 = 2400",
				"code": "SATQ",
				"options": null,
				"val": 14,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Using (x + a) (x + b) = x<sup>2</sup> + (a + b)x + ab, find <br> (i) 101 × 102 <br> (ii) 6.2 × 6.3 <br> (iii) 8.6 × 8.7 <br> (iv) 102 × 97",
				"ans": "(i) 101 × 102 <br> = (100 + 1) × (100 + 2) <br> = (100)2 + (1+ 2) × 100 + (1 × 2) <br> = 10000 +(3 × 100) + 2 <br> = 10000 + 300 + 2 = 10302 <br><br/> (ii) 6.2 × 6.3 <br> = (6.0 + 0.2) × (6.0 + 0.3) <br> = (6.0)2 + (0.2 + 0.3) × (6.0) + (0.2 × 0.3) <br> = 36.0 + (0.5 × 6.0) + (0.06) <br> = 36.0 + 3.0 + 0.06 = 39.06 <br><br/> (iii) 8.6 × 8.7 = (8.0 + 0.6) × (8.0 + 0.7) <br> = (8.0)2 + (0.6 + 0.7) × 8.0 + (0.6 × 0.7) <br> = 64.00 + (1.3 × 8.0) + 0.42 <br> = 64.00 + 10.4 + 0.42 = 74.82 <br><br/> (iv) 102 × 97 <br> = (100 + 2) × (100 – 3) <br> = (100)2 + (2 – 3) × 100 + {2 × (–3)} <br> = 10000 + {(–1) × 100} + (–6) <br> = 10000 – 100 – 6 = 10000 – 106 = 9894",
				"code": "SATQ",
				"options": null,
				"val": 15,
				"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": "Add: <br> (i) 3x(x – y + z), 2y(x – y + z) <br> (ii) 7a<sup>2</sup>bc, –3abc<sup>2</sup>, 3a<sup>2</sup>bc, 2abc<sup>2</sup>",
				"ans": "(i) We have <br> 3x(x – y + z) + 2y(x – y + z) <br> = (3x<sup>2</sup> – 3xy + 3xz) + (2xy – 2y<sup>2</sup> + 2yz) <br> = 3x<sup>2</sup> – 3xy + 2xy + 2yz + 3xz – 2y<sup>2</sup> <br> = 3x<sup>2</sup> – xy + 2yz + 3xz – 2y<sup>2</sup> <br><br/> (ii) We have <br> 7a<sup>2</sup>bc + (–3abc<sup>2</sup>) + 3a<sup>2</sup>bc + 2abc<sup>2</sup> <br> = 7a<sup>2</sup>bc – 3abc<sup>2</sup> + 3a<sup>2</sup>bc + 2abc<sup>2</sup> <br> = (7a<sup>2</sup>bc + 3a<sup>2</sup>bc) + (–3abc<sup>2</sup> + 2abc<sup>2</sup>) <br> = 10a<sup>2</sup>bc + (–abc<sup>2</sup>) = 10a<sup>2</sup>bc – abc<sup>2</sup>",
				"code": "SATQ",
				"options": null,
				"val": 16,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Subtract: <br> (i) 7x(3y + 7x) from 8x(2x – 7y) <br> (ii) 7b<sup>2</sup> + 5ab – 2a<sup>2</sup> + 13 from 5a<sup>2</sup> – 3ab + 4b<sup>2</sup> –9.",
				"ans": "(i) We have 7x(3y + 7x) & 8x(2x – 7y) <br> The required difference is given by 8x(2x – 7y) – 7x(3y + 7x) <br> = 16x<sup>2</sup> – 56xy – 21xy – 49x<sup>2</sup> <br> = (16x<sup>2</sup> – 49x<sup>2</sup>) + (–56xy – 21xy) <br> = – 33x<sup>2</sup> – 77xy <br><br/> (ii) We have, <br> (5a<sup>2</sup> – 3ab + 4b<sup>2</sup> – 9) – (7b<sup>2</sup> + 5ab – 2a<sup>2</sup> + 13) <br> = 5a<sup>2</sup> – 3ab + 4b<sup>2</sup> – 9 – 7b<sup>2</sup> – 5ab + 2a<sup>2</sup> – 13 <br> = (5a<sup>2</sup> + 2a<sup>2</sup>) – (3ab + 5ab) + (4b<sup>2</sup> – 7b<sup>2</sup>) – (9 + 13) <br> = 7a<sup>2</sup> – 8ab – 3b<sup>2</sup> – 22",
				"code": "SATQ",
				"options": null,
				"val": 17,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Multiply the following: <br> (i) –5x<sup>2</sup>yz, 11xz, 13xyz<sup>2</sup> <br> (ii) a, a<sup>5</sup>, a<sup>6</sup> <br> (iii) (a + 6), (b –7)",
				"ans": "(i) We have –5x<sup>2</sup>yz, 11xz, 13xyz<sup>2</sup> <br> ∴ –5x<sup>2</sup>yz × 11xz × 13xyz<sup>2</sup> = (–5 × 11 × 13)x<sup>2</sup>yz × xz × xyz<sup>2</sup> = –715x<sup>4</sup>y<sup>2</sup>z<sup>4</sup> <br><br/> (ii) We have a, a<sup>5</sup> & a<sup>6</sup> <br> ∴ a × a<sup>5</sup> × a<sup>6</sup> = a<sup>1 + 5 + 6</sup> = a<sup>12</sup> <br><br/> (iii) We have (a + 6), (b – 7) <br> (a + 6) × (b – 7) = a(b – 7) + 6(b – 7) = ab – 7a + 6b – 42",
				"code": "SATQ",
				"options": null,
				"val": 18,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Multiply the following:",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 19,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a23.jpg",
					"width": "223",
					"height": "86"
				},
				"ansimg": {
					"image": "ch9a22.jpg",
					"width": "413",
					"height": "408"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Simplify <br> (i) (3a + 2b)<sup>2</sup> – (3a – 2b)<sup>2</sup> <br> (ii) (2.5x + 1.5y)<sup>2</sup> + (2.5x – 1.5y)<sup>2</sup>",
				"ans": "(i) We have <br> (3a + 2b)<sup>2</sup> – (3a – 2b)<sup>2</sup> <br> = {(3a + 2b) + (3a – 2b)} {(3a + 2b) – (3a – 2b)} <br> ...{using the identity a<sup>2</sup> – b<sup>2</sup> = (a + b) (a – b)} <br> = {3a + 2b + 3a – 2b} {3a + 2b – 3a + 2b} <br> = 6a × 4b = (6 × 4)ab = 24ab <br><br/> (ii) We have (2.5x + 1.5y)<sup>2</sup> + (2.5x – 1.5y)<sup>2</sup> <br> = (2.5x)<sup>2</sup> + (1.5y)<sup>2</sup> + 2 × 2.5x × 1.5y + (2.5x)<sup>2</sup> + (1.5y)<sup>2</sup> – 2 × (2.5x) × (1.5y) ...[using the identity (a + b)2 = a<sup>2</sup> + b<sup>2</sup> + 2ab & (a – b)2 – a<sup>2</sup> + b<sup>2</sup> – 2ab] <br> = 6.25x<sup>2</sup> + 2.25y<sup>2</sup> + 6.25x<sup>2</sup> + 2.25y<sup>2</sup> <br> = (6.25 + 6.25)x<sup>2</sup> + (2.25 + 2.25)y<sup>2</sup> <br> = 12.5x<sup>2</sup> + 4.5y<sup>2</sup>",
				"code": "SATQ",
				"options": null,
				"val": 20,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Expand the following using suitable identities.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 21,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a24.jpg",
					"width": "174",
					"height": "76"
				},
				"ansimg": {
					"image": "ch9a25.jpg",
					"width": "454",
					"height": "273"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Factorise the following using the identity a<sup>2</sup> – b<sup>2</sup> = (a + b) (a – b)",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 22,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a26.jpg",
					"width": "128",
					"height": "69"
				},
				"ansimg": {
					"image": "ch9a27.jpg",
					"width": "528",
					"height": "187"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "The following expressions are the area of rectangle. Find the possible lengths & breadth of these rectangles. <br> (i) p<sup>2</sup> – 7p + 10 <br> (ii) m<sup>2</sup> + 9m + 20",
				"ans": "(i) We have <br> Area of rectangle = p<sup>2</sup> – 7p + 10 <br> = p<sup>2</sup> – (5 + 2)p + 10 <br> = p<sup>2</sup> – 5p + 2p + 10 <br> = p(p – 5) – 2(p – 5) = (p – 5) (p – 2) <br> ∴ The possible length & breadth are (p – 5) & (p – 2) <br><br/> (ii) We have <br> Area of rectangle = m<sup>2</sup> + 9m + 20 <br> = m<sup>2</sup> + (5 + 4)m + 20 <br> = m<sup>2</sup> + 5m + 4m + 20 <br> = m(m + 5) + 4 (m + 5) = (m + 5) (m + 4) <br> ∴ The possible length & breadth are (m + 5) & (m + 4)",
				"code": "SATQ",
				"options": null,
				"val": 22,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch9a26.jpg",
					"width": "128",
					"height": "69"
				},
				"ansimg": {
					"image": "ch9a27.jpg",
					"width": "528",
					"height": "187"
				}
			}
		],
		[
			{
				"heading": "Very short answer type questions.",
				"qus": "Identify the terms, their coefficient for each of the following expressions. <br> 7xyz<sup>2</sup> – 11xy",
				"ans": "There are two terms 7xyz<sup>2</sup> and –11xy. <br> Coefficients of 7xyz<sup>2</sup> is 7 and of –11xy is –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": 1
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Identify the terms, their coefficient for each of the following expressions. <br> 3 + 4a + 9a<sup>2</sup>",
				"ans": "There are three terms 3, 4a, and 9a<sup>2</sup>. <br> Coefficients of 3 is 1 ; of 4a is 4 and of 9a<sup>2</sup> is 9.",
				"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": "Identify the terms, their coefficient for each of the following expressions. <br> x<sup>2</sup>y<sup>2</sup> – 5x<sup>2</sup>y<sup>2</sup>z<sup>2</sup> + 3z<sup>2</sup>",
				"ans": "There are three terms x<sup>2</sup>y<sup>2</sup>, –5x<sup>2</sup>y<sup>2</sup>z<sup>2</sup>, 3z<sup>2</sup>. <br> Coefficients of x<sup>2</sup>y2 is 1 ; of –5x<sup>2</sup>y<sup>2</sup>z<sup>2</sup> is –5 and of 3z<sup>2</sup> is 3.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 3
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Identify the terms, their coefficient for each of the following expressions. <br> 11 – 4pd + 2qs – 7sp",
				"ans": "There are four terms 11, –4pd, 2qs and –7sp. <br> Coefficient of 11 is 1; of –4pd is –4; of 2qs is 2 and of –7sp is –7.",
				"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": "Identify the terms, their coefficient for each of the following expressions. <br> 0.9a – 0.12ab + 0.7b",
				"ans": "There are three terms 0.9a, – 0.12 ab and 0.7b <br> Coefficients of 0.9a is 0.9; of –0.12 ab is –0.12 and of 0.7b is 0.7.",
				"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": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 93x + 101y",
				"ans": "93x + 101y — Binomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 6
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 6x – 8y + 9xy",
				"ans": "6x – 8y + 9xy — Trinomial",
				"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": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 3000",
				"ans": "3000 — Monomial",
				"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": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 8z – 17z<sup>2</sup>",
				"ans": "8z – 17z<sup>2</sup> — Binomial",
				"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": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 10x + 20x<sup>2</sup> + 31x<sup>3</sup> + 51x<sup>4</sup>",
				"ans": "10x + 20x<sup>2</sup> + 31x<sup>3</sup> + 51x<sup>4</sup> — None of monomial, binomial and trinomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 9
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 3ab + 5bc + 13cd + 9da",
				"ans": "3ab + 5bc + 13cd + 9da — None of monomial, binomial and trinomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 10
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 11 + 13y + 17x<sup>4</sup>",
				"ans": "11 + 13y + 17x<sup>4</sup> — Trinomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 11
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 11pds",
				"ans": "11pds — Monomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 12
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 5y – 7y<sup>2</sup>",
				"ans": "5y – 7y<sup>2</sup> — Binomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 13
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 9p<sup>2</sup>d + 11pd<sup>2</sup>",
				"ans": "9p<sup>2</sup>d + 11pd<sup>2</sup> — Binomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 14
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 3y – 5y<sup>2</sup> + 6y<sup>3</sup>",
				"ans": "3y – 5y<sup>2</sup> + 6y<sup>3</sup> — Trinomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 15
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? <br> 3p + 4d",
				"ans": "3p + 4d — Binomial",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 16
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Add the following <br> (i) 3ab – 5bc, 2bc – 7ca, 5ca – 3ab <br> (ii) 7a – 3b + 2ab, 7b – 2c + 3bc, 5c – 3a + 2ac <br> (iii) 3p2q<sup>2</sup> – 5pq + 7, 11 + 9pq – 4p<sup>2</sup>q<sup>2</sup> <br> (iv) 3l<sup>2</sup> + 2m<sup>2</sup>, 5m<sup>2</sup> + 9n<sup>2</sup>, 7n<sup>2</sup> + 2l<sup>2</sup>, 3lm + 5mn + 7nl",
				"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": "ch9a1.jpg",
					"width": "453",
					"height": "268"
				},
				"val": 17
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "(i) Subtract 5a + 8ab + 9b + 13 from 9a – 10ab + 33b – 5. <br> (ii) Subtract 5xy + 9yz – 8zx from 7xy – 3yz – 4zx + 11xyz <br> (iii) Subtract 4p<sup>2</sup>q – 8pq + 9pq<sup>2</sup> – 7p + 11q – 12 from <br> 19 – 4p – 10q + 7pq – 3pq<sup>2</sup> + 11p<sup>2</sup>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": "ch9a2.jpg",
					"width": "326",
					"height": "298"
				},
				"val": 18
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the product of the following pairs of monomials. <br> (i) 3, 9p <br> (ii) –7p, 13p <br> (iii) –8p, 11pq <br> (iv) 18p, 0 <br> (v) 16p<sup>3</sup>, –5p",
				"ans": "(i) 3 × 9p = 27p <br> (ii) (–7p) × 13p = –91p<sup>2</sup> <br> (iii) (–8p) × 11pq = –88p<sup>2</sup>q <br> (iv) 18p × 0 = 0 <br> (v) 16p<sup>3</sup> × (–5p) = –80p<sup>4</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": 19
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the area of rectangles with the following pairs of monomials as their lengths and breadths respectively: <br> (i) (3p, 11q) <br> (ii) (30m, 25n) <br> (iii) (10x<sup>2</sup>, 125y<sup>2</sup>) <br> (iv) (12x, 9x<sup>2</sup>) <br> (v) (9mn, 8np)",
				"ans": "(i) Length = 3p; Breadth = 11q; Area of rectangle = 3p × 11q = 33pq <br> (ii) Length = 30m; Breadth = 25n; Area of rectangle = 30m × 25n = 750mn <br> (iii) Length = 10x<sup>2</sup>; Breadth = 125y<sup>2</sup>; Area of rectangle = 10x<sup>2</sup> × 125y<sup>2</sup> = 1250x<sup>2</sup>y<sup>2</sup> <br> (iv) Length = 12x; Breadth = 9x<sup>2</sup>; Area of rectangle = 12x × 9x<sup>2</sup> = 108x<sup>3</sup> <br> (v) Length = 9mn; Breadth = 8np; Area of rectangle = 9mn × 8np = 72mn2p",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": null,
					"width": null,
					"height": null
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 20
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Obtain the volume of rectangular boxes with the following length, breadth and height respectively. <br> (i) 25a, 6a<sup>2</sup>, 3a<sup>4</sup> <br> (ii) 4p, 16q, 16s <br> (iii) 3xy, 5x<sup>2</sup>y, 4xy<sup>2</sup> <br> (iv) 2a, 5b, 7c",
				"ans": "(i) l = 25a, b = 6a<sup>2</sup>, h = 3a<sup>4</sup> <br> Volume of the rectangular box = l × b × h = 25a × 6a<sup>2</sup> × 3a<sup>4</sup> = 450a7 <br> <br/> (ii) l = 4p, b = 16q, h = 16s <br> Volume of the rectangular box = l × b × h = 4p × 16q × 16s = 1024 pqs. <br><br/> (iii) l = 3xy, b = 5x<sup>2</sup>y, h = 4xy<sup>2</sup> <br> Volume of the rectangular box = l × b × h <br> = 3xy × 5x<sup>2</sup>y × 4xy<sup>2</sup> = 60x<sup>4</sup>y<sup>4</sup> <br><br/> (iv) l = 2a, b(breadth) = 5b, h = 7c <br> Volume of the rectangular box = l × b(breadth) × h <br> = 2a × 5b × 7c <br> = 70abc",
				"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": "Carry out the multiplication of the expressions in each of the following pairs. <br> (i) 16p, 7q + 11s <br> (ii) 3a<sup>2</sup> – 11, 16a <br> (iii) 5ab, 29a – 33b <br> (iv) 3pq + 11qs + 8sp, 0 <br> (v) 2a + 5b, 19a<sup>2</sup>b<sup>2</sup>",
				"ans": "(i) 16p × (7q + 11s) = 112pq + 176ps <br> <br/> (ii) 16a × (3a<sup>2</sup> – 11) = 48a<sup>3</sup> – 176a <br><br/> (iii) 5ab × (29a –33b) = 145a<sup>2</sup>b – 165ab<sup>2</sup> <br><br/> (iv) (0) × (3pq + 11qs + 8sp) = 0 <br><br/> (v) 19a<sup>2</sup>b<sup>2</sup> × (2a + 5b) = 38a<sup>3</sup>b<sup>2</sup> + 95a<sup>2</sup>b<sup>3</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": 22
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Multiply the binomials. <br> (i) (3x + 7) and (5x – 2) <br> (ii) (3a + b) and (2x + 3) <br> (iii) (2y – 3) and (3y – 5) <br> (iv) (5pq + 2q<sup>2</sup>) and (4pq – q<sup>2</sup>) <br> (v) (1.5l – 2.5m) and (1.5l + 2.5m)",
				"ans": "(i) (3x + 7) × (5x – 2) <br> = 15x<sup>2</sup> – 6x + 35x – 14 <br> = 15x<sup>2</sup> + 29x – 14 <br> <br/> (ii) (3a + b) × (2x + 3) <br> = 6ax + 9a + 2bx + 3b <br> = 6ax + 2bx + 9a + 3b <br> <br/> (iii) (2y – 3) × (3y – 5) = 6y<sup>2</sup> – 10y – 9y + 15 <br> = 6y<sup>2</sup> – 19y + 15 <br><br/> (iv) (5pq + 2q<sup>2</sup>) × (4pq – q<sup>2</sup>) <br> = 20p<sup>2</sup>q<sup>2</sup> – 5pq<sup>3</sup> + 8pq<sup>3</sup> – 2q<sup>4</sup> <br> <br/> (v) (1.5l – 2.5m) × (1.5l + 2.5m) <br> = 2.25l2 + 3.75lm – 3.75lm – 6.25m<sup>2</sup> <br> = 2.25l<sup>2</sup> – 6.25m<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": 23
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Find the product. <br> (i) (7 – 3x) (5 + 2x) <br> (ii) (5a<sup>2</sup> + b) (2a + 3b<sup>2</sup>) <br> (iii) (2x + 5y) (3x – 4y) <br> (iv) (3p<sup>2</sup> – 2q<sup>2</sup>) (5p + 3q)",
				"ans": "(i) (7 – 3x) (5 + 2x) <br> = 35 + 14x – 15x – 6x<sup>2</sup> <br> = 35 – x – 6x<sup>2</sup> <br> = –6x<sup>2</sup> – x + 35 <br><br/> (ii) (5a<sup>2</sup> + b) (2a + 3b<sup>2</sup>) <br> = 10a<sup>3</sup> + 15a<sup>2</sup>b<sup>2</sup> + 2ab + 3b<sup>3</sup> <br><br/> (iii) (2x + 5y) (3x – 4y) <br> = 6x<sup>2</sup> – 8xy + 15xy – 20y<sup>2</sup> <br> = 6x<sup>2</sup> + 7xy – 20y<sup>2</sup> <br><br/> (iv) (3p<sup>2</sup> – 2q<sup>2</sup>) (5p + 3q) <br> = 15p<sup>3</sup> + 9p<sup>2</sup>q – 10pq<sup>2</sup> – 6q<sup>3</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": 24
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Simplify <br> (i) (3a<sup>2</sup> – 2b<sup>2</sup>)<sup>2</sup> <br> (ii) (3x + 2)<sup>2</sup> –(2x – 3)<sup>2</sup> <br> (iii) (5m – 4n)<sup>2</sup>  + (5m + 4n)<sup>2</sup> <br> (iv) (2m + 3n)<sup>2</sup> + (3m + 2n)<sup>2</sup> <br> (v) (1.5p – 0.5q)<sup>2</sup> – (0.5q – 1.5q)<sup>2</sup> <br> (vi) (2ab + 3bc)<sup>2</sup> – 3ab<sup>2</sup>c <br> (vii) (3m<sup>2</sup> – n<sup>2</sup>m)<sup>2</sup> + 3m<sup>2</sup>n<sup>2</sup>",
				"ans": "(i) (3a<sup>2</sup> – 2b<sup>2</sup>)<sup>2</sup> = (3a<sup>2</sup>)<sup>2</sup> – 2(3a<sup>2</sup>)(2b<sup>2</sup>) + (2b<sup>2</sup>)<sup>2</sup> <br> = 9a<sup>4</sup> – 12a<sup>2</sup>b<sup>2</sup> + 4b<sup>4</sup> <br><br/> (ii) (3x + 2)<sup>2</sup> – (2x – 3)<sup>2</sup> = (3x)<sup>2</sup> + 2(3x) (2) + (2)<sup>2</sup> – {(2x)<sup>2</sup> – 2(2x) (3) +(3)<sup>2</sup>} <br> = 9x<sup>2</sup> + 12x + 4 – (4x<sup>2</sup> – 12x + 9) <br> = 9x<sup>2</sup> + 12x + 4 – 4x<sup>2</sup> + 12x – 9 = 5x<sup>2</sup> + 24x – 5 <br> <br/> (iii) (5m – 4n)<sup>2</sup> + (5m + 4n)<sup>2</sup> = {(5m)<sup>2</sup>– 2(5m)(4n) + (4n)<sup>2</sup>} + {(5m)<sup>2</sup> + 2(5m)(4n) + (4n)<sup>2</sup>} <br> = (25m<sup>2</sup> – 40mn + 16n<sup>2</sup>) + (25m<sup>2</sup> + 40mn + 16n<sup>2</sup>) = 50m<sup>2</sup> + 32n<sup>2</sup> <br><br/> (iv) (2m + 3n)<sup>2</sup> + (3m + 2n)<sup>2</sup> = (2m)<sup>2</sup> + 2(2m)(3n) + (3n)<sup>2</sup> + (3m)<sup>2</sup> + 2(3m)(2n) + (2n)<sup>2</sup> <br> = 4m2 + 12mn + 9n<sup>2</sup> + 9m<sup>2</sup> + 12mn + 4n<sup>2</sup> = 13m<sup>2</sup> + 13n<sup>2</sup> + 24mn <br><br/> (v) (1.5p – 0.5q)<sup>2</sup> – (0.5q – 1.5q)<sup>2</sup> = (1.5p)<sup>2</sup> – 2(1.5p) (0.5q) + (0.5q)<sup>2</sup> – {(0.5q)<sup>2</sup> – 2(0.5q) (1.5q) + (1.5q)<sup>2</sup>] <br> = 2.25p<sup>2</sup> – 1.5pq + 0.25q<sup>2</sup> – {0.25q<sup>2</sup> – 1.5q<sup>2</sup> + 2.25q<sup>2</sup>} <br> = 2.25p<sup>2</sup> – 1.5pq + 0.25q<sup>2</sup> – 0.25q<sup>2</sup> + 1.5q<sup>2</sup> – 2.25q<sup>2</sup> <br> = 2.25p<sup>2</sup> – 1.5pq + 1.5q<sup>2</sup> – 2.25q<sup>2</sup> <br><br/> (vi) (2ab + 3bc)<sup>2</sup> – 3ab<sup>2</sup>c = (2ab)<sup>2</sup> + 2(2ab) (3bc) + (3bc)<sup>2</sup> – 3ab<sup>2</sup>c <br> = 4a<sup>2</sup>b<sup>2</sup> + 12ab<sup>2</sup>c + 9b<sup>2</sup>c<sup>2</sup> – 3ab<sup>2</sup>c <br> = 4a<sup>2</sup>b<sup>2</sup> + 9b<sup>2</sup>c<sup>2</sup> + 9ab<sup>2</sup>c <br><br/> (vii) (3m<sup>2</sup> – n<sup>2</sup>m)<sup>2</sup> + 3m<sup>2</sup>n<sup>2</sup> = (3m<sup>2</sup>)<sup>2</sup> – 2(3m<sup>2</sup>) (n<sup>2</sup>m) + (n<sup>2</sup>m)<sup>2</sup> + 3m<sup>2</sup>n<sup>2</sup> <br> = 9m<sup>4</sup> – 6m<sup>3</sup>n<sup>2</sup> + n<sup>4</sup>m<sup>2</sup> + 3m<sup>2</sup>n<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": 25
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch9_un",
	"map": "ch9_map",
	"afq": "ch9_afq",
	"snc": "ch9_snc",
	"gowf": "ch9_gowf",
	"pbq": "ch9_pbq",
	"mtf": "ch9_mtf",
	"tf": "ch9_tf",
	"afow": "ch9_afow",
	"cs": "ch9_cs",
	"ctco": "ch9_ctco",
	"vsaq": "ch9_vsaq",
	"grade": "Grade 8",
	"mcq": "ch9_mcq",
	"dtf": "ch9_dtf",
	"grf": "ch9_grf",
	"fib": "ch9_fib",
	"saq": "ch9_saq",
	"laq": "ch9_laq",
	"nf": "ch9_nf",
	"co": "ch9_co",
	"jtf": "ch9_jtf",
	"yn": "ch9_yn",
	"ctt": "ch9_ctt"
},

{
	"subject": "Mathematics",
	"chapter": "ch10",
	"chapterName": "Chapter 10 - Visualising Solid Shapes",
	"all": [
		[],
		[
			{
				"heading": "State True or False.",
				"qus": "\n\t\tCube is not a regular polyhedron.\n\t\t_________\n\t",
				"ans": "False",
				"code": "TF",
				"val": 1
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tHexagonal prism is convex polyhedron.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 2
			},
			{
				"heading": "State True or False.",
				"qus": "\n\t\tEuler's formula is true for any polyhedron.\n\t\t_________\n\t",
				"ans": "True",
				"code": "TF",
				"val": 3
			}
		],
		[],
		[
			{
				"heading": "Fill in the blanks.",
				"qus": "Solid is made up of polygonal regions which are called ______________ of given solid.",
				"ans": "faces",
				"code": "FIB",
				"val": 1
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "If faces of polyhedron are made up of regular polygons and the same number of faces meet at each vertex, then that polyhedron is said to be ______________ polyhedron.",
				"ans": "regular",
				"code": "FIB",
				"val": 2
			},
			{
				"heading": "Fill in the blanks.",
				"qus": "A hexagonal prism has a ______________ as its base and a ______________ pyramid has a triangle as its base.",
				"ans": "hexagon, triangular",
				"code": "FIB",
				"val": 3
			},
		],
		[],
		[],
		[
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each of the given solid, the two views are given. Match each solid the corresponding top and front views. <br> (a) Cube <br> (b) Triangular Prism <br> (c) Square pyramid",
				"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": "ch10a1.jpg",
					"width": "349",
					"height": "404"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each of the given solid, the two views are given. Match each solid the corresponding top and front views. <br> (d) Cylinder <br> (e) Hexagonal Prism",
				"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": "ch10a2.jpg",
					"width": "394",
					"height": "320"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views. <br> (a) Pentagonal Prism <br> (b) Tetrahedron or Triangular Pyramid",
				"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": "ch10a3.jpg",
					"width": "461",
					"height": "364"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views. <br> (c) Pentagonal Cone <br> (d) Hexagonal Pyramid",
				"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": "ch10a4.jpg",
					"width": "506",
					"height": "445"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each given solid, identify the top view, front view and side view.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 5,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch10a5.jpg",
					"width": "281",
					"height": "285"
				},
				"ansimg": {
					"image": "ch10a8.jpg",
					"width": "388",
					"height": "242"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each given solid, identify the top view, front view and side view.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 6,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch10a6.jpg",
					"width": "172",
					"height": "416"
				},
				"ansimg": {
					"image": "ch10a9.jpg",
					"width": "367",
					"height": "342"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "For each given solid, identify the top view, front view and side view.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 7,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch10a7.jpg",
					"width": "183",
					"height": "163"
				},
				"ansimg": {
					"image": "ch10a10.jpg",
					"width": "307",
					"height": "135"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw the front view, side view and top view of the given objects.",
				"ans": null,
				"code": "SATQ",
				"options": null,
				"val": 8,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch10a11.jpg",
					"width": "147",
					"height": "346"
				},
				"ansimg": {
					"image": "ch10a12.jpg",
					"width": "482",
					"height": "346"
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Look at the given map on the city. <br> Answer the following: <br> (a) Colour the map as follows: Blue-water, Red-bus depot, Orange-locality, Yellow-post office, Green-city garden, Pink-market, Purple-B.Ed. college, Brown-cemetery <br> (b) Mark a green ‘X’ at the interaction of Road 'C' and Ring road, green ‘Y’ at the interaction of Road 'A' and CG Road. <br> (c) In red, draw a short street route from cemetery to bus depot. <br> (d) Which is further east, market or secondary school? <br> (e) Which is further north, post office or cemetery?",
				"ans": "Do it your self",
				"code": "SATQ",
				"options": null,
				"val": 9,
				"option1": [],
				"option2": [],
				"option3": [],
				"option4": [],
				"aoption1": [],
				"aoption2": [],
				"aoption3": [],
				"aoption4": null,
				"pic": {
					"image": "ch10a13.jpg",
					"width": "450",
					"height": "271"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null,
				}
			},
			{
				"heading": "Answer the following questions in short.",
				"qus": "Draw a map of your room using proper scale and symbols for different objects.",
				"ans": "Do it your self",
				"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": "Draw a map of your area using proper scale and symbols for various features like play ground, main building, garden, etc.",
				"ans": "Do it your self",
				"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": "Draw a map giving instructions to your uncle so that he reaches your school without any difficulty.",
				"ans": "Do it your self",
				"code": "SATQ",
				"options": null,
				"val": 12,
				"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": "Can a polyhedron have for its faces <br> (i) 4 squares? <br> (ii) 6 squares?",
				"ans": "(i) No. There is no polyhedron with four squares as its faces. <br> (ii) Yes. Cube is a polyhedron with six squares as its faces.",
				"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": "Which are pyramids among the following",
				"ans": "(II) and (III) are pyramids. <br> (II) is triangular pyramid or tetrahedron. <br> (III) is square pyramid.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch10a14.jpg",
					"width": "264",
					"height": "104"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 2
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Is there any common characteristic between polyhedrons namely triangular prism, octahedron and pentagonal cone? If yes, then state that characteristic.",
				"ans": "Yes. Triangular prism, octahedron and pentagonal cone have six vertices.",
				"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": "Verify Euler's formula for the following solids:",
				"ans": "Here, 'V' stands for number of vertices, 'F' stands for number of faces and 'E' stands for number of edges. <br/><br/>(i) V = 8, E = 12, F = 6 <br> ∴ V – E + F = 8 – 12 + 6 = 14 – 12 = 2 <br> So, Euler's formula is verified. <br/><br/> (ii) V = 6, E = 10, F= 6 <br> ∴ V – E + F = 6 – 10 + 6 = 12 – 10 = 2 <br> So, Euler's formula is verified. <br/><br/> (iii) V = 10, E = 15, F= 7 <br> ∴ V – E + F = 10 – 15 + 7 = 17 – 15 = 2 <br/> So, Euler's formula is verified. <br/><br/> (iv) V = 7, E = 12, F= 7 <br> ∴ V – E + F = 7 – 12 + 7 = 14 – 12 = 2 <br> So, Euler's formula is verified.",
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch10a15.jpg",
					"width": "517",
					"height": "148"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 4
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Can a polyhedron have 12 faces, 22 edges and 18 vertices?",
				"ans": "Number of vertices = V = 18 <br> Number of edges = E = 22 <br> Number of faces = F =12 <br> Any polyhedron satisfies Euler's formula. <br> Here, V – E + F = 18 – 22 + 12 = 30 – 22 = 8 ≠ 2 <br> Since, Euler's formula is not satisfied, such a polyhedron is not possible.",
				"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": "Using Euler's formula, find x, y, z.",
				"ans": "By Euler's formula, we have V – E + F = 2 <br/> (i) V – E + F = 2 <br/> ∴ 20 – 30 + F = 2 <br/> ∴ F – 10 = 2 <br/>∴ F = 12 <br/><br/> (ii) V – E + F = 2 <br/> ∴ V – 12 + 8 = 2 <br/> ∴ V – 4 = 2 <br/> ∴ V = 6 <br/><br/> (iii) V – E + F = 2 <br/> ∴ 12 – E + 20 = 2 <br/> ∴ 32 – E = 2 <br/> ∴ E = 32 – 2 <br/> ∴ E = 30" , 
				"code": "VSAQ",
				"option1": null,
				"option2": null,
				"option3": null,
				"aoption1": null,
				"aoption2": null,
				"aoption3": null,
				"pic": {
					"image": "ch10a16.jpg",
					"width": "231",
					"height": "94"
				},
				"ansimg": {
					"image": null,
					"width": null,
					"height": null
				},
				"val": 6
			},
			{
				"heading": "Very short answer type questions.",
				"qus": "Can a polyhedron have for its faces five pentagons?",
				"ans": "No. There is no polyhedron with five pentagons as its faces." , 
				"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
			}
		],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[],
		[]
	],
	"un": "ch10_un",
	"map": "ch10_map",
	"afq": "ch10_afq",
	"snc": "ch10_snc",
	"gowf": "ch10_gowf",
	"pbq": "ch10_pbq",
	"mtf": "ch10_mtf",
	"tf": "ch10_tf",
	"afow": "ch10_afow",
	"cs": "ch10_cs",
	"ctco": "ch10_ctco",
	"vsaq": "ch10_vsaq",
	"grade": "Grade 8",
	"mcq": "ch10_mcq",
	"dtf": "ch10_dtf",
	"grf": "ch10_grf",
	"fib": "ch10_fib",
	"saq": "ch10_saq",
	"laq": "ch10_laq",
	"nf": "ch10_nf",
	"co": "ch10_co",
	"jtf": "ch10_jtf",
	"yn": "ch10_yn",
	"ctt": "ch10_ctt"
},

{
    "subject": "Mathematics",
    "chapter": "ch11",
    "chapterName": "Chapter 11 - Mensuration",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of a rectangle with length 6 m and breadth 3 m is",
          "ans": "(b) 18 m<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 9 m<sup>2</sup>",
            "(b) 18 m<sup>2</sup>",
            "(c) 2 m<sup>2</sup>",
            "(d) 3 m<sup>2</sup>"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of a square with length 11 m is",
          "ans": "(a) 121 m<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 121 m<sup>2</sup>",
            "(b) 22 m<sup>2</sup>",
            "(c) 110 m<sup>2</sup>",
            "(d) 100 m<sup>2</sup>"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of a triangle with base 10 m and length of altitude 11 m is",
          "ans": "(d) 55 m<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 110 m<sup>2</sup>",
            "(b) 100 m<sup>2</sup>",
            "(c) 21 m<sup>2</sup>",
            "(d) 55 m<sup>2</sup>"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of a circle with radius 17 m is",
          "ans": "(c) 289 π m<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 17 π m<sup>2</sup>",
            "(b) 170 π m<sup>2</sup>",
            "(c) 289 π m<sup>2</sup>",
            "(d) 281 π m<sup>2</sup>"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of a parallelogram with base 11 m and height 19 m is",
          "ans": "(c) 6(x<sup>2</sup> – 6y<sup>2</sup>)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 30 m<sup>2</sup>",
            "(b) 190 m<sup>2</sup>",
            "(c) 209 m<sup>2</sup>",
            "(d) 200 m<sup>2</sup>"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The area of quadrilateral □PQRS shown in the following figure is __________.",
          "ans": "(c) 24 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch11_MCQ_06.jpg",
            "width": "150",
            "height": "130"
		  },
          "options": [
            "(a) 8 cm<sup>2</sup>",
            "(b) 48 cm<sup>2</sup>",
            "(c) 24 cm<sup>2</sup>",
            "(d) 14 cm<sup>2</sup>"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of trapezium □PQRS shown in the following figure is __________.",
          "ans": "(a) 30 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch11_MCQ_07.jpg",
            "width": "190",
            "height": "120"
		  },
          "options": [
            "(a) 30 cm<sup>2</sup>",
            "(b) 160 cm<sup>2</sup>",
            "(c) 17 cm<sup>2</sup>",
            "(d) 80 cm<sup>2</sup>"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of rhombus □ABCD shown in the following figure is __________.",
          "ans": "(d) 36 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch11_MCQ_08.jpg",
            "width": "125",
            "height": "100"
		  },
          "options": [
            "(a) 17 cm<sup>2</sup>",
            "(b) 72 cm<sup>2</sup>",
            "ch11_MCQ_08c.jpg",
            "(d) 36 cm<sup>2</sup>"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Area of Polygon ABCDE shown in the following figure is __________.",
          "ans": "(a) 65 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch11_MCQ_09.jpg",
            "width": "120",
            "height": "110"
		  },
          "options": [
            "(a) 65 cm<sup>2</sup>",
            "(b) 25 cm<sup>2</sup>",
            "(c) 392 cm<sup>2</sup>",
            "(d) 154 cm<sup>2</sup>"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The area of a trapezium shaped field is 600 m2. The distance between two parallel sides is 30 m and one of the parallel side is 12 m. Then the length or measure of another parallel side is __________.",
          "ans": "(c) 28 m",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "ch11_MCQ_10a.jpg",
            "(b) 240 m",
            "(c) 28 m",
            "(d) 30 m"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The area of a rhombus is 300 cm<sup>2</sup> and one of the diagonals is 30 cm. The length or measure of other diagonal is __________.",
          "ans": "(b) 20 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 10 cm",
            "(b) 20 cm",
            "(c) 21 cm",
            "(d) 18 cm"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The measures of a cuboid are 10 m × 8 m × 6 m. Then the total surface area of this cuboid = __________.",
          "ans": "(c) 376 m<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 320 m<sup>2</sup>",
            "(b) 240 m<sup>2</sup>",
            "(c) 376 m<sup>2</sup>",
            "(d) 356 m<sup>2</sup>"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The measures of a cuboid are 12 m × 10 m × 8 m. Then the lateral surface area of this cuboid = __________.",
          "ans": "(d) 352 m<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 350 m<sup>2</sup>",
            "(b) 480 m<sup>2</sup>",
            "(c) 300 m<sup>2</sup>",
            "(d) 352 m<sup>2</sup>"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The internal measures of a cuboidal room are 14 m × 10 m × 8 m. If the cost of white washing is ₹ 10 per m<sup>2</sup>, then the total cost of whitewashing all four walls = __________.",
          "ans": "(a) 3840 rupees",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3840 rupees",
            "(b) 3820 rupees",
            "(c) 3800 rupees",
            "(d) 3850 rupees"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the radius and height of a cylinder are 25 cm and 12 cm respectively, then the lateral(or curved) surface area of a cylinder = __________.",
          "ans": "(c) 600 π cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 500 π cm<sup>2</sup>",
            "(b) 590 π cm<sup>2</sup>",
            "(c) 600 π cm<sup>2</sup>",
            "(d) 550 π cm<sup>2</sup>"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the radius and height of cylinder are 30 cm and 8 cm, then the total surface area of a cylinder = __________.",
          "ans": "(b) 2280 π cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2300 π cm<sup>2</sup>",
            "(b) 2280 π cm<sup>2</sup>",
            "(c) 2200 π cm<sup>2</sup>",
            "(d) 2250 π cm<sup>2</sup>"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "In a building, there are 30 cylindrical pillars. The radius of each pillar is 25 cm and height is 3 m. If the cost of painting the curved surface area is ₹ 9 per m2, then the total cost of painting the curved surface area of all pillars = __________ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Take π = 3.14)",
          "ans": "(d) 1271.70 rupees",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1270.50 rupees",
            "(b) 1275.50 rupees",
            "(c) 1265.70 rupees",
            "(d) 1271.70 rupees"
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If 8 cm is a length or measure of a side of the cube, then total surface area = __________.",
          "ans": "(a) 384 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 384 cm<sup>2</sup>",
            "(b) 380 cm<sup>2</sup>",
            "(c) 400 cm<sup>2</sup>",
            "(d) 370 cm<sup>2</sup>"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the total surface area of cube is 54 m2, then the length or measure of a side of the cube = __________.",
          "ans": "(c) 3√6 m",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 6 m",
            "(b) 3 m",
            "(c) 3√6 m",
            "(d) 9 m"
          ],
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The measures of cuboid are 10 m × 7 m × 4 m. Then the volume of that cuboid = __________.",
          "ans": "(c) 280 m<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 70 m<sup>3</sup>",
            "(b) 28 m<sup>3</sup>",
            "(c) 280 m<sup>3</sup>",
            "(d) 281 m<sup>3</sup>"
          ],
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The volume of a cube with a side of a square face of cube 7 cm is __________.",
          "ans": "(b) 343 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 49 cm<sup>3</sup>",
            "(b) 343 cm<sup>3</sup>",
            "(c) 341 cm<sup>3</sup>",
            "(d) 349 cm<sup>3</sup>"
          ],
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If radius and height of a cylinder are 11 cm and 13 cm respectively, then volume of a cylinder = __________.",
          "ans": "(a) 1573 π cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1573 π cm<sup>3</sup>",
            "(b) 1859 π cm<sup>3</sup>",
            "(c) 143 π cm<sup>3</sup>",
            "(d) 24 π cm<sup>3</sup>"
          ],
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The height of a cuboid whose volume is 750 cm<sup>3</sup> and base area is 15 cm<sup>2</sup> = __________.",
          "ans": "(d) 50 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 51 cm",
            "(b) 765 cm",
            "(c) 49 cm",
            "(d) 50 cm"
          ],
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A room is in the form of a cuboid of measures 80 m × 60 m × 40 m. If the volume of one cuboidal box is 0.6 m<sup>3</sup>, then the number of cuboidal boxes that can be stored in the given room= __________.",
          "ans": "(b) 320000",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 32000",
            "(b) 320000",
            "(c) 3200",
            "(d) 330000"
          ],
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A rectangular paper of width 21 cm is rolled along its width and a cylinder of radius 25 cm is formed. The volume of the cylinder = __________.",
          "ans": "(d) 41250 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch11_MCQ_25.jpg",
            "width": "100",
            "height": "40"
          },
          "options": [
            "(a) 40000 cm<sup>3</sup>",
            "(b) 41350 cm<sup>3</sup>",
            "(c) 41300 cm<sup>3</sup>",
            "(d) 41250 cm<sup>3</sup>"
          ],
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A rectangular piece of paper 7 cm × 88 cm is folded without overlapping to make a cylinder of height 88 cm. The volume of the cylinder = __________.",
          "ans": "(c) 343 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch11_MCQ_25.jpg",
            "width": "100",
            "height": "40"
          },
          "options": [
            "(a) 243 cm<sup>3</sup>",
            "(b) 341 cm<sup>3</sup>",
            "(c) 343 cm<sup>3</sup>",
            "(d) 349 cm<sup>3</sup>"
          ],
          "val": 26
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If volume of a cube is 343 cm<sup>3</sup>. Then the length or measure of a side of that cube = __________.",
          "ans": "(c) 343 cm<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) √343 cm",
            "(b) 7 cm",
            "(c) 34.3 cm",
            "(d) 0.7 cm"
          ],
          "val": 27
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, then how many 1 cubic centimetre cubes will have exactly one of their faces painted?",
          "ans": "(c) 54",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 27",
            "(b) 42",
            "(c) 54",
            "(d) 142"
          ],
          "val": 28
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A regular hexagon is inscribed in a circle of radius r. The perimeter of the regular hexagon is",
          "ans": "(b) 6r",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3r",
            "(b) 6r",
            "(c) 9r",
            "(d) 12r"
          ],
          "val": 29
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The volume of a cube is 64 cm<sup>2</sup>. Its surface area is",
          "ans": "(c) 96 cm<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 16 cm<sup>2</sup>",
            "(b) 64 cm<sup>2</sup>",
            "(c) 96 cm<sup>2</sup>",
            "(d) 128 cm<sup>2</sup>"
          ],
          "val": 30
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The volume of a cube whose edge is 3x, is",
          "ans": "(a) 27x<sup>3</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 27x<sup>3</sup>",
            "(b) 9x<sup>3</sup>",
            "(c) 6x<sup>3</sup>",
            "(d) 3x<sup>3</sup>" 
          ],
          "val": 31
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is",
          "ans": "(a) 6 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 6 cm",
            "(b) 8 cm",
            "(c) 12 cm",
            "(d) 24 cm"
          ],
          "val": 32
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "A covered wooden box has the inner measures 115 cm, 75 cm and 35 cm and thickness of wood is 2.5 cm. The volume of the wood is",
          "ans": "Nasir",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 85000 cm<sup>3</sup>",
            "(b) 80000 cm<sup>3</sup>",
            "(c) 82125 cm<sup>3</sup>",
            "(d) 84000 cm<sup>3</sup>"
          ],
          "val": 33
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively, are melted to form a single cube. The edge of the new cube is.",
          "ans": "(a) 12 cm",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 12 cm",
            "(b) 24 cm",
            "(c) 18 cm",
            "(d) 20 cm"
          ],
          "val": 34
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n               Top and base of a cylinder are congruent and parallel to each other.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n               The areas of any two faces of a cube are equal.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n               The areas of any two faces of a cuboid are equal.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n               A cube of side 3 cm painted on all its faces, when sliced into 1 cm3 cubes, will have exactly 1 cube with none of its faces painted.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n               The surface area of a cube formed by cutting a cuboid of dimensions 2 × 1 × 1 in 2 equal parts, is 2 sq units.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 5
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "Mensuration = __________ × __________",
          "ans": "length, breadth",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Area of a square = __________.",
          "ans": "(side)<sup>2</sup>",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "          ",
          "ans": "base, altitude",
          "code": "FIB",
          "pic": {
            "image": "ch11_FIB_03.jpg",
            "width": "385",
            "height": "40"
          },
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Area of a circle = π × __________.",
          "ans": "radius)<sup>2</sup>",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Area of a Parallelogram = __________ × __________.",
          "ans": "base, height",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "                 ",
          "ans": "height, sum of parallel sides",
          "code": "FIB",
          "pic": {
            "image": "ch11_FIB_06.jpg",
            "width": "385",
            "height": "40"
          },
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Area of a rhombus is half the product of its __________.",
          "ans": "diagonals",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two dimensional figures can be identified as the __________ of three dimensional shapes.",
          "ans": "faces",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Cube, triangular pyramid (tetrahedron) have all __________ faces.",
          "ans": "congruent",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Cylinders in which the line–segment joining the centre of circular faces is perpendicular to the base are known as right circular cylinders _______________.",
          "ans": "right circular cylinders",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A cuboid has __________ pairs of identical faces.",
          "ans": "three",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If l, b and h are length, width and height of a cuboid respectively, then the total surface area of cuboid = _______________ and the lateral surface area of a cuboid = _______________.",
          "ans": "2(lb + bh + hl), 2h(l +b)",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The total surface area of cuboid = _______________ + 2 × area of base.",
          "ans": "lateral surface area",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If l is a length or measure of a side of the cube, then total surface area = __________.",
          "ans": " 6 <i>l</i><sup>2</sup>",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If radius and height of a cylinder are r and h respectively, then the lateral (or curved) surface area of a cylinder = __________ and the total surface area of a cylinder = _______________.",
          "ans": "2 πrh, 2 πr(r+h)",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Amount of space occupied by a three dimensional object is called its __________. ",
          "ans": "Volume",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Volume of cuboid = __________ × __________ × __________ If l, b and h are length, breadth and height of a cuboid respectively, then volume of cuboid = __________.",
          "ans": "length, breadth, height and lbh",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Volume of cuboid = _______________ × height.",
          "ans": "area of the base",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The __________ is a special case of cuboid.",
          "ans": "cube",
          "code": "FIB",
          "val": 19
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If l is length or measure of a side of a face of a cube, then Volume of cube = __________.",
          "ans": "<i>l</i><sup>3</sup>",
          "code": "FIB",
          "val": 20
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Lateral surface of a cylinder is _______________ to the base of that cylinder.",
          "ans": "perpendicular",
          "code": "FIB",
          "val": 21
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If r and h are radius and height of a cylinder respectively, then volume of cylinder = __________.",
          "ans": "π r2 h",
          "code": "FIB",
          "val": 22
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "1 mL = _____ cm<sup>3</sup>.",
          "ans": "1",
          "code": "FIB",
          "val": 23
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "1 L = __________ cm<sup>3</sup>.",
          "ans": "1000",
          "code": "FIB",
          "val": 24
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "1 m<sup>3</sup> = __________ cm<sup>3</sup> = __________ L",
          "ans": "1000000, 1000",
          "code": "FIB",
          "val": 25
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The perimeter of a rectangle becomes __________ times its original perimeter, if its length and breath are doubled.",
          "ans": "2",
          "code": "FIB",
          "val": 26
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Opposite faces of a cuboid are __________ in area.",
          "ans": "equal",
          "code": "FIB",
          "val": 27
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Total surface area of a cylinder of radius h and height r is _______________.",
          "ans": "2πh (r + h)",
          "code": "FIB",
          "val": 28
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Volume of a cylinder with radius r and height h is __________.",
          "ans": "pr2h",
          "code": "FIB",
          "val": 29
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cm3 cubes, then number of such cubes that will have exactly two of their faces painted, is __________.",
          "ans": "24",
          "code": "FIB",
          "val": 30
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Carry out the division: 32x<sup>4</sup> ÷ 64x",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_01.jpg",
            "width": "540",
            "height": "300"
          }
        },
      
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the common factors of 13x, 39.",
          "ans": "13x = 13 × x <br>&nbsp;&nbsp;39 = 3 × 13 <br>Common factor = 13",
          "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
          }
        },
        
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch11_pbq",
    "gowf": "ch11_gowf",
    "afow": "ch11_afow",
    "cs": "ch11_cs",
    "afq": "ch11_afq",
    "fib": "ch11_fib",
    "grade": "Grade 8",
    "mcq": "ch11_mcq",
    "vsaq": "ch11_vsaq",
    "laq": "ch11_laq",
    "tf": "ch11_tf",
    "co": "ch11_co",
    "nf": "ch11_nf",
    "mtf": "ch11_mtf",
    "yn": "ch11_yn",
    "saq": "ch11_saq",
    "dtf": "ch11_dtf",
    "map": "ch11_map",
    "ctt": "ch11_ctt",
    "un": "ch11_un",
    "ctco": "ch11_ctco",
    "grf": "ch11_grf",
    "snc": "ch11_snc",
    "jtf": "ch11_jtf"
  },
  
{
    "subject": "Mathematics",
    "chapter": "ch12",
    "chapterName": "Chapter 12 - Exponents and Powers",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "In 5<sup>n</sup>, n is known as",
          "ans": "(d) exponent",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) base",
            "(b) constant",
            "(c) variable",
            "(d) exponent"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "           ",
          "ans": "(a) directly with each other",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch12_MCQ_02.jpg",
            "width": "170",
            "height": "50"
		  },
          "ansimg": {
            "image": "ch12_MCQ_02a.jpg",
            "width": "50",
            "height": "40"
          },
          "options": [
            "ch12_MCQ_02a.jpg",
            "ch12_MCQ_02b.jpg",
            "ch12_MCQ_02c.jpg",
            "ch12_MCQ_02d.jpg"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "   ",
          "ans": "(d) sometimes directly and sometimes inversely with each other.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch12_MCQ_03.jpg",
            "width": "330",
            "height": "50"
		  },
          "ansimg": {
            "image": "ch12_MCQ_03c.jpg",
            "width": "70",
            "height": "50"
          },
          "options": [
            "ch12_MCQ_03a.jpg",
            "ch12_MCQ_03b.jpg",
            "ch12_MCQ_03c.jpg",
            "ch12_MCQ_03d.jpg"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "For any two non-zero rational numbers x and y, x<sup>4</sup> ÷ y<sup>4</sup> is equal to",
          "ans": "(c) (x ÷ y)<sup>4</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (x ÷ y)<sup>0</sup>",
            "(b) (x ÷ y)<sup>1</sup>",
            "(c) (x ÷ y)<sup>4</sup>",
            "(d) (x ÷ y)<sup>8</sup>"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The usual form for 2.03 × 10<sup>–5</sup> is",
          "ans": "(d) 0.0000203",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 0.203",
            "(b) 0.00203",
            "(c) 203000",
            "(d) 0.0000203"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The standard form for 234000000 is",
          "ans": "(a) 2.34 × 10<sup>8</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2.34 × 10<sup>8</sup>",
            "(b) 0.234 × 10<sup>10</sup>",
            "(c) 2.34 × 10<sup>–8</sup>",
            "(d) 0.234 × 10<sup>–9</sup>"
          ],
          "val": 6
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n               (–5)<sup>–2</sup> × (–5)<sup>–3</sup> = (–5)<sup>–6</sup>.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n               5º = 5\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "     ",
          "ans": "True",
          "code": "TF",
          "pic": {
            "image": "ch12_TF_03.jpg",
            "width": "200",
            "height": "40"
          },
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "      ",
          "ans": "True",
          "code": "TF",
          "pic": {
            "image": "ch12_TF_04.jpg",
            "width": "100",
            "height": "50"
          },
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n               The usual form for 2 × 10<sup>–2</sup> is not equal to 0.02.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n               The standard form for 203000 is 2.03 × 10<sup>5</sup>.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n               We need to convert numbers in standard form into numbers with the same exponents\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 7
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "For any non-zero integer a, a<sup>–m</sup> = __________, where m is a positive integer.",
          "ans": "direct",
          "code": "FIB",
          "ansimg": {
            "image": "ch12_FIB_01.jpg",
            "width": "550",
            "height": "70"
          },
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "__________ is the multiplicative inverse of am. <br>(where a is non-zero integer and m is any integer.)",
          "ans": "a<sup>–m</sup>",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "a<sup>0</sup> = __________",
          "ans": "1",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "__________ = (ab)<sup>m</sup>",
          "ans": "a<sup>m</sup> × b<sup>m</sup>",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a<sup>m</sup>)<sup>n</sup> = __________",
          "ans": "a<sup>mn</sup>",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "         ",
          "ans": null,
          "code": "FIB",
          "pic": {
            "image": "ch12_FIB_06.jpg",
            "width": "168",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_FIB_06_Ans.jpg",
            "width": "40",
            "height": "40"
          },
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "             ",
          "ans": "a<sup>m – n</sup>",
          "code": "FIB",
          "pic": {
            "image": "ch12_FIB_07.jpg",
            "width": "141",
            "height": "50"
          },
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When we have to add numbers in standard form, we convert them into numbers with the __________ exponents.",
          "ans": "same",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "0.000005 m = 5 × __________ m.",
          "ans": "10<sup>–6</sup>",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "1.325 × 10<sup>–5</sup> m = __________ m.",
          "ans": "0.00001325",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "a<sup>3</sup> × a<sup>–10</sup> = __________.",
          "ans": "a<sup>–7</sup>",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "5<sup>0</sup> = _____.",
          "ans": "1",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "3<sup>3</sup> × 3<sup>–3</sup> = __________.",
          "ans": "1",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Very small numbers can be expressed in standard form by using __________ exponents.",
          "ans": "negative",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The standard form of 12340000 is __________.",
          "ans": "1.234 ×10<sup>7</sup>",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The usual form of 2.39461 × 10<sup>6</sup> is __________.",
          "ans": "2394610",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The value of 3 × 10<sup>–7</sup> is eual to __________.",
          "ans": "0.0000003",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "On dividing 85 by __________, we get 8.",
          "ans": "8<sup>4</sup>",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "On multiplying 2<sup>10</sup> by __________, we get 2<sup>5</sup>.",
          "ans": "2<sup>–5</sup>",
          "code": "FIB",
          "val": 19
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Evaluate:",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_LATQ_01.jpg",
            "width": "60",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_LATQ_01_Ans.jpg",
            "width": "274",
            "height": "298"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the value of m for which 6<sup>m</sup> ÷ 6<sup>–2</sup> = 6<sup>6</sup>",
          "ans": "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6<sup>m</sup> ÷ 6<sup>–2</sup> = 6<sup>6</sup> <br>∴&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6<sup>m – (–2)</sup> = 6<sup>6</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[∵ a<sup>m</sup> ÷ a<sup>n</sup> = a<sup>m–n</sup>] <br>∴&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6<sup>m + 2</sup> = 6<sup>6</sup> <br>Comparing exponents on both sides, we get <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;m + 2 = 6 <br>∴&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;m = 6 – 2 <br>∴&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;m = 4",
          "code": "LATQ",
          "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 detail.",
          "qus": "Evaluate:",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_LATQ_03.jpg",
            "width": "120",
            "height": "60"
          },
          "ansimg": {
            "image": "ch12_LATQ_03_Ans.jpg",
            "width": "240",
            "height": "250"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Evaluate:",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_LATQ_04.jpg",
            "width": "120",
            "height": "60"
          },
          "ansimg": {
            "image": "ch12_LATQ_04_Ans.jpg",
            "width": "349",
            "height": "250"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Simplify:",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_LATQ_05.jpg",
            "width": "100",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_LATQ_05_Ans.jpg",
            "width": "220",
            "height": "230"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Simplify:",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_LATQ_06.jpg",
            "width": "100",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_LATQ_06_Ans.jpg",
            "width": "280",
            "height": "250"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Evaluate: 3<sup>–4</sup>",
          "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": "ch12_SATQ_01.jpg",
            "width": "170",
            "height": "90"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Evaluate: (–5)<sup>–3</sup>",
          "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": "ch12_SATQ_02.jpg",
            "width": "197",
            "height": "90"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Evaluate: ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_SATQ_03.jpg",
            "width": "50",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_SATQ_03_Ans.jpg",
            "width": "190",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify and express the result in power notation with positive exponent: <br>(−2)<sup>4</sup> ÷ (−2)<sup>8</sup>",
          "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": "ch12_SATQ_04.jpg",
            "width": "270",
            "height": "120"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify and express the result in power notation with positive exponent:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_SATQ_05.jpg",
            "width": "50",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_SATQ_05_Ans.jpg",
            "width": "220",
            "height": "130"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify and express the result in power notation with positive exponent:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_SATQ_06.jpg",
            "width": "80",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_SATQ_06_Ans.jpg",
            "width": "290",
            "height": "260"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify and express the result in power notation with positive exponent: <br>(2<sup>−6</sup> ÷ 2<sup>−8</sup>) × 2<sup>−4</sup>",
          "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": "ch12_SATQ_07.jpg",
            "width": "340",
            "height": "170"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Simplify and express the result in power notation with positive exponent: <br>4<sup>–2</sup> × (–9)<sup>–2</sup>",
          "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": "ch12_SATQ_08.jpg",
            "width": "400",
            "height": "220"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the value of: <br>(3<sup>–1</sup> × 9<sup>–1</sup>) ÷ 3<sup>2</sup>",
          "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": "ch12_SATQ_09.jpg",
            "width": "230",
            "height": "310"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the value of:",
          "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": "ch12_SATQ_10.jpg",
            "width": "340",
            "height": "350"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the value of: ",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_SATQ_11.jpg",
            "width": "150",
            "height": "50"
          },
          "ansimg": {
            "image": "ch12_SATQ_11_Ans.jpg",
            "width": "550",
            "height": "210"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the value of: <br>(2<sup>–1</sup> + 4<sup>–1</sup> + 6<sup>–1</sup>)<sup>0</sup>",
          "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": "ch12_SATQ_12_Ans.jpg",
            "width": "526",
            "height": "250"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the value of:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_SATQ_13.jpg",
            "width": "526",
            "height": "250"
          },
          "ansimg": {
            "image": "ch12_SATQ_13_Ans.jpg",
            "width": "400",
            "height": "240"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Evaluate: <br>(6<sup>–1</sup> × 4<sup>–1</sup>) × 3<sup>–1</sup>",
          "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": "ch12_SATQ_14_Ans.jpg",
            "width": "400",
            "height": "240"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Express the number appearing in the following statement in standard form:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch12_SATQ_15.jpg",
            "width": "280",
            "height": "40"
          },
          "ansimg": {
            "image": "ch12_SATQ_15_Ans.jpg",
            "width": "200",
            "height": "120"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Express the number appearing in the following statement in standard form: <br>Charge of an electron is 0.000000000000000048 electrostatic unit.",
          "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": "ch12_SATQ_16_Ans.jpg",
            "width": "430",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Express the number appearing in the following statement in standard form: <br>Distance from the earth to the Sun is 149,600,000,000 m.",
          "ans": "Distance from the Earth to the Sun is in 1,49,600,000,000 m <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 149,600,000,000 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 1.496 × 10<sup>11</sup> m",
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Express the number appearing in the following statement in standard form: <br>Diameter of the red blood cell is 0.000007 m.",
          "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": "ch12_SATQ_18_Ans.jpg",
            "width": "322",
            "height": "120"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Express the number appearing in the following statement in standard form: <br>Thickness of a thin paper is 0.008 mm.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 19,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch12_SATQ_19_Ans.jpg",
            "width": "370",
            "height": "90"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In a stock, there are 8 books each of thickness 40 mm and 10 paper sheets each of thickness 0.032 mm. What is the total thickness of the stock?",
          "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": "ch12_SATQ_20_Ans.jpg",
            "width": "430",
            "height": "210"
          }
        }
      ],
      [
        {
          "heading": "Very short answer type questions.",
          "qus": "Express 0.0000000000073 in standard form.",
          "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": "ch12_VSAQ_01.jpg",
            "width": "310",
            "height": "70"
          },
          "val": 1
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Express 0.00000000000382 in standard form.",
          "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": "ch12_VSAQ_02.jpg",
            "width": "325",
            "height": "70"
          },
          "val": 2
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Express 4510000000000000 in standard form.",
          "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": "ch12_VSAQ_03.jpg",
            "width": "333",
            "height": "70"
          },
          "val": 3
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Express 0.00000000127 in standard form.",
          "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": "ch12_VSAQ_04.jpg",
            "width": "270",
            "height": "70"
          },
          "val": 4
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Express 43890000000 in standard form.",
          "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": "ch12_VSAQ_05.jpg",
            "width": "270",
            "height": "70"
          },
          "val": 5
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Express the number 5.18 × 10<sup>–5</sup> in usual form.",
          "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": "ch12_VSAQ_06.jpg",
            "width": "180",
            "height": "70"
          },
          "val": 6
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Express the number 3.2 × 10<sup>6</sup> in usual form.",
          "ans": "3.2 × 106 = 3.2 × 1000000 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 3200000",
          "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": "Express the number 5 × 10<sup>–4</sup> in usual form.",
          "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": "ch12_VSAQ_08.jpg",
            "width": "143",
            "height": "70"
          },
          "val": 8
        },
        {
          "heading": "Very short answer type questions.",
          "qus": "Express the number 3.0031 × 10<sup>7</sup> in usual form.",
          "ans": "3.0031 × 10<sup>7<sup> = 3.0031 × 10000000 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 30031000",
          "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": "Express the number 1.7 × 10<sup>10</sup> in usual form.",
          "ans": "1.7 × 10<sup>10<sup> = 1.7 × 10000000000 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 17000000000",
          "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": "Express the number 8.73246 × 10<sup>7</sup> in usual form.",
          "ans": "8.73246 × 10<sup>7<sup> = 8.73246 × 10000000<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 87324600",
          "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
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch12_pbq",
    "gowf": "ch12_gowf",
    "afow": "ch12_afow",
    "cs": "ch12_cs",
    "afq": "ch12_afq",
    "fib": "ch12_fib",
    "grade": "Grade 8",
    "mcq": "ch12_mcq",
    "vsaq": "ch12_vsaq",
    "laq": "ch12_laq",
    "tf": "ch12_tf",
    "co": "ch12_co",
    "nf": "ch12_nf",
    "mtf": "ch12_mtf",
    "yn": "ch12_yn",
    "saq": "ch12_saq",
    "dtf": "ch12_dtf",
    "map": "ch12_map",
    "ctt": "ch12_ctt",
    "un": "ch12_un",
    "ctco": "ch12_ctco",
    "grf": "ch12_grf",
    "snc": "ch12_snc",
    "jtf": "ch12_jtf"
  },
  
{
    "subject": "Mathematics",
    "chapter": "ch13",
    "chapterName": "Chapter 13 - Direct and Inverse Proportions",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "When <i>u</i> ∝ <i>v</i>. when <i>u</i> = 10 <i>v</i> = 15 which of the following is not a possible pair of corresponding values of <i>u</i> and <i>v</i>?",
          "ans": "(c) 15 and 20",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2 and 3",
            "(b) 8 and 12",
            "(c) 15 and 20",
            "(d) 20 and 30"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Assuming land to be uniformly fertile, the area of land and the yield on it vary _______________.",
          "ans": "(a) directly with each other",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) directly with each other",
            "(b) inversely with each other",
            "(c) neither directly nor inversely with each other",
            "(d) sometimes directly and sometimes inversely with each other."
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The number of Teeth and the age of a person vary",
          "ans": "(d) sometimes directly and sometimes inversely with each other.",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) directly with each other",
            "(b) inversely with each other",
            "(c) neither directly nor inversely with each other",
            "(d) sometimes directly and sometimes inversely with each other."
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If two quantities x and y vary directly with each other, then",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "ansimg": {
            "image": "ch13_MCQ_04a.jpg",
            "width": "140",
            "height": "35"
          },
          "options": [
            "ch13_MCQ_04a.jpg",
            "(b) x – y remains constant",
            "(c) x + y remains constant",
            "(d) x, y remains"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Both x and y vary inversely with each other. When x is 10, y is 6, which of the following is not a possible pair of corresponding values of x and y?",
          "ans": "(d) 45 and 1.3",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 12 and 5",
            "(b) 15 and 4",
            "(c) 25 and 2.4",
            "(d) 45 and 1.3"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "By travelling at a speed of 48 km/h. Car can finish a certain journey in 10 hours. To cover the same distance in 8 hours, the speed of the car should be",
          "ans": "(a) 60 km/h",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 60 km/h",
            "(b) 80 km/h",
            "(c) 30 km/h",
            "(d) 40 km/h"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following vary inversely with each other?",
          "ans": "(d) Speed and time taken",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Speed and distance covered",
            "(b) Distance covered and taxi fare",
            "(c) Distance travelled and time taken",
            "(d) Speed and time taken"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Both u and v vary directly with each other. When <i>u</i> is 10, <i>v</i> is 15, which of the following is not a possible pair of corresponding values of <i>u</i> and <i>v</i>?",
          "ans": "(c) 15 and 20",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2 and 3",
            "(b) 8 and 12",
            "(c) 15 and 20",
            "(d) 25 and 37.5"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Both x and y vary inversely with each other when x is 10, y is 6, which of the following is not a possible pair of corresponding values of x and y?",
          "ans": "(d) 45 and 1.3",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 12 and 5",
            "(b) 15 and 4",
            "(c) 25 and 2.4",
            "(d) 45 and 1.3"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The number of teeth and the age of a person vary",
          "ans": "(d) sometimes directly and sometimes inversely with each other",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) directly with each other",
            "(b) inversely with each other",
            "(c) neither directly nor inversely with each other",
            "(d) sometimes directly and sometimes inversely with each other"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following vary inversely with each other?",
          "ans": "(d) Speed and time taken",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) Speed and distance covered",
            "(b) Distance covered and taxi fare",
            "(c) Distance travelled and time taken",
            "(d) Speed and time taken"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for",
          "ans": "(c) 120 days",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 30 days",
            "(b) 96/5 days",
            "(c) 120 days",
            "(d) 40 days"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If two quantities x and y vary directly with each other, then",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "ansimg": {
            "image": "ch13_MCQ_13a.jpg",
            "width": "140",
            "height": "35"
          },
          "options": [
            "ch13_MCQ_13a.jpg",
            "(b) x – y remains constant",
            "(c) x + y remains constant",
            "(d) xy remains constant"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "If two quantities p and q vary inversely with each other, then",
          "ans": "(b) 3x + 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "ansimg": {
            "image": "ch13_MCQ_14a.jpg",
            "width": "140",
            "height": "35"
          },
          "options": [
            "ch13_MCQ_14a.jpg",
            "(b) p + q remains constant",
            "(c) p × q remains constant",
            "(d) p – q remains constant"
          ],
          "val": 14
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n               When the speed is kept fixed, time and distance vary inversely with each other.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n               When the distance is kept fixed, speed and time vary directly with each other.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Length of a side of a square and its area vary directly with each other.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If x and y are in direct proportion, then (x – 1) and (y – 1) are also in direct proportion.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n               When two quantities are related in such a manner that if one increases, the other also increases, then they always vary directly.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n               When the speed is kept fixed, time and distance vary inversely with each other\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Length of a side of an equilateral triangle and its perimeter vary inversely with each other\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If x and y are in inverse proportion, then (x + 1) and (y + 1) are also in inverse proportion.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If one angle of a triangle is kept fixed, then the measure of the remaining two angles vary inversely with each other.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n               When two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Two quantities p & q are said to vary directly with each other, if for some rational number k, pq = k.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Length of a side of square shape box & its area vary directly with each other.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If a tree 25 m high casts a shadow of 15 m, then the height of a pole that casts a shadow of 6 m under similar conditions is 10 m.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If x and y are in inverse proportion, i.e. xy = k(constant), then (x + 2) & (y – 2) are also in inverse proportion.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 14
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If b varies directly as t<sup>2</sup>, then we can write bt<sup>2</sup> = k, where k is some constant.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 15
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If p varies inversely as q and when p = 5, q = 8 then for p = 7, the value of q is 10.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 16
        },
        {
          "heading": "State True or False.",
          "qus": "\n               For fixed time period and rate of interest, the simple interest is directly proportional to principal.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 17
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "If x = 5y, then x and y are in __________ proportion with each other.",
          "ans": "direct",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When two quantities x and y are in __________ proportion or vary __________, they are written as x ∞ y.",
          "ans": "direct, directly",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Two quantities are said to vary __________ with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.",
          "ans": "directly",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If x varies directly as y, then <br>&nbsp;&nbsp;&nbsp; x&nbsp;&nbsp;&nbsp;12&nbsp;&nbsp;&nbsp;6 <br>&nbsp;&nbsp;&nbsp;&nbsp;y&nbsp;&nbsp;&nbsp;48&nbsp;&nbsp;&nbsp;?",
          "ans": "24",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When the speed remains constant, the distance travelled is __________ proportional to the time.",
          "ans": "directly",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If two quantities x and y vary directly with each other, then __________ of their corresponding values remains constant.",
          "ans": "ratio",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "  ",
          "ans": "inversely",
          "code": "FIB",
          "pic": {
            "image": "ch13_FIB_07.jpg",
            "width": "550",
            "height": "70"
          },
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Both x and y are said to be vary __________ with each other, if for some positive number k, xy = k.",
          "ans": "inversely",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If two quantities p and q vary inversely with each other, then their corresponding values remain constant inversely __________.",
          "ans": "inversely",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "It x varies inversely as y and x = 4 when y = 6, when x = 3 then value of y = __________.",
          "ans": "8",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If 45 persons can complete a work in 20 days, then the time taken by 75 persons will be __________ days.",
          "ans": "12",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If p = 6q, then p and q vary __________ with each other",
          "ans": "directly",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If xy = 20, then x and y vary __________ with each other.",
          "ans": "inversely",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "When two quantities p and q are in __________ proportion or vary __________ they are written as x ∝ y.",
          "ans": "direct, directly",
          "code": "FIB",
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If x varies inversely as y then",
          "ans": null,
          "code": "FIB",
          "ansimg": {
            "image": "ch13_FIB_15.jpg",
            "width": "50",
            "height": "40"
          },
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If x varies directly as y, then <br>&nbsp;&nbsp;&nbsp; x&nbsp;&nbsp;&nbsp;13&nbsp;&nbsp;&nbsp;5 <br>&nbsp;&nbsp;&nbsp;&nbsp;y&nbsp;&nbsp;&nbsp;52&nbsp;&nbsp;&nbsp;.....",
          "ans": "20",
          "code": "FIB",
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A bus is travelling 25 km in one hour. The distance travelled by the bus in 12 minutes is __________.",
          "ans": "5 km",
          "code": "FIB",
          "val": 17
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "In a reality show, the prize money of ₹ 50,000 is to be divided equally amongst the winners. Complete the following table & find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?",
          "ans": "A table of the given information is as follows:",
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13_LATQ_01.jpg",
            "width": "550",
            "height": "50"
          },
          "ansimg": {
            "image": "ch13_LATQ_01_Ans.jpg",
            "width": "550",
            "height": "382"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Rajesh is making a wheel of a bicycle using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?",
          "ans": "A table of the given information is as follows:",
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13_LATQ_02.jpg",
            "width": "550",
            "height": "50"
          },
          "ansimg": {
            "image": "ch13_LATQ_02_Ans.jpg",
            "width": "550",
            "height": "345"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Rajesh is making a wheel of a bicycle using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.",
          "ans": "A table of the given information is as follows:",
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13_LATQ_02.jpg",
            "width": "550",
            "height": "50"
          },
          "ansimg": {
            "image": "ch13_LATQ_03_Ans.jpg",
            "width": "550",
            "height": "437"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Rajesh is making a wheel of a bicycle using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. How many spokes would be needed if the angle between a pair of consecutive spokes is 40º?",
          "ans": "A table of the given information is as follows:",
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch13_LATQ_02.jpg",
            "width": "550",
            "height": "50"
          },
          "ansimg": {
            "image": "ch13_LATQ_04_Ans.jpg",
            "width": "550",
            "height": "409"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Which of the following are in inverse proportion? <br>(i) The number of children working on a project and the time taken to complete the project. <br>(ii) The time taken by a car to complete the journey and the distance covered in uniform speed. <br>(iii) Area of farm which is sown and the crop harvested. <br>(iv) The population of mumbai and the area of land per person.",
          "ans": "(i) It is in inverse proportion because if there are more children, then it will take lesser time to complete the project. <br>(ii) It is not in inverse proportion because in more time the car may cover more distance with a uniform speed. <br>(iii) No, it is not in inverse proportion because in more area, more quantity of crops can be harvested. <br>(iv) It is in inverse proportion because with increasing population, the land availability per person will decrease simultaneously.",
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "If a box of chocolates is divided among 36 children, they will get 5 chocolates each. How many would each get, if the number of the children is reduced by 6?",
          "ans": "Number of remaining children = 36 – 6 = 30. Let the number of chocolates which each of the 30 students will get, be x. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_06.jpg",
            "width": "490",
            "height": "165"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "An orphanage has enough food to feed 30 children in that orphanage for 7 days. How long would the food last if there were 5 more children in that orphanage?",
          "ans": "Let the number of days that the food will last if there were 5 more children in the orphanage be x. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_07.jpg",
            "width": "550",
            "height": "235"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A wireman estimates that 4 persons could rewire Vaibhav’s house in 3 days. If he uses 3 persons instead of hour, how long should they take to complete the job?",
          "ans": "Let the number of days required by 3 persons to complete the job be x. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_08.jpg",
            "width": "550",
            "height": "271"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A batch of Bisleri bottles was packed in 20 boxes with 12 bottles in each box. If the same batch is packed using 30 bottles in each box, how many boxes would be filled?",
          "ans": "Let the number of boxes filled by using 30 bottles in each box, be x. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_09.jpg",
            "width": "550",
            "height": "290"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A compack company required 35 machines to produce a given number of compacks in 60 days. How many machines would be required to produce the same number of compacks in 50 days?",
          "ans": "Let the number of machines required to produce compack in 50 days be x. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_10.jpg",
            "width": "550",
            "height": "209"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A bus takes 3 hours to reach a destination by travelling at the speed of 40 km/h. How long will it take when the bus travels at the speed of 60 km/h?",
          "ans": "Let the time taken by the bus to reach the destination, while travelling with a speed of 60 km/hr be x hours. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_11.jpg",
            "width": "532",
            "height": "275"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Three persons could fit new door in house in 4 days. <br>(i) One of the persons fell ill before the work started. How long would the job take now? <br>(ii) How many persons would be needed to fit the door in one day?",
          "ans": "(i) Let the number of days required by one man to fit all the doors be x. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_12.jpg",
            "width": "550",
            "height": "480"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "A college has 7 lectures a day each of 40 minutes duration. How long would each lectures be if the college has 8 lectures a day assuming the number of college hours to be the same?",
          "ans": "Let the duration of each lectures when there are 8 lectures a day in the college, be x minutes. The following table is obtained.",
          "code": "LATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_LATQ_13.jpg",
            "width": "550",
            "height": "220"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Following are the car parking charges near a bus stop up to 4 hours ₹ 80 8 hours ₹ 120 12 hours ₹ 160 24 hours ₹ 180. Check if the parking charges are in direct proportion to the parking time.",
          "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": "ch13_SATQ_01.jpg",
            "width": "550",
            "height": "220"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A mixture of paint is prepared by mixing 1 part of blue pigments with 9 parts of base. In the following table, find the parts of base that need to be added.",
          "ans": "The given mixture of paint is prepared by mixing 1 part blue pigments with 9 parts of base. For more parts of blue pigments, the parts of the base will also be more. Therefore, the part of blue pigments & the parts of base are in direct proportion. The given information in the form of a table is as follows:",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_02.jpg",
            "width": "550",
            "height": "244"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In question 2 above, if 1 part of blue pigment requires 60 ml of base, how much blue pigment should we mix with 1500 ml of base?",
          "ans": "Let the parts of blue pigment required to mix with 1500 ml of base be x. The given information in the form of a table is as follows:",
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_03.jpg",
            "width": "440",
            "height": "280"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A machine in a soft drink factory fills 900 bottles in six hours. How many bottles will it fill in four hours?",
          "ans": "Let the number of bottles filled by the machine in four hours be x. The given information in the form of a table is as follows.",
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_04.jpg",
            "width": "510",
            "height": "240"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A photograph of a bacteria enlarged 60,000 times attains a length of 6 cm. What is the actual length of the bacteria? If the photograph is enlarged 30,000 times only, what would be its enlarged length?",
          "ans": "Let the actual length of bacteria be x cm & the enlarged length of bacteria be y cm, if the photograph is enlarged for 30,000 times. The given information in the form of a table is as follows:",
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_05.jpg",
            "width": "550",
            "height": "415"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "In a model of a boat, the mast is 7 cm high, while the mast of the actual ship is 14 m high. If the length of the boat is 24 m, how long is the model boat?",
          "ans": "Let the length of the mast of the model boat be x cm. The given information in the form of a table is as follows:",
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_06.jpg",
            "width": "436",
            "height": "244"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Suppose 2 kg of wheat contains 7 × 10<sup>6</sup> crystals. How many wheat crystals are there in <br>(i) 4 kg of wheat? <br>(ii) 1.2 kg of wheat?",
          "ans": "(i) Let the number of wheat crystals in 4 kg of wheat be x. The given information in the form of a table is as follows:",
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_07.jpg",
            "width": "536",
            "height": "429"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Chaitali has a road map with a scale of 1 cm representing 17 km. She drives on a road for 68 km. What would be her distance covered in the map?",
          "ans": "Let the distance represented on the map be x cm. The given information in the form of a table is as follows:",
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_08.jpg",
            "width": "550",
            "height": "215"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A 4 m 40 cm high vertical pole casts a shadow 2 m 20 cm long. Find at the same time: <br>(i) the length of the shadow casts by another pole 10 m 50 cm high <br>(ii) the height of a pole which casts a shadow 5 m long.",
          "ans": "Let the length of the shadow of the other pole be x m (1 m = 100 cm). The given information in the form of a table is as follows:",
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch13_SATQ_09.jpg",
            "width": "550",
            "height": "540"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A bus travels 16 km in 20 minutes. If the speed remains the same, how far can it travel in 4 hours?",
          "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": "ch13_SATQ_10.jpg",
            "width": "484",
            "height": "390"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch13_pbq",
    "gowf": "ch13_gowf",
    "afow": "ch13_afow",
    "cs": "ch13_cs",
    "afq": "ch13_afq",
    "fib": "ch13_fib",
    "grade": "Grade 8",
    "mcq": "ch13_mcq",
    "vsaq": "ch13_vsaq",
    "laq": "ch13_laq",
    "tf": "ch13_tf",
    "co": "ch13_co",
    "nf": "ch13_nf",
    "mtf": "ch13_mtf",
    "yn": "ch13_yn",
    "saq": "ch13_saq",
    "dtf": "ch13_dtf",
    "map": "ch13_map",
    "ctt": "ch13_ctt",
    "un": "ch13_un",
    "ctco": "ch13_ctco",
    "grf": "ch13_grf",
    "snc": "ch13_snc",
    "jtf": "ch13_jtf"
  },
  
{
    "subject": "Mathematics",
    "chapter": "ch14",
    "chapterName": "Chapter 14 - Factorisation",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "Common factor of 90 & 120 is",
          "ans": "(c) 30",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 90",
            "(b) 120",
            "(c) 30",
            "(d) 1"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "(x + 3) (x – 2) =",
          "ans": "(b) x<sup>2</sup> + x – 6",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) x<sup>2</sup> + x + 6",
            "(b) x<sup>2</sup> + x – 6",
            "(c) x + 3",
            "(d) x – 2"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Common factor of 5 & 7 is",
          "ans": "(d) 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 5",
            "(b) 7",
            "(c) 35",
            "(d) 1"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "6x – 2xy =",
          "ans": "(b) 2x (3 – y)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1",
            "(b) 2x (3 – y)",
            "(c) x (3 – 2y)",
            "(d) (2x – 2xy)"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "6x<sup>2</sup> – 36y<sup>2</sup>",
          "ans": "(c) 6(x<sup>2</sup> – 6y<sup>2</sup>)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (6x – 6y) (6x + 6y)",
            "(b) 6 (x – 6y) (x + 6y)",
            "(c) 6(x<sup>2</sup> – 6y<sup>2</sup>)",
            "(d) 6(x – y) (x + y)"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "(x – 2) (x + 2)",
          "ans": "(a) x<sup>2</sup> – 4",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) x<sup>2</sup> – 4",
            "(b) x<sup>2</sup> + 4",
            "(c) x – 2",
            "(d) x + 2"
          ],
          "val": 6
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Prime factorisation of 24m<sup>3<,sup>n<sup>2</sup> is",
          "ans": "(c) 2 × 2 × 2 × 3 × m × m × m × n × n",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2 × 12m<sup>3</sup>n<sup>2</sup>",
            "(b) 8 × 3mn",
            "(c) 2 × 2 × 2 × 3 × m × m × m × n × n",
            "(d) 12 × 2m × m × m × n × n"
          ],
          "val": 7
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "x<sup>4</sup> – y<sup>4</sup>",
          "ans": "(d) (x<sup>2</sup> – y<sup>2</sup>) (x<sup>2</sup> + y<sup>2</sup>)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (x<sup>2</sup> – y<sup>2</sup>) (x<sup>2</sup> – y<sup>2</sup>)",
            "(b) (x<sup>2</sup> + y<sup>2</sup>) (x – y)",
            "(c) x × x × x × x + y × y × y × y",
            "(d) (x<sup>2</sup> – y<sup>2</sup>) (x<sup>2</sup> + y<sup>2</sup>)"
          ],
          "val": 8
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "y<sup>2</sup> + 7y + 12 =",
          "ans": "(c) 2 × 2 × 2 × 3 × m × m × m × n × n",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (x – 5)<sup>2</sup>",
            "(b) (y – 3) (y – 4)",
            "(c) (y + 3) (y + 4)",
            "(d) (y + 4)<sup>2</sup>"
          ],
          "val": 9
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "(a<sup>2</sup> – b<sup>2</sup>) ÷ (a – b) =",
          "ans": "(b) a + b",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (a – b)",
            "(b) a + b",
            "(c) 1",
            "(d) a<sup>2</sup> – b<sup>2</sup>"
          ],
          "val": 10
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "90x<sup>2</sup>y<sup>2</sup>z<sup>2</sup> ÷ 10xyz",
          "ans": "(a) 9xyz",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 9xyz",
            "(b) 10xyz",
            "(c) 1",
            "(d) 90xyz"
          ],
          "val": 11
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "54a<sup>3</sup>b<sup>3</sup>c<sup>3</sup> ÷ 18a<sup>3</sup>b<sup>3</sup>c<sup>3</sup>",
          "ans": "(c) 3",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3abc",
            "(b) 3a<sup>2</sup>b<sup>2</sup>c<sup>2</sup>",
            "(c) 3",
            "(d) 0"
          ],
          "val": 12
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "13y<sup>2</sup>z<sup>2</sup> ÷ 13yz",
          "ans": "(b) yz",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 13",
            "(b) yz",
            "(c) 13yz",
            "(d) 1"
          ],
          "val": 13
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "3x + 3 ÷ 3",
          "ans": "(b) 3x + 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3",
            "(b) 3x + 1",
            "(c) 3x + 3",
            "(d) x + 1"
          ],
          "val": 14
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Common factor of 24xy & 36x<sup>2</sup>y<sup>2</sup> is",
          "ans": "(a) 12xy",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 12xy",
            "(b) 12x<sup>2</sup>y<sup>2</sup>",
            "(c) 9xy",
            "(d) x<sup>3</sup>y<sup>3</sup>"
          ],
          "val": 15
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "",
          "ans": "(c) 3x + 5y",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "pic": {
            "image": "ch14_MCQ_16.jpg",
            "width": "90",
            "height": "50"
          },
          "options": [
            "(a) 3x<sup>2</sup> + 5y<sup>2</sup>",
            "(b) 3x – 5y",
            "(c) 3x + 5y",
            "(d) 1"
          ],
          "val": 16
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "a<sup>2</sup> + 25a ÷ a =",
          "ans": "(b) a<sup>2</sup> + 25",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) a + 25a",
            "(b) a<sup>2</sup> + 25",
            "(c) a<sup>2</sup>",
            "(d) a + 25"
          ],
          "val": 17
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "m<sup>2</sup> – n<sup>2</sup> =",
          "ans": "(d) (m + n) (m – n)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) m<sup>2</sup>",
            "(b) n<sup>2</sup>",
            "(c) m + n",
            "(d) (m + n) (m – n)"
          ],
          "val": 18
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The sum of –7pq and 2pq is",
          "ans": "(d) –5pq",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) –9pq",
            "(b) 9pq",
            "(c) 5pq",
            "(d) –5pq"
          ],
          "val": 19
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Square of 3x – 4y is",
          "ans": "(d) 9x<sup>2</sup> + 16y<sup>2</sup> – 24xy",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 9x<sup>2</sup> – 16y<sup>2</sup>",
            "(b) 6x<sup>2</sup> – 8y<sup>2</sup>",
            "(c) 9x<sup>2</sup> + 16y<sup>2</sup> + 24xy",
            "(d) 9x<sup>2</sup> + 16y<sup>2</sup> – 24xy"
          ],
          "val": 20
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "t<sup>2</sup> – u<sup>2</sup> is equal to",
          "ans": "(c) (t + u) (t – u)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (t – u)<sup>2</sup>",
            "(b) (t – u) (t – u)",
            "(c) (t + u) (t – u)",
            "(d) (t + u) (t + u)"
          ],
          "val": 21
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Factorised form of r<sup>2</sup> – 10r + 21 is",
          "ans": "(b) (r – 7) (r – 3)",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) (r – 1) (r – 4)",
            "(b) (r – 7) (r – 3)",
            "(c) (r – 7) (r + 3)",
            "(d) (r + 7) (r + 3)"
          ],
          "val": 22
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "On dividing 57p<sup>2</sup>qr by 114pq, we get",
          "ans": null,
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "ansimg": {
            "image": "ch14_MCQ_23c.jpg",
            "width": "60",
            "height": "40"
          },
          "options": [
            "ch14_MCQ_23a.jpg",
            "ch14_MCQ_23b.jpg",
            "ch14_MCQ_23c.jpg",
            "(d) 2pr"
          ],
          "val": 23
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The common factor of 3ab and 2cd is",
          "ans": "(a) 1",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 1",
            "(b) –1",
            "(c) a",
            "(d) c"
          ],
          "val": 24
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The value of (–27x<sup>2</sup>y) ÷ (–9xy) is (d)",
          "ans": "(d) 3x",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3xy",
            "(b) –3xy",
            "(c) –3x",
            "(d) 3x"
          ],
          "val": 25
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "The value of (a + b)<sup>2</sup> + (a – b)<sup>2</sup> is",
          "ans": "(c) 2a<sup>2</sup> + 2b<sup>2</sup>",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 2a + 2b",
            "(b) 2a – 2b",
            "(c) 2a<sup>2</sup> + 2b<sup>2</sup>",
            "(d) 2a<sup>2</sup> – 2b<sup>2</sup>"
          ],
          "val": 26
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n               A number written as a product of Prime factors is a factorisation.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Prime factors of 91 is 13 and 7.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Common factors of 140x – 28y is 14.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n               1 is a factor of any number.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n               m<sup>2</sup> – 6m = m × m – 6 × m\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 5
        },
        {
          "heading": "State True or False.",
          "qus": "\n               9x<sup>2</sup> – 16y<sup>2</sup> = (3x – 4y) (3x + 4y)\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 6
        },
        {
          "heading": "State True or False.",
          "qus": "\n               3m<sup>2</sup> + 9m + 6 = (3m + 3)<sup>2</sup>\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 7
        },
        {
          "heading": "State True or False.",
          "qus": "\n               7p<sup>2</sup> + 21q<sup>2</sup> = (7p – 3q) (7p + 3q)\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 8
        },
        {
          "heading": "State True or False.",
          "qus": "\n               (1 + m)<sup>2</sup> = 1 + m<sup>2</sup>\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 9
        },
        {
          "heading": "State True or False.",
          "qus": "\n               When we divide a polynomial by monomial we always get monomial.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 10
        },
        {
          "heading": "State True or False.",
          "qus": "\n               38x<sup>3</sup>y<sup>2</sup>z ÷ 19xy<sup>2</sup> = 2x<sup>2</sup>z\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 11
        },
        {
          "heading": "State True or False.",
          "qus": "\n               We could divide trinomial by the monomial using the cancellation method.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 12
        },
        {
          "heading": "State True or False.",
          "qus": "\n               When we divide Algebraic Expressions by monomial we always get numerals.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 13
        },
        {
          "heading": "State True or False.",
          "qus": "\n               12xmyn ÷ 6xmyn = 2\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 14
        },
        {
          "heading": "State True or False.",
          "qus": "\n               When we square a monomial, the numerical coefficient and each factor has to be squared.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 15
        },
        {
          "heading": "State True or False.",
          "qus": "\n               (3x + 2)<sup>2</sup> = 3x<sup>2</sup> + 6x + 4\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 16
        },
        {
          "heading": "State True or False.",
          "qus": "\n               3x + 2x = 5x<sup>2</sup>\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 17
        },
        {
          "heading": "State True or False.",
          "qus": "\n               4a<sup>2</sup> – 9b<sup>2</sup> = (4a – 9b) (4a + 9b)\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 18
        },
        {
          "heading": "State True or False.",
          "qus": "\n               30m<sup>4</sup>n<sup>2</sup> ÷ 3m<sup>2</sup>n = 10m<sup>2</sup>n\n               _________\n            ",
          "ans": "Ture",
          "code": "TF",
          "val": 19
        },
        {
          "heading": "State True or False.",
          "qus": "\n               (a – b)<sup>2</sup> = a<sup>2</sup> – b<sup>2</sup>.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 20
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Factorised form of p<sup>2</sup> + 30p + 216 is (p + 18) (p – 12).\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 21
        },
        {
          "heading": "State True or False.",
          "qus": "\n               (9x – 51) ÷ 9 is x – 51.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 22
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Subtraction of 5a<sup>2</sup>b<sup>2</sup>c<sup>2</sup> from –7a<sup>2</sup>b<sup>2</sup>c<sup>2</sup> is –12a<sup>2</sup>b<sup>2</sup>c<sup>2</sup>.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 23
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Factorisation of –3a<sup>2</sup> + 3ab + 3ac is 3a(–a – b – c).\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 24
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Common factors of 12a<sup>2</sup>b<sup>2</sup> + 4ab<sup>2</sup> – 32 is 4.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 25
        },
        {
          "heading": "State True or False.",
          "qus": "\n               (a + b) (a –b) = a<sup>2</sup> – b<sup>2</sup>.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 26
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "Prime factor form of 50 is __________.",
          "ans": "2 × 5 × 5",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "2x + 4 = __________.",
          "ans": "2(x + 2)",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "5xy + 7 + 5y + 7x = __________.",
          "ans": "(5y + 7) (x + 1)",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Common factors of 11x & 121 is __________.",
          "ans": "11",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "–9x + 6 = __________.",
          "ans": "3(–3x + 2)",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a – b)<sup>2</sup> = __________.",
          "ans": "a<sup>2</sup> – 2ab + b<sup>2</sup>",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a + b)<sup>2</sup> = __________.",
          "ans": "a<sup>2</sup> + 2ab + b<sup>2</sup>",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a + b) (a – b) = __________.",
          "ans": "a<sup>2</sup> – b<sup>2</sup>",
          "code": "FIB",
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "17abc – 34ab<sup>2</sup> = __________.",
          "ans": "17ab(c – 2b)",
          "code": "FIB",
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(m + 1)<sup>2</sup> = _______________.",
          "ans": "m<sup>2</sup> + 2m + 1",
          "code": "FIB",
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(x – 5)<sup>2</sup> = __________.",
          "ans": "x<sup>2</sup> – 10x + 25",
          "code": "FIB",
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "25x<sup>2</sup> – 49y<sup>2</sup> = (5x – 7y) __________.",
          "ans": " (5x + 7y)",
          "code": "FIB",
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(14x<sup>2</sup> – 21y<sup>2</sup>) ÷ 7 = __________.",
          "ans": "2x<sup>2</sup> – 3y<sup>2</sup>",
          "code": "FIB",
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": " ",
          "ans": "–49",
          "code": "FIB",
          "pic": {
            "image": "ch14_FIB_14.jpg",
            "width": "180",
            "height": "40"
          },
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "100x<sup>2</sup> ÷ 10x = __________.",
          "ans": "10x",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "2xyz ÷ 4x<sup>2</sup>y<sup>2</sup>z<sup>2</sup> = __________ ",
          "ans": null,
          "code": "FIB",
          "ansimg": {
            "image": "ch14_FIB_16.jpg",
            "width": "42",
            "height": "40"
          },
          "val": 16
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "3x<sup>3</sup> + 9x<sup>2</sup> + 27x ÷ 3x = __________.",
          "ans": "x<sup>2</sup> + 3x + 9",
          "code": "FIB",
          "val": 17
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(x – 5)<sup>2</sup> = _______________.",
          "ans": "x<sup>2</sup> – 10x + 25",
          "code": "FIB",
          "val": 18
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a + b)<sup>2</sup> = _______________.",
          "ans": "a<sup>2</sup> + 2ab + b<sup>2</sup>",
          "code": "FIB",
          "val": 19
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(m<sup>2</sup> – n<sup>2</sup>) = _______________.",
          "ans": "(m – n) (m + n)",
          "code": "FIB",
          "val": 20
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "3x<sup>2</sup>y<sup>2</sup> – 7x<sup>2</sup>y<sup>2</sup> = __________.",
          "ans": "–4x<sup>2</sup>y<sup>2</sup>",
          "code": "FIB",
          "val": 21
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "21x<sup>2</sup>y<sup>2</sup> ÷ 3xy = __________.",
          "ans": "7xy",
          "code": "FIB",
          "val": 22
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a – b) __________ = a2 – 2ab + b2.",
          "ans": "(a – b)",
          "code": "FIB",
          "val": 23
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Factorised form of 18 mn + 10mnp is _______________.",
          "ans": "2mn(9 + 5p)",
          "code": "FIB",
          "val": 24
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "38x<sup>2</sup>y<sup>2</sup>z ÷ 19xy<sup>2</sup> is equal to __________.",
          "ans": "2xz",
          "code": "FIB",
          "val": 25
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "  ",
          "ans": "x + 1",
          "code": "FIB",
          "pic": {
            "image": "ch14_FIB_26.jpg",
            "width": "275",
            "height": "40"
          },
          "val": 26
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "(a + b)<sup>2</sup> – 2ab = _____ + _____.",
          "ans": "a<sup>2</sup>, b<sup>2</sup>",
          "code": "FIB",
          "val": 27
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The factorisation of x<sup>2</sup> – 4 is _______________.",
          "ans": "(x + 2) (x – 2)",
          "code": "FIB",
          "val": 28
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Factorised form of 4y<sup>2</sup> – 12y + 9 is _______________.",
          "ans": "(2y – 3) (2y – 3)",
          "code": "FIB",
          "val": 29
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Carry out the division: 32x<sup>4</sup> ÷ 64x",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_01.jpg",
            "width": "540",
            "height": "300"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Carry out the division: –49y<sup>3</sup> ÷ 7y<sup>2</sup>",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_02.jpg",
            "width": "300",
            "height": "160"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Divide as directed. <br>5(23x + 1) (9x + 5) ÷ (23x + 1) <br>(ii)52xy(x + 5) (m – 11) ÷ 13x(m – 11) <br>(iii) 29uvr(u + v) (v + r) (r + u) ÷ 58uv(v + r) (r + u) <br>(iv) 20(w + 51) (y2 + 5y + 3) ÷ 5(w + 51) <br>(v) t(t + 1) (t + 2) (t + 3) ÷ t(t + 2)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_03.jpg",
            "width": "544",
            "height": "373"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise the expression and divide: (x<sup>2</sup> – 7x + 12) ÷ (x – 4)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_04.jpg",
            "width": "415",
            "height": "180"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise the expression and divide: (s<sup>2</sup> – 14s – 32) ÷ (s + 2)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_05.jpg",
            "width": "415",
            "height": "180"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise the expression and divide: (p<sup>2</sup> + 5p – 6) ÷ (p – 1)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_06.jpg",
            "width": "415",
            "height": "180"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise the expression and divide: 4yz(z<sup>2</sup> – 4z – 117) ÷ 2z(z – 13)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_07.jpg",
            "width": "471",
            "height": "218"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise the expression and divide: 5ab(a<sup>2</sup> – b<sup>2</sup>) ÷ 2a(a + b)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_08.jpg",
            "width": "447",
            "height": "198"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Factorise the expression and divide: 18cd(9c<sup>2</sup> – 16d<sup>2</sup>) ÷ 9cd(3c + 4d)",
          "ans": null,
          "code": "LATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_LATQ_09.jpg",
            "width": "523",
            "height": "174"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the common factors of 13x, 39.",
          "ans": "13x = 13 × x <br>&nbsp;&nbsp;39 = 3 × 13 <br>Common factor = 13",
          "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": "Find the common factors of 3x, 33xy.",
          "ans": "&nbsp;&nbsp;3x = 3 × x <br>33x = 3 × 11 × x × y <br>common factor = 3 × x",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the common factors of 14pq, 21p<sup>2</sup>q<sup>2</sup>.",
          "ans": "&nbsp;&nbsp;&nbsp;14pq = 2 × 7 × p × q <br>21p<sup>2</sup>q<sup>2</sup> = 3 × 7 × p × p × q × q <br>common factor = 7 × p × q",
          "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 the common factors of 2m, 5m<sup>2</sup>, 4.",
          "ans": "&nbsp;2m = 2 × m <br>5m<sup>2</sup> = 5 × m × m <br>4 = 2 × 2 <br>common factor = 1",
          "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 the common factors of 8xyz, 32xy<sup>2</sup>, 16x<sup>2</sup>y.",
          "ans": "8xyz = 2 × 2 × 2 × x × y × z <br>32x<sup>2</sup>y<sup>2</sup> = 2 × 2 × 2 × 2 × 2x × x × y × y <br>16x<sup>2</sup>y = 2 × 2 × 2 × 2 × x × x × y <br>common factor = 2 × 2 × 2 × x × y",
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find the common factors of 12x<sup>3</sup>, –3x<sup>2</sup>, 24x.",
          "ans": "12x<sup>3</sup> = 2 × 2 × 3 × x × x × x <br>–3x<sup>2</sup> = –1 × 3 × x × x <br>24x = 2 × 2 × 2 × 3 × x <br>common factor = 3 × x",
          "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": "Find the common factors of 5pq, 10qr, 15rp.",
          "ans": "5pq = 5 × p × q <br>10qr = 2 × 5 × q × r <br>15rp = 3 × 5 × r × p <br>common factor = 5",
          "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": "Find the common factors of 11x<sup>2</sup>y<sup>3</sup>, 10x<sup>3</sup>y<sup>2</sup>, 22x<sup>2</sup>y<sup>2</sup>z.",
          "ans": "11x<sup>2</sup>y<sup>3</sup> = 11 × x × x × y × y × y <br>10x<sup>3</sup>y<sup>2</sup> = 2 × 5 × x × x × x × y × y <br>22x<sup>2</sup>y<sup>2</sup>z = 2 × 11 × x × x × y × y × z <br>common factor = x × x × y × y = x<sup>2</sup>y<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 7x – 56",
          "ans": "= 7 × x – 7 × 8 <br>= 7 × (x – 8)",
          "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": "Factorise the expression: 6p – 36q",
          "ans": "= 6 × p – 6 × 6 × q <br>= 6 × (p – 6q)",
          "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": "Factorise the expression: 5q<sup>2</sup> + 10q",
          "ans": "= 5 × q × q + 2 × 5 × q <br>= 5 × q (q + 2) <br>= 5q(q + 2)",
          "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": "Factorise the expression: –16z + 10z<sup>3</sup>",
          "ans": "= (–1) × 2 × 2 × 2 × 2 × z + 2 × 5 × z × z × z <br>= 2 × z (–1 × 2 × 2 × 2 + 5 × z × z) <br>= 2z(– 8 + 5z<sup>2</sup>)",
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 6l<sup>2</sup>m + 30alm",
          "ans": "= 2 × 3 × l × l × m + 2 × 3 × 5 × a × l × m <br>= 2 × 3 × l × m × (l + 5a) <br>= 6lm (l + 5a)",
          "code": "SATQ",
          "options": null,
          "val": 13,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 13s<sup>2</sup>r – 39sr<sup>2</sup>",
          "ans": "= 13 × s × s × r – 3 × 13 × s × r × r <br>= 13 × s × r × (s – 3r) <br>= 13sr(s – 3r)",
          "code": "SATQ",
          "options": null,
          "val": 14,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 30a<sup>2</sup> – 15b<sup>2</sup> + 6c<sup>2</sup>",
          "ans": "= 2 × 3 × 5 × a × a – 3 × 5 × b × b + 2 × 3 × c × c <br>= 3 × (2 × 5 × a × a – 5 × b × b + 2 × c × c) <br>= 3(10a<sup>2</sup> – 5b<sup>2</sup> + 2c<sup>2</sup>)",
          "code": "SATQ",
          "options": null,
          "val": 15,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: xm<sup>2</sup>n + ym<sup>2</sup>n + zm<sup>2</sup>p",
          "ans": "= x × m × m × n + y × m × m × n + z × m × m × p <br>= m × m (x × n + y × n + z × p) <br>= m<sup>2</sup> (xn + yn + zp)",
          "code": "SATQ",
          "options": null,
          "val": 16,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: x<sup>2</sup>] + xt + 8x + 8t",
          "ans": "= x × x + x × t + 8 × x + 8 × t <br>= x × (x + t) + 8 × (x + t) <br>= (x + 8) (x + t)",
          "code": "SATQ",
          "options": null,
          "val": 17,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: 12xy – 6x + 4y – 2",
          "ans": "= 2 × 6 × x × y – 6 × x + 2 × 2 × y – 2 <br>= 6 × x × (2y – 1) + 2 × (2y – 1) <br>= 6x (2y – 1) + 2 × (2y – 1) <br>= (6x + 2) (2y – 1)",
          "code": "SATQ",
          "options": null,
          "val": 18,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: fm + gm – ft – gt",
          "ans": "f × m + g × m – f × t – g × t <br>m × (f + g) – t × (f + g) <br>= (m – t) (f + g)",
          "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": "Factorise: 35pq + 245q + 35 + 5p",
          "ans": "= 5 × 7 × p × q + 5 × 7 × 7 × q + 5 × 7 + 5 × p <br>= 5 × 7 × q (p + 7) + 5 × (7 + p) <br>= 35q (p + 7) + 5 × (7 + p) <br>= (35q + 5) (7 + p)",
          "code": "SATQ",
          "options": null,
          "val": 20,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: a<sup>2</sup> + 10a + 21",
          "ans": "= a<sup>2</sup> + 7a + 3a + 21 <br>= a(a + 7) + 3(a + 7) <br>= (a + 3) (a + 7)",
          "code": "SATQ",
          "options": null,
          "val": 21,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: <i>l</i><sup>2</sup> – 7<i>l</i> + 12",
          "ans": "= <i>l</i><sup>2</sup> – 4l – 3<i>l</i> + 12 <br>= <i>l</i>(<i>l</i> – 4) – 3(<i>l</i> – 4) <br>= (<i>l</i> – 3) (<i>l</i> – 4)",
          "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": "Factorise the expression: 25w<sup>2</sup> + 20w + 4",
          "ans": "= 25w<sup>2</sup> + 10w + 10w + 4 <br>= 5w(5w + 2) + 2(5w + 2) <br>= (5w + 2) (5w + 2) <br>= (5w + 2)<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 23,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 49y<sup>2</sup> + 42yz + 9z<sup>2</sup>",
          "ans": "= 49y<sup>2</sup> + 21yz + 21yz + 9z<sup>2</sup> <br>= 7y(7y + 3z) + 3z(7y + 3z) <br>= (7y + 3z) (7y + 3z) <br>= (7y + 3z)<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": "Answer the following questions in short.",
          "qus": "Factorise the expression: 11x<sup>2</sup> – 22x + 11",
          "ans": "= 11x<sup>2</sup> – 11x – 11x + 11 <br>= 11x(x – 1) – 11(x – 1) <br>= (11x – 11) (x – 1) <br>= 11(x – 1) (x – 1) <br>= 11(x – 1)<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 25,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 121b<sup>2</sup> – 88bt + 16t<sup>2</sup>",
          "ans": "= 121b<sup>2</sup> – 44bt – 44bt + 16t<sup>2</sup> <br>= 11b(11b – 4t) – 4t(11b – 4t) <br>= (11b – 4t) (11b – 4t) <br>= (11b – 4t)<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 26,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: (p + q)<sup>2</sup> – 4pq",
          "ans": "= p<sup>2</sup> + 2pq+q<sup>2</sup> – 4pq <br>= p<sup>2</sup> – 2pq + q<sup>2</sup> <br>= p<sup>2</sup> – pq – pq + q<sup>2</sup> <br>= p(p – q) – q(p – q) <br>= (p – q) (p – q) = (p – q)<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 27,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: c<sup>4</sup> + 2c<sup>2</sup>d<sup>2</sup> + d<sup>4</sup>",
          "ans": "= c<sup>4</sup> + c<sup>2</sup>d<sup>2</sup> + c<sup>2</sup>d<sup>2</sup> + d<sup>4</sup> <br>= c<sup>2</sup>(c<sup>2</sup> + d<sup>2</sup>) + d<sup>2</sup>(c<sup>2</sup> + d<sup>2</sup>) <br>= (c<sup>2</sup> + d<sup>2</sup>) (c<sup>2</sup> + d<sup>2</sup>) <br>=(c<sup>2</sup> + d<sup>2</sup>)<sup>2</sup>",
          "code": "SATQ",
          "options": null,
          "val": 28,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: 9p<sup>2</sup> – 4q<sup>2</sup>",
          "ans": "= (3p)<sup>2</sup> – (2q)<sup>2</sup> <br>= (3p + 2q) (3p – 2q)",
          "code": "SATQ",
          "options": null,
          "val": 29,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: 112b<sup>2</sup> – 63a<sup>2</sup>",
          "ans": "= 16 × 7b<sup>2</sup> – 9 × 7a<sup>2</sup> <br>= 7(16b<sup>2</sup> – 9a<sup>2</sup>) = 7[(4b)<sup>2</sup> – (3a)<sup>2</sup>] <br>= 7(4b + 3a) (4b – 3a)",
          "code": "SATQ",
          "options": null,
          "val": 30,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: 36x<sup>2</sup> – 49",
          "ans": "= (6x)<sup>2</sup> – (7)<sup>2</sup> <br>= (6x + 7) (6x – 7)",
          "code": "SATQ",
          "options": null,
          "val": 31,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: 121x<sup>5</sup> – 225x<sup>3</sup>",
          "ans": "= x<sup>3</sup>(121x<sup>2</sup> – 225) <br> = x<sup>3</sup>[(11x)<sup>2</sup> – (15)<sup>2</sup>]<br> = x<sup>3</sup>(11x + 15) (11x – 15)",
          "code": "SATQ",
          "options": null,
          "val": 32,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: (s + r)<sup>2</sup> – (s – r)<sup>2</sup>",
          "ans": "= s<sup>2</sup> + 2sr + r<sup>2</sup> – (s<sup>2</sup> – 2sr + r<sup>2</sup>) <br>= <del>s<sup>2</sup></del> + 2sr + <del>r<sup>2</sup></del> – <del>s<sup>2</sup></del> + 2sr – <del>r<sup>2</sup></del> = 4sr",
          "code": "SATQ",
          "options": null,
          "val": 33,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: 81x<sup>2</sup>y<sup>2</sup> – 16",
          "ans": "= (9xy)<sup>2</sup> – (4)<sup>2</sup> <br>= (9xy + 4) (9xy – 4)",
          "code": "SATQ",
          "options": null,
          "val": 34,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: (t<sup>2</sup> – 2tp + p<sup>2</sup>) – z<sup>2</sup>",
          "ans": "= (t – p)<sup>2</sup> – (z)<sup>2</sup> <br>= (t – p + z) (t – p – z)",
          "code": "SATQ",
          "options": null,
          "val": 35,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: 81a<sup>2</sup> – 4b<sup>2</sup> + 24bc + 108 ac",
          "ans": "= (9a)<sup>2</sup> – (2b)<sup>2</sup> + 12c (2b + 9a) <br>= (9a – 2b) (9a + 2b) + 12c (9a + 2b) <br>= (9a + 2b) (9a – 2b + 12c)",
          "code": "SATQ",
          "options": null,
          "val": 36,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: ay<sup>2</sup> + by",
          "ans": "= a × y × y + b × y <br>= y × (ay + b) <br>= y(ay + b)",
          "code": "SATQ",
          "options": null,
          "val": 37,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 7p<sup>2</sup> + 35q<sup>2</sup>",
          "ans": "= 7 × p × p + 5 × 7 × q × q <br>= 7 × (p × p + 5 × q × q) <br>= 7(p<sup>2</sup> + 5q<sup>2</sup>)",
          "code": "SATQ",
          "options": null,
          "val": 38,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 23x<sup>3</sup> + 23xy<sup>2</sup> + 23xz<sup>2</sup>",
          "ans": "= 23 × x × x × x + 23 × x × y × y + 23 × x × z × z <br>= 23 × x(x × x + y × y + z × z) <br>= 23x(x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup>)",
          "code": "SATQ",
          "options": null,
          "val": 39,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: fh<sup>2</sup> + gh<sup>2</sup> + gk<sup>2</sup> + fk<sup>2</sup>",
          "ans": "= f × h × h + g × h × h + g × k × k + f × k × k <br>= h × h (f + g) + k × k (g + f) <br>= h<sup>2</sup> (f + g) + k<sup>2</sup> (f + g) <br>= (h<sup>2</sup> + k<sup>2</sup>) (f + g)",
          "code": "SATQ",
          "options": null,
          "val": 40,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: (su + s) + u + 1",
          "ans": "= su + s + u + 1 <br>= s(u + 1) + 1(u + 1) <br>= (s + 1) (u + 1)",
          "code": "SATQ",
          "options": null,
          "val": 41,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: g(g + k) + g(g + k)",
          "ans": "= (g + g) (g + k) <br>= 2g (g + k)",
          "code": "SATQ",
          "options": null,
          "val": 42,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 6b<sup>2</sup> – 24b – 5bz + 20z",
          "ans": "= 6b(b – 4) – 5z(b – 4) <br>= (6b – 5z) (b – 4)",
          "code": "SATQ",
          "options": null,
          "val": 43,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expression: 20ab + 8a + 5b + 2",
          "ans": "= 4a(5b + 2) + 1(5b + 2) <br>= (4a + 1) (5b + 2)",
          "code": "SATQ",
          "options": null,
          "val": 44,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: k<sup>4</sup> – u<sup>4</sup>",
          "ans": "= (k<sup>2</sup>)<sup>2</sup> – (u<sup>2</sup>)<sup>2</sup> <br>= (k<sup>2</sup> + u<sup>2</sup>) (k<sup>2</sup> – u<sup>2</sup>) <br>= (k<sup>2</sup> + u<sup>2</sup>) [(k)<sup>2</sup> – (u)<sup>2</sup>] <br>= (k<sup>2</sup> + u<sup>2</sup>) (k + u) (k – u)",
          "code": "SATQ",
          "options": null,
          "val": 45,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: p<sup>4</sup> – 256",
          "ans": "= (p<sup>2</sup>)<sup>2</sup> – (16)<sup>2</sup> <br>= (p<sup>2</sup> + 16) (p<sup>2</sup> – 16) <br>= (p<sup>2</sup> + 16) [(p)<sup>2</sup> – (4)<sup>2</sup>] <br>= (p<sup>2</sup> + 16) (p + 4) (p – 4)",
          "code": "SATQ",
          "options": null,
          "val": 46,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: m<sup>4</sup> – (s + l)<sup>4</sup>",
          "ans": "= (m<sup>2</sup>)<sup>2</sup> – [(s + l)<sup>2</sup>]<sup>2</sup> <br>= (m<sup>2</sup> + (s + l)<sup>2</sup>) (m<sup>2</sup> – (s + l)<sup>2</sup>) <br>= (m<sup>2</sup> + (s + l)<sup>2</sup>) [(m)<sup>2</sup> – (s + l)<sup>2</sup>] <br>= (m<sup>2</sup> + (s + l)<sup>2</sup>) (m + s + l) (m – s – l)",
          "code": "SATQ",
          "options": null,
          "val": 47,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise: x<sup>4</sup> – (p – q)<sup>4</sup>",
          "ans": "= (x<sup>2</sup>)<sup>2</sup> – ((p – q)<sup>2</sup>)<sup>2</sup> = (x<sup>2</sup> + (p – q)<sup>2</sup>)(x<sup>2</sup> – (p – q)<sup>2</sup>) <br>= (x<sup>2</sup> + (p – q)<sup>2</sup>) [(x)<sup>2</sup> – (p – q)<sup>2</sup>] <br>= [x<sup>2</sup> + (p – q)<sup>2</sup>] [(x + p – q) (x – p +q)]",
          "code": "SATQ",
          "options": null,
          "val": 48,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expressions: q<sup>2</sup> + 7q + 10",
          "ans": "= q<sup>2</sup> + 2q + 5q + 10 <br>= q(q + 2) + 5(q + 2) <br>= (q + 5) (q + 2)",
          "code": "SATQ",
          "options": null,
          "val": 49,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expressions: q<sup>2</sup> – 13q + 40",
          "ans": "= q<sup>2</sup> – 8q – 5q + 40 <br>= q(q – 8) – 5(q – 8) <br>= (q – 5) (q – 8)",
          "code": "SATQ",
          "options": null,
          "val": 50,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Factorise the expressions: k<sup>2</sup> + 12k + 35",
          "ans": "= k<sup>2</sup> + 5k +7k + 35 <br>= k(k + 5) + 7(k + 5) <br>= (k + 7) (k + 5)",
          "code": "SATQ",
          "options": null,
          "val": 51,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Carry out the division: 66pm<sup>2</sup>r<sup>3</sup> ÷ 33mr<sup>2</sup>",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 52,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_52.jpg",
            "width": "400",
            "height": "150"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Carry out the division: 51x<sup>3</sup>y<sup>3</sup>z<sup>3</sup> ÷ 68xy<sup>2</sup>z<sup>3</sup>",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 53,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_53.jpg",
            "width": "451",
            "height": "166"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Divide the polynomial 5x<sup>2</sup> – 2x by the monomial 3x.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 54,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_54.jpg",
            "width": "377",
            "height": "160"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Divide the polynomial 5y<sup>8</sup> – 6y<sup>6</sup> + 7y<sup>4</sup> by the monomial y<sup>4</sup>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 55,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_55.jpg",
            "width": "440",
            "height": "130"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Divide the polynomial 12(k<sup>3</sup>l<sup>2</sup>m<sup>2</sup> +k<sup>2</sup>l<sup>3</sup>m<sup>2</sup>) + k<sup>2</sup>l<sup>2</sup>m<sup>3</sup> by the monomial 3k<sup>2</sup>l<sup>2</sup>m<sup>2</sup>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 56,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_56.jpg",
            "width": "530",
            "height": "160"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Divide the polynomial y<sup>3</sup> + 2y<sup>2</sup> + 4y by the monomial 2y.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 57,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_57.jpg",
            "width": "410",
            "height": "160"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Divide the polynomial p<sup>4</sup>q<sup>5</sup> – p<sup>7</sup>q<sup>9</sup> by the monomial p<sup>3</sup>q<sup>4</sup>.",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 58,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_58.jpg",
            "width": "480",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Work out the division: (14y – 35) ÷ 7",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 59,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_59.jpg",
            "width": "450",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Work out the division: (x – 3) ÷ (2x – 6)",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 60,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_60.jpg",
            "width": "450",
            "height": "100"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Work out the division: 26m(10m + 35) ÷ 13(2m + 7)",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 61,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_61.jpg",
            "width": "520",
            "height": "140"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Work out the division: 33x<sup>2</sup>y<sup>2</sup>(7z – 56) ÷ 66xy(z – 8)",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 62,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_62.jpg",
            "width": "520",
            "height": "140"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Work out the division: 96klm (3k – 12) (5l – 30) ÷ 144(k – 4) (l – 6)",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 63,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch14_SATQ_63.jpg",
            "width": "550",
            "height": "170"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Find and correct the errors in the given mathematical statement: <br>6(x – 5) = 6x – 5",
          "ans": "LHS = 6(x – 5) = 6x – 30 ≠ RHS <br>Hence, the correct mathematical statement is 6(x – 5) = 6x – 30.",
          "code": "SATQ",
          "options": null,
          "val": 64,
          "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 and correct the errors in the given mathematical statement: <br>y(4x + 9) = 4x<sup>2</sup> + 9",
          "ans": "LHS = y(4x + 9) = 4xy + 9y ≠ RHS <br>Hence, the correct mathematical statement is y(4x + 9) = 4xy + 9y.",
          "code": "SATQ",
          "options": null,
          "val": 65,
          "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 and correct the errors in the given mathematical statement: <br>5m + 10y = 15my",
          "ans": "LHS = 5m + 10y ≠ RHS <br>Hence, the correct mathematical statement is 5m + 10y = 5m + 10y.",
          "code": "SATQ",
          "options": null,
          "val": 66,
          "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 and correct the errors in the given mathematical statement: <br>l + 2l + 3l = 5l",
          "ans": "LHS = l + 2l + 3l = 6l ≠ RHS <br>Hence, the correct mathematical statement is l + 2l + 3l = 6l.",
          "code": "SATQ",
          "options": null,
          "val": 67,
          "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 and correct the errors in the given mathematical statement: <br>5t + 3t + 4t – 10t = 0",
          "ans": "LHS = 5t + 3t + 4t – 10t <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 12t – 10t = 2t ≠ RHS <br>Hence, the correct mathematical statement is 5t + 3t + 4t – 10t = 2t.",
          "code": "SATQ",
          "options": null,
          "val": 68,
          "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 and correct the errors in the given mathematical statement: <br>6x + 5x = 11x<sup>2</sup>",
          "ans": "LHS = 6x + 5x = 11x ≠ RHS <br>Hence, the correct mathematical statement is 6x + 5x = 11x.",
          "code": "SATQ",
          "options": null,
          "val": 69,
          "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 and correct the errors in the given mathematical statement: <br>(3x)<sup>2</sup> + 3(9x) + 7 = 3x<sup>2</sup> + 27x + 7",
          "ans": "LHS = (3x)2 + 3(9x) + 7 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 9x2 + 27x + 7 ≠ RHS <br>Hence, the correct mathematical statement is (3x)2 + 3(9x) + 7 = 9x2 + 27x + 7.",
          "code": "SATQ",
          "options": null,
          "val": 70,
          "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 and correct the errors in the given mathematical statement: <br>(7x)<sup>2</sup> + 30x = 49x + 30x",
          "ans": "LHS = (7x)2 + 30 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 49x2 + 30x ≠ RHS <br>Hence, the correct mathematical statement is (7x)<sup>2</sup> + 30x = 49x<sup>2</sup> + 30x.",
          "code": "SATQ",
          "options": null,
          "val": 71,
          "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 and correct the errors in the given mathematical statement: <br>(6x + 1)<sup>2</sup> = 6x<sup>2</sup> + 12x + 1",
          "ans": "LHS = (6x + 1)<sup>2</sup> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (6x)<sup>2</sup> + 2(6x) (1) + (1)<sup>2</sup> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 36x<sup>2</sup> + 12x + 1 ≠ RHS <br>Hence, the correct mathematical statement is (6x + 1)<sup>2</sup> = 36x<sup>2</sup> + 12x + 1.",
          "code": "SATQ",
          "options": null,
          "val": 72,
          "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": "Substituting x = –2 in x<sup>2</sup> + 5x + 6 gives (–2)<sup>2</sup> + 5(–2) = 4 – 10 = – 6",
          "ans": "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; LHS = x<sup>2</sup> + 5x + 6 <br>Putting x = –2 in given expression, <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (–2)<sup>2</sup> + 5(–2) + 6 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 4 – 10 + 6 = 0 ≠ RHS <br>Hence, x<sup>2</sup> + 5x + 4 gives (–2)<sup>2</sup> + 5(–2) + 6 = 4 – 10 + 6 = 0.",
          "code": "SATQ",
          "options": null,
          "val": 73,
          "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": "Substituting x = –2 in x<sup>2</sup> – 5x + 6 gives (–2)<sup>2</sup> – 5(–2) + 6 = 4 – 10 + 6 = 0",
          "ans": "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; LHS = x<sup>2</sup> + 5x + 6 <br>Putting x = –2 in given expression, <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (–2)<sup>2</sup> – 5(–2) + 6 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 4 + 10 + 6 = 20 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 20 ≠ RHS <br>Hence, x<sup>2</sup> – 5x + 6 gives (–2)<sup>2</sup> – 5(–2) + 6 = 4 + 10 + 6 = 20.",
          "code": "SATQ",
          "options": null,
          "val": 74,
          "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": "Substituting x = –2 in x<sup>2</sup> – 5x gives (–2)<sup>2</sup> + 5(–2) = –4 – 10 = –14",
          "ans": "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; LHS = x<sup>2</sup> – 5x <br>Putting x = –2 in given expression, <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (–2)<sup>2</sup> – 5(–2) <br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 4 + 10 = 14 ≠ RHS <br>Hence, x<sup>2</sup> – 5x gives (–2)<sup>2</sup> – 5(–2) = 4 + 10 = 14.",
          "code": "SATQ",
          "options": null,
          "val": 75,
          "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": "Correct the mathematical statement: <br>(c – 3)<sup>2</sup> = c<sup>2</sup> – 9",
          "ans": "LHS = (c – 3)<sup>2</sup> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= (c)<sup>2</sup> – 2(c)(3) + (3)<sup>2</sup> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= c<sup>2</sup> – 6c + 9 ≠ RHS <br>Hence, the correct mathematical statement is (c – 3)2 = c2 – 6c + 9.",
          "code": "SATQ",
          "options": null,
          "val": 76,
          "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": "Correct the mathematical statement: <br>(z + 8)<sup>2</sup> = z<sup>2</sup> + 64",
          "ans": "LHS = (z + 8)<sup>2</sup> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= (z)<sup>2</sup> + 2(z) (8) + (8)<sup>2</sup> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= z<sup>2</sup> + 16z + 64 ≠ RHS <br>Hence, the correct mathematical statement is (z + 8)<sup>2</sup> = z<sup>2</sup> + 16z + 64.",
          "code": "SATQ",
          "options": null,
          "val": 77,
          "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": "Correct the mathematical statement: <br>(4a + 5b)(a – b) = 4a<sup>2</sup> – 5b<sup>2</sup>",
          "ans": "LHS = (4a + 5b)(a – b) <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 4a × a – 4a × b + 5b × a – 5b × b <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 4a<sup>2</sup> – 4ab + 5ab – 5b<sup>2</sup> <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 4a<sup>2</sup> + ab – 5b<sup>2</sup> ≠ RHS <br>Hence, the correct mathematical statement is (4a + 5b) (a – b) = 4a<sup>2</sup> + ab – 5b<sup>2</sup>.",
          "code": "SATQ",
          "options": null,
          "val": 78,
          "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": "Correct the mathematical statement: <br>(p + 11)(p + 2) = p<sup>2</sup> + 22.",
          "ans": "LHS = (p + 11) (p + 2) <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= p × p + p × 2 + 11 × p + 11 × 2 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= p<sup>2</sup> + 2p + 11p + 22 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= p<sup>2</sup> + 13p + 22 ≠ RHS <br>Hence, the correct mathematical statement is (p + 11) (p + 2) = p<sup>2</sup> + 13p + 22.",
          "code": "SATQ",
          "options": null,
          "val": 79,
          "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": "Correct the mathematical statement: <br>(q – 11) (q + 2) = q<sup>2</sup> – 22",
          "ans": "LHS = (q – 11) (q + 2) <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= q × q + q × (2) – 11 × q – 11 × (2) <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= q<sup>2</sup> + 2q – 11q – 22 <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= q<sup>2</sup> – 9q – 22 ≠ RHS <br>Hence, the correct mathematical statement is (q – 11) (q + 2) = q<sup>2</sup> – 9q – 22.",
          "code": "SATQ",
          "options": null,
          "val": 80,
          "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": "Correct the mathematical statement:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 81,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14_SATQ_81.jpg",
            "width": "70",
            "height": "50"
          },
          "ansimg": {
            "image": "ch14_SATQ_81_Ans.jpg",
            "width": "426",
            "height": "105"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Correct the mathematical statement:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 82,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14_SATQ_82.jpg",
            "width": "150",
            "height": "50"
          },
          "ansimg": {
            "image": "ch14_SATQ_82_Ans.jpg",
            "width": "426",
            "height": "105"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Correct the mathematical statement:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 83,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14_SATQ_83.jpg",
            "width": "100",
            "height": "50"
          },
          "ansimg": {
            "image": "ch14_SATQ_83_Ans.jpg",
            "width": "401",
            "height": "80"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Correct the mathematical statement:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 84,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14_SATQ_84.jpg",
            "width": "100",
            "height": "50"
          },
          "ansimg": {
            "image": "ch14_SATQ_84_Ans.jpg",
            "width": "360",
            "height": "80"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Correct the mathematical statement:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 85,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14_SATQ_85.jpg",
            "width": "100",
            "height": "50"
          },
          "ansimg": {
            "image": "ch14_SATQ_85_Ans.jpg",
            "width": "400",
            "height": "80"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Correct the mathematical statement:",
          "ans": null,
          "code": "SATQ",
          "options": null,
          "val": 86,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch14_SATQ_86.jpg",
            "width": "100",
            "height": "50"
          },
          "ansimg": {
            "image": "ch14_SATQ_86.jpg",
            "width": "410",
            "height": "80"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch14_pbq",
    "gowf": "ch14_gowf",
    "afow": "ch14_afow",
    "cs": "ch14_cs",
    "afq": "ch14_afq",
    "fib": "ch14_fib",
    "grade": "Grade 8",
    "mcq": "ch14_mcq",
    "vsaq": "ch14_vsaq",
    "laq": "ch14_laq",
    "tf": "ch14_tf",
    "co": "ch14_co",
    "nf": "ch14_nf",
    "mtf": "ch14_mtf",
    "yn": "ch14_yn",
    "saq": "ch14_saq",
    "dtf": "ch14_dtf",
    "map": "ch14_map",
    "ctt": "ch14_ctt",
    "un": "ch14_un",
    "ctco": "ch14_ctco",
    "grf": "ch14_grf",
    "snc": "ch14_snc",
    "jtf": "ch14_jtf"
  },
  
{
    "subject": "Mathematics",
    "chapter": "ch15",
    "chapterName": "Chapter 15 - Introduction to Graphs",
    "all": [
      [],
      [
        {
          "heading": "State True or False.",
          "qus": "\n               Histogram has adjacent bars over the intervals\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 1
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "Graphs are __________ representations of data collected.",
          "ans": "visual",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A _______________ is used to show comparison among categories",
          "ans": "bar graph",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A _______________ is used to compare parts of a whole.",
          "ans": "pie-graph",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A __________ is a bar graph that shows data in intervals.",
          "ans": "histogram",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A _______________ displays data that changes continuously over periods of time.",
          "ans": "line graph",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "A line graph which is a whole unbroken line is called a _______________.",
          "ans": "linear graph",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "For fixing a point on the graph sheet we need, _______________ and _______________.",
          "ans": "x-coordinate, y-coordinate",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "From the following graph fill in the blank:",
          "ans": "H",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_08.jpg",
            "width": "470",
            "height": "252"
          },
          "val": 8
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "From the following graph fill in the blank:",
          "ans": "K",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_09.jpg",
            "width": "470",
            "height": "252"
          },
          "val": 9
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "From the following graph fill in the blank:",
          "ans": "Z",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_10.jpg",
            "width": "470",
            "height": "252"
          },
          "val": 10
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "From the following graph fill in the blank:",
          "ans": "(2, 0)",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_11.jpg",
            "width": "355",
            "height": "252"
          },
          "val": 11
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "From the following graph fill in the blank:",
          "ans": "(5, 5)",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_12.jpg",
            "width": "355",
            "height": "252"
          },
          "val": 12
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "From the following graph fill in the blank:",
          "ans": "(0, 3)",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_13.jpg",
            "width": "355",
            "height": "252"
          },
          "val": 13
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "From the following graph fill in the blank:",
          "ans": "(4, 0)",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_14.jpg",
            "width": "355",
            "height": "252"
          },
          "val": 14
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "The relation betwen independent variable and dependent variable can be shown through a __________.",
          "ans": "graph",
          "code": "FIB",
          "val": 15
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "Hardik can ride a bike constantly at a speed of 40 kms/hour. Using a time-distance graph given in the following graph for this situation, <br>(i) the time taken by Hardik to ride 60 km is 1.5 hours.",
          "ans": "(i) 1.5 <br>(ii) 100",
          "code": "FIB",
          "pic": {
            "image": "ch15_FIB_16.jpg",
            "width": "478",
            "height": "276"
          },
          "val": 16
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw the graphs for the following table of values, with suitable scale on the axes.",
          "ans": "Scale: <br>Horizontal: 1 unit = 1 banana <br>Vertical: 1 unit = 3 rupees",
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_LATQ_01.jpg",
            "width": "421",
            "height": "60"
          },
          "ansimg": {
            "image": "ch15_LATQ_01_Ans.jpg",
            "width": "281",
            "height": "226"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw the graphs for the following table of values, with suitable scale on the axes and answer the following. <br>(i) How much distance did the bike cover during the period 6.30 a.m. to 7 a.m.? <br>(ii) What was the time when the bike had covered a distance 87.5 kms since its start?",
          "ans": "(i) The distance covered by the bike during the period 6.30 a.m. to 7 a.m. (or in half hour) = 17.5 km. <br>(ii) The time when the bike had covered a distance 87.5 kms since its start = 6.30 a.m.",
          "code": "LATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_LATQ_02.jpg",
            "width": "390",
            "height": "55"
          },
          "ansimg": {
            "image": "ch15_LATQ_02_Ans.jpg",
            "width": "440",
            "height": "230"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw the graphs for the following table of values, with suitable scale on the axes and answer the following. <br>(i) Does the graph pass through the origin? <br>(ii) Use the graph to find the interest on ₹ 5000 for a year. <br>(iii) To get an interest of ₹ 245 per year, how much money should be deposited?",
          "ans": "(i) Yes, the graph passes through the origin. <br>(ii) The interest on ₹ 5000 for a year = 175 rupees. <br>(iii) 7000 rupees should be deposited to get an interest of ₹ 245 per year.",
          "code": "LATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_LATQ_03.jpg",
            "width": "480",
            "height": "55"
          },
          "ansimg": {
            "image": "ch15_LATQ_03_Ans.jpg",
            "width": "300",
            "height": "310"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw a graph for the following. Is it a linear graph?",
          "ans": "Yes, the graph is linear.",
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_LATQ_04.jpg",
            "width": "450",
            "height": "60"
          },
          "ansimg": {
            "image": "ch15_LATQ_04_Ans.jpg",
            "width": "320",
            "height": "250"
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Draw a graph for the following. Is it a linear graph?",
          "ans": "No, the graph is not linear.",
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_LATQ_05.jpg",
            "width": "450",
            "height": "60"
          },
          "ansimg": {
            "image": "ch15_LATQ_05_Ans.jpg",
            "width": "450",
            "height": "350"
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "The following graph shows the temperature of a patient in a hospital recorded every hour. <br>(a) What was the patient's temperature at 10 a.m.? <br>(b) When was the patient's temperature 35°C? <br>(c) The patient's temperature was the same two times during <br>the period given. What were these two times? <br>(d) What was the temperature at 11:30 am? How did you arrive at your answer? <br>(e) During which periods did the patient's temperature showed on upward trend?",
          "ans": "(a) Patient's temperature at 10 a.m. was 36°C <br>(b) Patient's temperature at 8 a.m. was 35°C <br>(c) Patient's temperature was same, i.e., 38°C at 11 a.m. and 12 p.m. <br>(d) Patient's temperature at 11:30 am/, was 38°C (as the temperature was constatnt from 11 a.m. to 12 p.m.) <br>(e) Patient's temperature showed an upward trend from 7 a.m. to 9 a.m. and then again from 10 a.m. to 11 a.m.",
          "code": "SATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_SATQ_01.jpg",
            "width": "322",
            "height": "230"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The following line graph shows the yearly sales figures for a manufacturing company. <br>(a) What were the sales in (i) 2012 (ii) 2015? <br>(b) Compute the difference between the sales in 2011 and 2015? <br>(c) In which year, was there the greatest difference between the sales as compared to its pervious year?",
          "ans": "(a)(i) Sales in 2012 were ₹ 3 crore (ii) Sales in 2015 were ₹ 11 crore <br> (b) Difference between the sales in 2011 and 2015 = ₹ 11 crore – ₹ 6 crore = ₹ 5 crore <br>(c) In the year 2013, the difference between the sales as compared to its previous year is the greatest i.e., sales in the year 2013 – 2012 = ₹ 7 crore",
          "code": "SATQ",
          "options": null,
          "val": 2,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_SATQ_02.jpg",
            "width": "356",
            "height": "281"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "For an experiment in botany, two different plants, plant P and plant Q were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. <br>The results are shown by the following graph: <br>(a) How high was plant P after (i) 2 weeks (ii) 3 weeks? <br>(b) How high was plant Q after (i) 2 weeks (ii) 3 weeks? <br>(c) How much did plant P grow during 3rd week? <br>(c) How much did  plant P grow during 3rd week? <br>(d) How much did plant Q grow from the end of the 2nd week to the end of the 3rd week? <br>(e) During which week did plant P grow most? <br>(f) During which week did plant Q grow most?",
          "ans": "(a) Height of plant P after (i) 2 weeks was 2 cm (ii) 3 weeks was 3 cm <br> (b) Height of plant Q after (i) 2 weeks was 3 cm (ii) 3 weeks was 3.5 cm <br>(c) Growth of plant P during the 3rd week = 3 cm – 2 cm = 1 cm <br>(d) Growth of plant Q from the end of the 2nd week to the end of the 3rd week = 3.5 cm – 3 cm = 0.5 cm <br>(e) Plant P grew most during the 1st week = 1.5 cm <br>(f) Plant Q grew most during the 2nd week = 3 cm – 1 cm = 2 cm",
          "code": "SATQ",
          "options": null,
          "val": 3,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_SATQ_03.jpg",
            "width": "292",
            "height": "277"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "The following graph shows the temperature forecast and the actual temperature for each day of a week: <br>(a) On which days was the forecast temperature the same as the actual temperature? <br>(b) What was the maximum actual temperature during the week? <br>(c) What was the minimum forecast temperature during the week? <br>(d) On which day did the actual temperature differ the most from the forecast temperature?",
          "ans": "(a) Forecast temperature was same as the actual temperature on Monday, i.e., 15°C, on Thursday, i.e., 25°C and on Sunday, i.e., 25°C <br>(b) Maximum actual temperature during the week was 40°C <br>(c) Minimum forecast temperature during the week was 15°C <br>(d) The difference between the actual temperature and the forecast temperature was the most on Friday, i.e., about 10°C",
          "code": "SATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_SATQ_04.jpg",
            "width": "356",
            "height": "281"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Use the table below to draw linear graph. <br>The number of days a hill side city received snow in different years",
          "ans": "The number of days the hill side city received snow in different years",
          "code": "SATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_SATQ_05.jpg",
            "width": "280",
            "height": "56"
          },
          "ansimg": {
            "image": "ch15_SATQ_05_Ans.jpg",
            "width": "318",
            "height": "308"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Use the table below to draw linear graph. <br>Population (in thousands) of men and women in a village in different years",
          "ans": "Population (in thousand) of men and women in a village in different years",
          "code": "SATQ",
          "options": null,
          "val": 6,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_SATQ_06.jpg",
            "width": "384",
            "height": "85"
          },
          "ansimg": {
            "image": "ch15_SATQ_06_Ans.jpg",
            "width": "318",
            "height": "308"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph: <br>(a) How much time did the person take for the travel? <br>(b) How far is the place of the merchant from the town? <br>(c) Did the person stop on his way? Explain. <br>(d) During which period did he ride fastest?",
          "ans": "(a) The person took 4 hours for the travel, i.e., starting from 10 a.m. to 2p.m. <br>(b) The merchant's place from the town is at a distance of 30 km. <br>(c)As can be seen from the graph, the distance travelled between 12:00 p.m. to 1:00 p.m. is NIL, hence during that time, the person stopped. <br>(d)The person rode the fastest beween 10 a.m. to 11 a.m. when he covered a distance of about 12.5 km in an hour.",
          "code": "SATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": "ch15_SATQ_07.jpg",
            "width": "318",
            "height": "308"
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Plot the points A (3, 0), B (3, 3), C (3, 4), D (3, 2) on a graph sheet.Which of them lie on a line?",
          "ans": "All the four points lie on a line",
          "code": "SATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15_SATQ_08_Ans.jpg",
            "width": "221",
            "height": "168"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Plot the points P (1, 4), Q (2, 4), R (3, 4), S (4, 4) on a graph sheet.Which of them lie on a line?",
          "ans": "All the four points lie on a line",
          "code": "SATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15_SATQ_09_Ans.jpg",
            "width": "221",
            "height": "168"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Plot the points A (2, 1), B (4, 1), C (4, 3), D (2, 3) on a graph sheet.Which of them lie on a line?",
          "ans": "All the four points do not lie on a straight line",
          "code": "SATQ",
          "options": null,
          "val": 10,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15_SATQ_10_Ans.jpg",
            "width": "221",
            "height": "168"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Draw the line passing through (1, 3) and (3, 1). Find the coordinates of the points at which this line meets the x-axis and y-axis",
          "ans": "The line passing through (1, 3) and (3, 1) meets the line x-axis at V (4, 0) and the y-axis at W (0, 4)",
          "code": "SATQ",
          "options": null,
          "val": 11,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15_SATQ_11_Ans.jpg",
            "width": "261",
            "height": "168"
          }
        },
        {
          "heading": "Answer the following questions in short.",
          "qus": "Write the co-ordinates of the vertices of each of these adjoining figures.",
          "ans": "(i) For square OABC → 0 = (0, 0), A = (2, 0), B = (2, 2), C = (0, 2) <br>(ii) For traingle PQR → P = (4, 5), Q = (3, 3), R = (5, 3) <br>(iii) For parallelogram WXYZ → W = (6, 4), X = (7, 2), Y = (7, 5), Z = (6, 7)",
          "code": "SATQ",
          "options": null,
          "val": 12,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": "ch15_SATQ_12_Ans.jpg",
            "width": "271",
            "height": "206"
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch15_pbq",
    "gowf": "ch15_gowf",
    "afow": "ch15_afow",
    "cs": "ch15_cs",
    "afq": "ch15_afq",
    "fib": "ch15_fib",
    "grade": "Grade 8",
    "mcq": "ch15_mcq",
    "vsaq": "ch15_vsaq",
    "laq": "ch15_laq",
    "tf": "ch15_tf",
    "co": "ch15_co",
    "nf": "ch15_nf",
    "mtf": "ch15_mtf",
    "yn": "ch15_yn",
    "saq": "ch15_saq",
    "dtf": "ch15_dtf",
    "map": "ch15_map",
    "ctt": "ch15_ctt",
    "un": "ch15_un",
    "ctco": "ch15_ctco",
    "grf": "ch15_grf",
    "snc": "ch15_snc",
    "jtf": "ch15_jtf"
  },
  
{
    "subject": "Mathematics",
    "chapter": "ch16",
    "chapterName": "Chapter 16 - Playing with Numbers",
    "all": [
      [
        {
          "heading": "Multiple Choice Question.",
          "qus": "If the difference between the sum of digits at its odd places and that of digits at the even places of a number is divisible by 11, then that number is divisible by __________.",
          "ans": "(c) 11",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3",
            "(b) 9",
            "(c) 11",
            "(d) 7"
          ],
          "val": 1
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following number is divisible by 10?",
          "ans": "(a)730",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a)730",
            "(b) 932",
            "(c) 555",
            "(d) 351"
          ],
          "val": 2
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following number is divisible by 5?",
          "ans": "(d) 435",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 333",
            "(b) 198",
            "(c) 543",
            "(d) 435"
          ],
          "val": 3
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following number is divisible by 2?",
          "ans": "(b) 372",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 411",
            "(b) 372",
            "(c) 503",
            "(d) 991"
          ],
          "val": 4
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following number is divisible by 9?",
          "ans": "(a) 3573",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3573",
            "(b) 2369",
            "(c) 3735",
            "(d) 9781"
          ],
          "val": 5
        },
        {
          "heading": "Multiple Choice Question.",
          "qus": "Which of the following number is divisible by 3?",
          "ans": "(c) 5232",
          "code": "MCQ",
          "width": null,
          "height": null,
          "optn": null,
          "options": [
            "(a) 3710",
            "(b) 7523",
            "(c) 5232",
            "(d) 9953"
          ],
          "val": 6
        }
      ],
      [
        {
          "heading": "State True or False.",
          "qus": "\n               If the division N ÷ 2 leaves a remainder 1, then ones digit of N might be 1, 3, 5, 7 or 9.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 1
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If the division N ÷ 2 leaves no remainder (i.e., zero remainder), the ones digit of N might be 0, 2, 4, 6 or 8.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 2
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If a number is divisible by any number m, then it will also be divisible by each of the factors of m.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 3
        },
        {
          "heading": "State True or False.",
          "qus": "\n               If the number abcd is divisible by 11, then [(<i>b</i> + <i>d</i>) – (<i>a</i> + <i>c</i>)] must be 0 or multiples of 11.\n               _________\n            ",
          "ans": "True",
          "code": "TF",
          "val": 4
        },
        {
          "heading": "State True or False.",
          "qus": "\n               Every odd number is divisible by 2.\n               _________\n            ",
          "ans": "False",
          "code": "TF",
          "val": 5
        }
      ],
      [],
      [
        {
          "heading": "Fill in the blanks.",
          "qus": "If ones digit of a number is 0, then that number is divisible by __________.",
          "ans": "10",
          "code": "FIB",
          "val": 1
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the ones digit of a number is 0 or 5, then that number is divisible by __________.",
          "ans": "5",
          "code": "FIB",
          "val": 2
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the ones digit of a number is 0, 2, 4, 6 or 8, then that number is divisible by __________.",
          "ans": "2",
          "code": "FIB",
          "val": 3
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "It the sum of the digits of a number is divisible by 9, then that number is divisible by __________.",
          "ans": "9",
          "code": "FIB",
          "val": 4
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the sum of the digits of a number is divisible by 3, then that number is divisible by __________.",
          "ans": "3",
          "code": "FIB",
          "val": 5
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the division N ÷ 5 leaves a remainder of 3, then the ones digit of N is __________ or __________.",
          "ans": "3, 8",
          "code": "FIB",
          "val": 6
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the division N ÷ 5 leaves a remainder of 1, then the ones digit of N is __________ or __________.",
          "ans": "1, 6",
          "code": "FIB",
          "val": 7
        },
        {
          "heading": "Fill in the blanks.",
          "qus": "If the division N ÷ 5 leaves a remainder of 4, then the ones digit of N is __________ or __________.",
          "ans": "4, 9",
          "code": "FIB",
          "val": 8
        }
      ],
      [
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved.<br>&nbsp;&nbsp;&nbsp;&nbsp;2 A <br><u>&nbsp;+ 3 5&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;B 4",
          "ans": "The addition of A and 5 is giving 4, i.e., a number whose ones digit is 4. This is possible only when digit A is 9. In that case, the addition of A (9) and 5 will give 14 and thus, 1 will be the carry for the next step. <br>In the next step, 1 + 2 + 3 = 6. <br>Therefore, the addition is as follows: <br>&nbsp;&nbsp;&nbsp;&nbsp;2 9 <br><u>&nbsp;+ 3 5&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;6 4 <br>Clearly, B is 6. <br>Hence, A and B are 9 and 6 respectively.",
          "code": "LATQ",
          "options": null,
          "val": 1,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved.<br>&nbsp;&nbsp;&nbsp;&nbsp;5 A <br><u>&nbsp;+ 9 7&nbsp;</u> <br>&nbsp;C B 4",
          "ans": "The addition of A and 7 is giving 4, i.e., a number whose ones digit is 4. This is possible only when digit A is 7. In that case, the addition of A and 7 will give 14 and thus, 1 will be the carry for the next step. <br>In the next step, 1 + 5 + 9 = 15 <br>Therefore, the addition is as follows: <br>&nbsp;&nbsp;&nbsp;&nbsp;5 7 <br><u>&nbsp;+ 9 7&nbsp;</u> <br>&nbsp;&nbsp;15 4 <br>Clearly, B and C are 5 and 1 respectively. <br>Hence, A, B and C are 7, 5 and 1 respectively.",
          "code": "LATQ",
          "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 detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved.<br>&nbsp;&nbsp;&nbsp;1 A <br><u>&nbsp;&nbsp;&nbsp;× A&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;7 A",
          "ans": "The multiplication of A with A itself gives a number whose ones digit is A again. This happen only when A = 1, 5 or 6. <br>If A = 1, then the multiplication will be 11 × 1 = 11, However, here the tens digit is given as 7. <br>Therefore, A = 1 is not possible. Similarly, if A = 5, then the multiplication will be 15 × 5 = 75. <br>Thus, A should be 5. If A = 6, then the multiplication will be 16 × 6 = 96 ≠ 76. Therefore, A = 6 is not possible. <br>The multiplication is as follows: <br>&nbsp;&nbsp;&nbsp;1 5 <br><u>&nbsp;&nbsp;&nbsp;× 5&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;7 5 <br>Hence, the value of A is 5.",
          "code": "LATQ",
          "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 detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved.<br>&nbsp;&nbsp;&nbsp;&nbsp;A B <br><u>&nbsp;+ 4 8&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;7 A",
          "ans": "The addition of A and 4 is giving 7. There can be two cases. <br>(1) First step is not producing a carry. <br>In that case, A comes to be 3 as 3 + 4 = 7. Considering the first step in which the addition of B and 8 is giving A (i. e., 3), B should be a number such that the units digit of this addition comes to be 3. It is possible only when B = 5. In this case, A = 5 + 8 = 13. However, A is a single digit number. Hence, it is not possible. <br>(2) First step is producing a carry. <br>In that case, A comes to be 2 as 1 + 2 + 4 = 7.<br>Considering the first step in which the addition of B and 8 is giving A (i.e., 2), B should be a number such that the units digit of this addition comes to be 2. It is possible only when B = 4 and 4 + 8 = 12. <br>&nbsp;&nbsp;&nbsp;&nbsp;2 4 <br><u>&nbsp;+ 4 8&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;7 2 <br>Hence, the values of A and B are 2 and 4 respectively.",
          "code": "LATQ",
          "options": null,
          "val": 4,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved.<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A B <br>&nbsp;<u>&nbsp;&nbsp;&nbsp;&nbsp;× 7&nbsp;</u> <br>&nbsp;C A B",
          "ans": "The multiplication of 7 and B gives a number whose ones digit is B again. <br>Hence, B must be 0 or 5. <br>Let B be 5. <br>Multiplication of first step = 7 × 5 = 35. <br>3 will be a carry for the next step. <br>We have 7 × A + 3 = CA <br>This is not possible for any value of A. <br>Hence, B must be 0 only. If B = 0, then there will be no carry for the next step. <br>We should obtain 7 × A = CA <br>That is, the one's digit of 7 × A should be A. <br>This is possible when A = 5 or 0. <br>However, A can not be 0 as AB is a two-digit number. <br>Therefore, A must be 5 only. <br>The multiplication is as follows: <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5 0 <br>&nbsp;<u>&nbsp;&nbsp;&nbsp; × 7&nbsp;</u> <br>&nbsp;&nbsp;3 5 0 <br>Hence, the values of A, B and C are 5, 0 and 3 respectively.",
          "code": "LATQ",
          "options": null,
          "val": 5,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved.<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A B <br>&nbsp;<u>&nbsp;&nbsp;&nbsp;&nbsp;× 6&nbsp;</u> <br>&nbsp;B B B",
          "ans": "The multiplication of 6 and B gives a number whose one's digit is B again. <br>It is possible only when B = 0, 2, 4, 6 or 8. <br>If B = 0, then the product will be 0. Therefore, this value of B is not possible. <br>If B = 2, then B × 6 = 12 and 1 will be a carry for the next step. <br>6A + 1 = BB =22 ⇒ 6A = 21 and hence, any integer value of A is not possible. <br>If B = 4, then B × 6 = 24 and 2 will be a carry for the next step. <br>6A + 2 = BB = 44 ⇒ 6A = 42 and hence, A = 7 <br>The multiplication is as follows:<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;7 4 <br>&nbsp;<u>&nbsp;&nbsp;&nbsp;&nbsp;× 6&nbsp;</u> <br>&nbsp;&nbsp;4 4 4 <br>Hence, the values of A and B are 7 and 4 respectively. <br>If B = 6, then B × 6 = 36 and 3 will be a carry for the next step. <br>6A + 3 = BB = 66 ⇒ 6A = 63 and hence, any integer value of A is not possible. <br>If B = 8, then B × 6 = 48 and 4 will be a carry for the next step. <br>235 235 Class-VIII <br>6A + 4 = BB = 88 ⇒ 6A = 84 and hence, A = 14. <br>However, A is a single digit number. Therefore, this value of A is not possible. <br>Hence, the value of A and B are 7 and 4 respectively.",
          "code": "LATQ",
          "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 detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved.<br>&nbsp;&nbsp;&nbsp;&nbsp;A 5 <br><u>&nbsp;+ 3 B&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;B 0",
          "ans": "The addition of 5 and B is giving 0 i.e., a number whose ones digit is 0. This is possible only when digit B is 5. <br>In that case, the addition of 5 and B will give 10 and thus, 1 will be the carry for the next step. <br>In the next step, 1 + A + 3 = B <br>Clearly, A is 1 as 1 + 1 + 3 = 5 = B <br>Therefore, the addition is as follows:<br>&nbsp;&nbsp;&nbsp;&nbsp;1 5 <br><u>&nbsp;+ 3 5&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;5 0 <br>Hence, the values of A and B are 1 and 5 respectively.",
          "code": "LATQ",
          "options": null,
          "val": 7,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved. <br>&nbsp;&nbsp;&nbsp;&nbsp;3 A B <br><u>&nbsp;+ A B 3&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;B 9 9",
          "ans": "The addition of B and 3 is giving 9, i.e., a number whose ones digit is 9. <br>This is possible only when digit B is 6. <br>In the next step. <br>A + B = 9 <br>Clearly, A is 3. <br>In the next step, 3 + A = B or 3 + 3 = 6. <br>Therefore, the addition is as follows: <br>&nbsp;&nbsp;&nbsp;&nbsp;3 3 6 <br><u>&nbsp;+ 3 6 3&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;6 9 9 <br>Hence, the values of A and B are 3 and 6 respectively.",
          "code": "LATQ",
          "options": null,
          "val": 8,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        },
        {
          "heading": "Answer the following questions in detail.",
          "qus": "Find the values of the letters in the following and give reasons for the steps involved. <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2 3 A <br><u>&nbsp;+ 3 A B&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;A 8 9",
          "ans": "The addition of A and B is giving 9, i.e., a number whose ones digit is 9. The sum can be 9 only as the sum of two single digit numbers cannot be 19. <br>Therefore, there will not be any carry in this step. <br>In the next step, 3 + A = 8 <br>It is possible only, when A = 5 <br>In the next step, 2 + 3 = A = 5 <br>Clearly, A is 5. <br>We know that the addition of A and B is giving 9. As A is 5, therefore, B is 4. <br>Therefore, the addition is as follows: <br>&nbsp;&nbsp;&nbsp;&nbsp;3 3 5 <br><u>&nbsp;+ 3 5 4&nbsp;</u> <br>&nbsp;&nbsp;&nbsp;&nbsp;5 8 9 <br>Hence, the values of A and B are 5 and 4 respectively.",
          "code": "LATQ",
          "options": null,
          "val": 9,
          "option1": [],
          "option2": [],
          "option3": [],
          "option4": [],
          "aoption1": [],
          "aoption2": [],
          "aoption3": [],
          "aoption4": null,
          "pic": {
            "image": null,
            "width": null,
            "height": null
          },
          "ansimg": {
            "image": null,
            "width": null,
            "height": null
          }
        }
      ],
      [],
      [
        {
          "heading": "Answer the following questions in short.",
          "qus": "If 3y 46 is a multiple of 9, where y is a digit, what is the value of y?",
          "ans": "Here, 3y 46 is a multiple of 9.So, 3y 46 is divisible by 9.  <br>So, the addition 3 + y + 4 +6 = y + 13 is divisible by 9. <br>∴ y + 13 = 18 (∵ y ≥ 0 and y is a single digit number.) <br>∴ y = 5",
          "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": "If z 243 is a multiple of 9, where z is a digit, what is the value of z ? You will find that there are two answers for the last problem. Why is this so?",
          "ans": "Here, z 243 is a multiple of 9. <br>∴ z 243 is divisible by 9. <br>∴ The addition z + 2 + 4 + 3 = z + 9 is divisible by 9. <br>∴ z + 9 = 9 and z + 9 = 18 (∵ z ≥ 0 and z is a single digit number.) <br>∴ z = 0 and z = 9 <br>Here, there are two answers of z. <br>The addition of given number is z + 9. Now, sum of two single digit numbers is less than or equal to 18. <br>So, there are only two possibilities for value of z + 9, one is 9 and another one is 18. Therefore, there are two answers of z.",
          "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": "If 48x is a multiple of 3, where x is a digit, what is the value of x?",
          "ans": "Since 48x is a multiple of 3, its sum of digits 4 + 8 + x i.e. x + 12 is a multiple of 3. So, x + 12 is one of these numbers: 12, 15, 18, 21,...... <br>But since x is a single digit number, it can only be that x + 12 = 12 or 15 or 18 or 21. <br>Therefore, x = 0 or 3 or 6 or 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": "If z 801 is a multiple of 3, where z is a digit, what might be the values of z?",
          "ans": "Here, z 801 is a multiple of 3. <br>∴ z 801 is divisible by 3. <br>∴ The addition z + 8 + 0 + 1 = z + 9 is divisible by 3. <br>∴ z + 9 = 9 or z + 9 = 12 or z + 9 = 15 or z + 9 = 18 <br>(∵ z ≥ 0 and z is a single digit number.) <br>∴ z = 0 or z = 3 or z = 6 or z = 9.",
          "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
          }
        }
      ],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      [],
      []
    ],
    "pbq": "ch16_pbq",
    "gowf": "ch16_gowf",
    "afow": "ch16_afow",
    "cs": "ch16_cs",
    "afq": "ch16_afq",
    "fib": "ch16_fib",
    "grade": "Grade 8",
    "mcq": "ch16_mcq",
    "vsaq": "ch16_vsaq",
    "laq": "ch16_laq",
    "tf": "ch16_tf",
    "co": "ch16_co",
    "nf": "ch16_nf",
    "mtf": "ch16_mtf",
    "yn": "ch16_yn",
    "saq": "ch16_saq",
    "dtf": "ch16_dtf",
    "map": "ch16_map",
    "ctt": "ch16_ctt",
    "un": "ch16_un",
    "ctco": "ch16_ctco",
    "grf": "ch16_grf",
    "snc": "ch16_snc",
    "jtf": "ch16_jtf"
  }

]

Youez - 2016 - github.com/yon3zu
LinuXploit