{"id":4502,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/"},"modified":"2018-05-04T15:01:33","modified_gmt":"2018-05-04T09:31:33","slug":"ncert-solutions-class-12-maths-miscellaneous-5","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/","title":{"rendered":"NCERT Solutions class 12 Maths Miscellaneous"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Applications_of_Integrals\" >NCERT Solutions class 12 Maths\u00a0Applications of Integrals<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#2_Find_the_area_between_the_curves_and\" >2. Find the area between the curves \u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-2\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#3_Find_the_area_of_the_region_lying_in_the_first_quadrant_and_bounded_by_and\" >3. Find the area of the region lying in the first quadrant and bounded by \u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-3\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#4_Sketch_the_graph_of_and_evaluate\" >4. Sketch the graph of \u00a0and evaluate \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-4\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#5_Find_the_area_bounded_by_the_curve_between_and\" >5. Find the area bounded by the curve \u00a0between \u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-5\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#6_Find_the_area_enclosed_by_the_parabola_and_the_line\" >6. Find the area enclosed by the parabola \u00a0and the line \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-6\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#7_Find_the_area_enclosed_by_the_parabola_and_the_line\" >7. Find the area enclosed by the parabola \u00a0and the line \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-7\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#8_Find_the_area_of_the_smaller_region_bounded_by_the_ellipse_and_the_line\" >8. Find the area of the smaller region bounded by the ellipse \u00a0and the line \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-8\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#9_Find_the_area_of_the_smaller_region_bounded_by_the_ellipse_and_the_line\" >9. Find the area of the smaller region bounded by the ellipse \u00a0and the line \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#11Using_the_method_of_integration_find_the_area_enclosed_by_the_curve\" >11.Using the method of integration, find the area enclosed by the curve \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#12Find_the_area_bounded_by_the_curves\" >12.Find the area bounded by the curves .<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#13Using_the_method_of_integration_find_the_area_of_the_triangle_whose_vertices_are_A_2_0_B_4_5_and_C_6_3\" >13.Using the method of integration, find the area of the triangle whose vertices are A (2, 0), B (4, 5) and C (6, 3).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#14Using_the_method_of_integration_find_the_area_of_the_region_bounded_by_the_lines_and\" >14.Using the method of integration, find the area of the region bounded by the lines: \u00a0\u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#15Find_the_area_of_the_region\" >15.Find the area of the region .<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#16Choose_the_correct_answer\" >16.Choose the correct answer:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#17Choose_the_correct_answer\" >17.Choose the correct answer:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#18Choose_the_correct_answer\" >18.Choose the correct answer:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#19Choose_the_correct_answer\" >19.Choose the correct answer:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#NCERT_Solutions_class_12_Maths_Miscellaneous-9\" >NCERT Solutions class 12 Maths Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/#CBSE_App_for_Class_12\" >CBSE App for Class 12<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Miscellaneous Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-application-of-integrals\/1292\/ncert-solutions\/5\/\">NCERT solutions for Applications of Integrals \u00a0<\/a>as PDF.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20Part-02%20.jpg\" alt=\"NCERT Solutions class 12 Maths Miscellaneous\" width=\"201\" height=\"258\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Applications_of_Integrals\"><\/span>NCERT Solutions class 12 Maths\u00a0Applications of Integrals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><strong>1. Find the area under the given curves and given lines:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image001.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/><\/strong><strong>axis.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image003.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/><\/strong><strong>axis.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong>Equation of the curve (parabola) is<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image004.png\" \/>\u00a0\u2026\u2026..(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 42\" style=\"height: 145px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image005.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Required area bounded by curve (i), vertical line <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image006.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image010.png\" \/>\u00a0sq. units<\/p>\n<p style=\"text-align: justify;\"><strong>\u00a0(ii)<\/strong>Equation of the curve<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image011.png\" \/>\u00a0\u2026..(i)<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 44\" style=\"height: 124px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image012.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\">It is clear that curve (i) passes through the origin because <img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image013.png\" \/>\u00a0from (i) <img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\">Table of values for curve <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image011.png\" \/>for <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image015.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image016.png\" \/>\u00a0(given)<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 40.5pt;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image017.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">1<\/p>\n<\/td>\n<td style=\"width: 1.0in;\">\n<p style=\"text-align: center;\">2<\/p>\n<\/td>\n<td style=\"width: 67.5pt;\">\n<p style=\"text-align: center;\">3<\/p>\n<\/td>\n<td style=\"width: 1.0in;\">\n<p style=\"text-align: center;\">4<\/p>\n<\/td>\n<td style=\"width: 67.5pt;\">\n<p style=\"text-align: center;\">5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 40.5pt;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image018.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">1<\/p>\n<\/td>\n<td style=\"width: 1.0in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 21px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image019.png\" \/><\/p>\n<\/td>\n<td style=\"width: 67.5pt;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 21px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image020.png\" \/><\/p>\n<\/td>\n<td style=\"width: 1.0in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image021.png\" \/><\/p>\n<\/td>\n<td style=\"width: 67.5pt;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 21px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image022.png\" \/><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Required shaded area between the curve <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image011.png\" \/>, vertical lines <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image023.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image024.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image026.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 44px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 624.8 sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Find_the_area_between_the_curves_and\"><\/span><strong>2. Find the area between the curves <\/strong><strong><img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image029.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image030.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of one curve (straight line) is <img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image029.png\" \/>\u00a0\u2026..(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 47\" style=\"height: 166px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equation of second curve (parabola) is <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image004.png\" \/>\u00a0\u2026..(ii)<\/p>\n<p style=\"text-align: justify;\">Solving eq. (i) and (ii), we get <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image032.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image015.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image033.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 21px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Points of intersection of line (i) and parabola (ii) are O (0, 0) and A (1, 1).<\/p>\n<p style=\"text-align: justify;\">Now Area of triangle OAM<\/p>\n<p style=\"text-align: justify;\">= Area bounded by line (i) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image036.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image037.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image039.png\" \/>\u00a0sq. units<\/p>\n<p style=\"text-align: justify;\">Also Area OBAM = Area bounded by parabola (ii) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image036.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image040.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image041.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image042.png\" \/>\u00a0sq. units<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Required area OBA between line (i) and parabola (ii)<\/p>\n<p style=\"text-align: justify;\">= Area of triangle OAM \u2013 Area of OBAM<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image043.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image044.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-2\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Find_the_area_of_the_region_lying_in_the_first_quadrant_and_bounded_by_and\"><\/span><strong>3. Find the area of the region lying in the first quadrant and bounded by <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image045.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image046.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the curve (parabola) is <img decoding=\"async\" style=\"height: 24px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 48\" style=\"height: 146px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image049.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image050.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image049.png\" \/><img decoding=\"async\" style=\"height: 45px; width: 54px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image051.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Here required shaded area of the region lying in first quadrant bounded by parabola (i), <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\">and the horizontal lines <img decoding=\"async\" style=\"height: 21px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image034.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image052.png\" \/>\u00a0is<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 51px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image053.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image054.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 109px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image058.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image059.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image060.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-3\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Sketch_the_graph_of_and_evaluate\"><\/span><strong>4. Sketch the graph of <\/strong><strong><img decoding=\"async\" style=\"height: 27px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image061.png\" \/><\/strong><strong>\u00a0and evaluate <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image062.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the given curve is <img decoding=\"async\" style=\"height: 27px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image061.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 50\" style=\"height: 184px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image063.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image064.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image061.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image065.png\" \/>\u00a00 for all real <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Graph of curve is only above the <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis i.e., in first and second quadrant only.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/><img decoding=\"async\" style=\"height: 27px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image061.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image066.png\" \/><\/p>\n<p style=\"text-align: justify;\">If <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image066.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image065.png\" \/>\u00a00<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image049.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image067.png\" \/>\u00a0\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">And<img decoding=\"async\" style=\"height: 27px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image061.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image068.png\" \/><\/p>\n<p style=\"text-align: justify;\">If <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image066.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image069.png\" \/>\u00a00<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image049.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image070.png\" \/>\u00a0 \u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Table of values for <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image071.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image067.png\" \/><\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image017.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image072.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image073.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image074.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image018.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">0<\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">1<\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">2<\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">3<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Table of values for <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image071.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image070.png\" \/><\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image017.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image072.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image075.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image076.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image077.png\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image018.png\" \/><\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">0<\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">1<\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">2<\/p>\n<\/td>\n<td style=\"width: .5in;\">\n<p style=\"text-align: center;\">3<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Now,<img decoding=\"async\" style=\"height: 49px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image078.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image079.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 49px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image081.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 49px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image082.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image083.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image084.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image085.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image086.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-4\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_Find_the_area_bounded_by_the_curve_between_and\"><\/span><strong>5. Find the area bounded by the curve <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image087.png\" \/><\/strong><strong>\u00a0between <\/strong><strong><img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image032.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 19px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image088.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the curve is <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image087.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image064.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image089.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image090.png\" \/>\u00a0i.e., graph is in first and second quadrant.<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 21px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image091.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image092.png\" \/>\u00a0i.e., graph is in third and fourth quadrant.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 51\" style=\"height: 151px; width: 237px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image093.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">If tangent is parallel to <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis, then <img decoding=\"async\" style=\"height: 41px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image094.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image049.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image095.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image049.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\">Table of values for curve <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image087.png\" \/>\u00a0between <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image032.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image097.png\" \/><\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image017.png\" \/><\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\">0<\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image098.png\" \/><\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image099.png\" \/><\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image100.png\" \/><\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 19px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image101.png\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image018.png\" \/><\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\">0<\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\">1<\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\">0<\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\"><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image074.png\" \/><\/p>\n<\/td>\n<td style=\"width: .7in;\">\n<p style=\"text-align: center;\">0<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Now Required shaded area = Area OAB + Area BCD<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image102.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image103.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 35px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image104.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 30px; width: 244px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image105.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 30px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image106.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 2 + 2 = 4 sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-5\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Find_the_area_enclosed_by_the_parabola_and_the_line\"><\/span><strong>6. Find the area enclosed by the parabola <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image107.png\" \/><\/strong><strong>\u00a0and the line <\/strong><strong><img decoding=\"async\" style=\"height: 17px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image108.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of parabola is <img decoding=\"async\" style=\"height: 24px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image107.png\" \/>\u00a0\u2026\u2026..(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 53\" style=\"height: 159px; width: 205px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image109.png\" \/><\/p>\n<p style=\"text-align: justify;\">The area enclosed between the parabola <img decoding=\"async\" style=\"height: 24px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image107.png\" \/>\u00a0and line <img decoding=\"async\" style=\"height: 17px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image110.png\" \/>\u00a0is represented by shaded area OADO.<\/p>\n<p style=\"text-align: justify;\">Here Points of intersection of curve (i) and line <img decoding=\"async\" style=\"height: 17px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image110.png\" \/>\u00a0are O (0, 0) and A<img decoding=\"async\" style=\"height: 45px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image111.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Now Area ODAM = Area of parabola and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 77px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image112.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 100px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image113.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 55px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image114.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 47px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image115.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image116.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Again Area of <img decoding=\"async\" style=\"height: 19px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image117.png\" \/>\u00a0= Area between line <img decoding=\"async\" style=\"height: 17px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image110.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 77px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image118.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 59px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image119.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image120.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image121.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 44px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image122.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Requires shaded area = Area ODAM \u2013 Area of <img decoding=\"async\" style=\"height: 19px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image117.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image123.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image122.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 47px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image124.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image125.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-6\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Find_the_area_enclosed_by_the_parabola_and_the_line\"><\/span><strong>7. Find the area enclosed by the parabola <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image126.png\" \/><\/strong><strong>\u00a0and the line <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image127.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the parabola is<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image126.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 54\" style=\"height: 209px; width: 197px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image128.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image049.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image129.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equation of the line is <img decoding=\"async\" style=\"height: 21px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image130.png\" \/>\u00a0\u2026\u2026(ii)<\/p>\n<p style=\"text-align: justify;\">In the graph, points of intersection are B (4, 12) and C<img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image131.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Now, Area ABCD = <img decoding=\"async\" style=\"height: 51px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image132.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image133.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image134.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 45 sq. units<\/p>\n<p style=\"text-align: justify;\">Again, Area CDO + Area OAB = <img decoding=\"async\" style=\"height: 51px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image135.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image136.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image137.png\" \/>\u00a0= 18 sq. units<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Required area = Area ABCD \u2013 (Area CDO + Area OAB)<\/p>\n<p style=\"text-align: justify;\">= 45 \u2013 18 = 27 sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-7\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_Find_the_area_of_the_smaller_region_bounded_by_the_ellipse_and_the_line\"><\/span><strong>8. Find the area of the smaller region bounded by the ellipse <\/strong><strong><img decoding=\"async\" style=\"height: 44px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image138.png\" \/><\/strong><strong>\u00a0and the line <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image139.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the ellipse is<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 56\" style=\"height: 146px; width: 206px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image140.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image138.png\" \/>\u00a0\u2026\u2026\u2026(i)<\/p>\n<p style=\"text-align: justify;\">Here intersection of ellipse (i) with <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis are<\/p>\n<p style=\"text-align: justify;\">A (3, 0) and A\u2019<img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image141.png\" \/>\u00a0and intersection of ellipse (i) with <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image142.png\" \/>\u00a0axis are B (0, 2) and B\u2019<img decoding=\"async\" style=\"height: 27px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image143.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Also, the points of intersections of ellipse (i) and line <img decoding=\"async\" style=\"height: 41px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image144.png\" \/>\u00a0are A (3, 0) and B (0, 2).<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Area OADB = Area between ellipse (i) (arc AB of it) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image145.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image146.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image147.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 253px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image148.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image149.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image150.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image100.png\" \/>\u00a0sq. units\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Again Area of triangle OAB = Area bounded by line AB and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image151.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 59px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image152.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image153.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image154.png\" \/>\u00a0sq. units \u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Now Required shaded area = Area OADB \u2013 Area OAB<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image155.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image156.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-8\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_Find_the_area_of_the_smaller_region_bounded_by_the_ellipse_and_the_line\"><\/span><strong>9. Find the area of the smaller region bounded by the ellipse <\/strong><strong><img decoding=\"async\" style=\"height: 44px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image157.png\" \/><\/strong><strong>\u00a0and the line <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image158.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of ellipse is <img decoding=\"async\" style=\"height: 44px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image157.png\" \/>\u00a0\u2026\u2026..(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 57\" style=\"height: 157px; width: 222px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image159.png\" \/><\/p>\n<p style=\"text-align: justify;\">Area between arc AB of the ellipse and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image160.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image161.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 184px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image162.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image163.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image164.png\" \/>\u00a0\u2026\u2026\u2026..(ii)<\/p>\n<p style=\"text-align: justify;\">Also Area between chord AB and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image165.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image166.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image167.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image168.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image169.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now Required area<\/p>\n<p style=\"text-align: justify;\">= Area between arc AB of the ellipse and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis \u2013 Area between chord AB and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image170.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>10.Find the area of the region enclosed by the parabola <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image171.png\" \/><\/strong><strong>\u00a0the line <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image172.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/><\/strong><strong>\u00a0axis.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of parabola is <img decoding=\"async\" style=\"height: 24px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image173.png\" \/>\u00a0\u2026\u2026\u2026\u2026(i)<\/p>\n<p style=\"text-align: justify;\">Equation of line is <img decoding=\"async\" style=\"height: 21px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image172.png\" \/>\u00a0\u2026\u2026\u2026\u2026(ii)<\/p>\n<p style=\"text-align: justify;\">Here the two points of intersections of parabola (i) and line (ii) are A<img decoding=\"async\" style=\"height: 27px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image174.png\" \/>\u00a0and B (2, 4).<\/p>\n<p style=\"text-align: justify;\">Area ALODBM = Area bounded by parabola (i) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image175.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image176.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image177.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image178.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image179.png\" \/>\u00a0= 3 sq. units<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 59\" style=\"height: 165px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image180.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">AlsoArea of trapezium ALMB =\u00a0Area bounded by line (ii) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image181.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image182.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image183.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image184.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image185.png\" \/>\u00a0sq. units<\/p>\n<p style=\"text-align: justify;\">Now Required area = Area of trapezium ALMB \u2013 Area ALODBM<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image186.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11Using_the_method_of_integration_find_the_area_enclosed_by_the_curve\"><\/span><strong>11.Using the method of integration, find the area enclosed by the curve <\/strong><strong><img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image187.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the curve (graph) is<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 60\" style=\"height: 175px; width: 185px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image188.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 27px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image189.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">The area bounded by the curve (i) is represented by the shaded region ABCD.<\/p>\n<p style=\"text-align: justify;\">The curve intersects the axes at points A (1, 0), B (0, 1), C<img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image190.png\" \/>\u00a0and D<img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image191.png\" \/><\/p>\n<p style=\"text-align: justify;\">It is observed clearly that given curve is symmetrical about <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis and <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image142.png\" \/>axis.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Area bounded by the curve<\/p>\n<p style=\"text-align: justify;\">= Area of square ABCD<\/p>\n<p style=\"text-align: justify;\">= 4 x <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image192.png\" \/>OAB<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image193.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image194.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image195.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image196.png\" \/>\u00a0= 2 sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12Find_the_area_bounded_by_the_curves\"><\/span><strong>12.Find the area bounded by the curves <\/strong><strong><img decoding=\"async\" style=\"height: 30px; width: 163px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image197.png\" \/><\/strong><strong>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>The area bounded by the curves <img decoding=\"async\" style=\"height: 30px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image198.png\" \/>\u00a0is represented by the shaded region.<\/p>\n<p style=\"text-align: justify;\">It is clearly observed that the required area is symmetrical about <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image142.png\" \/>axis.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Required area<\/p>\n<p style=\"text-align: justify;\">= Area between parabola <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image004.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis between limits <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image032.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image015.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 49px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image199.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image200.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 54px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image201.png\" \/>\u00a0\u2026\u2026\u2026..(i)<\/p>\n<p>And Area of ray <img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image029.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis,<\/p>\n<p><img decoding=\"async\" id=\"Picture 62\" style=\"height: 147px; width: 194px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image202.jpg\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 49px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image199.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image203.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image204.png\" \/>\u00a0\u2026\u2026\u2026..(ii)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0 Required shaded area in first quadrant<\/p>\n<p>= Area between ray <img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image029.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image205.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis \u2013\u00a0Area between parabola <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image004.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis in first quadrant<\/p>\n<p style=\"text-align: justify;\">= Area given by eq. (ii) \u2013 Area given by eq. (i) = <img decoding=\"async\" style=\"height: 41px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image206.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13Using_the_method_of_integration_find_the_area_of_the_triangle_whose_vertices_are_A_2_0_B_4_5_and_C_6_3\"><\/span><strong>13.Using the method of integration, find the area of the triangle whose vertices are A (2, 0), B (4, 5) and C (6, 3).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Vertices of the given triangle are A (2, 0), B (4, 5) and C (6, 3).<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 63\" style=\"height: 186px; width: 206px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image207.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equation of side AB is <img decoding=\"async\" style=\"height: 41px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image208.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image209.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equation of side BC is <img decoding=\"async\" style=\"height: 41px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image210.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image211.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equation of side AC is <img decoding=\"async\" style=\"height: 41px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image212.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image213.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now, Required shaded area = Area <img decoding=\"async\" style=\"height: 17px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image214.png\" \/>\u00a0+ Area of trapezium BLMC \u2013 Area <img decoding=\"async\" style=\"height: 19px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image215.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 294px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image216.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 59px; width: 273px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image217.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 407px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image218.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 215px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image219.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image220.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 5 + 8 \u2013 6 = 7 sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14Using_the_method_of_integration_find_the_area_of_the_region_bounded_by_the_lines_and\"><\/span><strong>14.Using the method of integration, find the area of the region bounded by the lines: <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image221.png\" \/><\/strong><strong>\u00a0<\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image222.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image223.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of one line <img decoding=\"async\" style=\"height: 24px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image224.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 21px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image225.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">Equation of second line <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image226.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 21px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image222.png\" \/><\/p>\n<p style=\"text-align: justify;\">And Equation of third line <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image227.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 21px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image223.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 64\" style=\"height: 215px; width: 264px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image228.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Here, vertices of triangle ABC are A (2, 0), B (4, 3) and C (1, 2).<\/p>\n<p style=\"text-align: justify;\">Now, Required area of triangle<\/p>\n<p style=\"text-align: justify;\">= Area of trapezium CLMB \u2013 Area <img decoding=\"async\" style=\"height: 19px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image229.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 11px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image230.png\" \/>\u00a0Area <img decoding=\"async\" style=\"height: 17px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image231.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 301px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image232.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 59px; width: 293px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image233.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 379px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image234.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image235.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image236.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image237.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15Find_the_area_of_the_region\"><\/span><strong>15.Find the area of the region <\/strong><strong><img decoding=\"async\" style=\"height: 30px; width: 228px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image238.png\" \/><\/strong><strong>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of parabola is <img decoding=\"async\" style=\"height: 24px; width: 54px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image239.png\" \/>\u00a0\u2026\u2026(i)<\/p>\n<p style=\"text-align: justify;\">And equation of circle is <img decoding=\"async\" style=\"height: 24px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image240.png\" \/>\u00a0\u2026\u2026(ii)<\/p>\n<p style=\"text-align: justify;\">Here, the two points of intersection of parabola (i) and circle (ii) are A<img decoding=\"async\" style=\"height: 45px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image241.png\" \/>\u00a0and B<img decoding=\"async\" style=\"height: 45px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image242.png\" \/><\/p>\n<p style=\"text-align: justify;\">Required shaded area OADBO (Area of the circle which is interior to the parabola)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 65\" style=\"height: 199px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image243.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">= 2 x Area OADO = 2 [Area OAC + Area CAD]\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 80px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image244.png\" \/><\/p>\n<p style=\"text-align: justify;\">=<img decoding=\"async\" style=\"height: 112px; width: 248px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image245.png\" \/><\/p>\n<p style=\"text-align: justify;\">=<img decoding=\"async\" style=\"height: 83px; width: 263px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image246.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image247.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image248.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16Choose_the_correct_answer\"><\/span><strong>16.Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Area bounded by the curve <img decoding=\"async\" style=\"height: 24px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image249.png\" \/>\u00a0the <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis and the ordinate <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image250.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image015.png\" \/>\u00a0is:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image251.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image252.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image253.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image254.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the curve is <img decoding=\"async\" style=\"height: 24px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image255.png\" \/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>Y<\/strong><\/p>\n<p style=\"text-align: justify;\">To find: Area OBN (<img decoding=\"async\" style=\"height: 24px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image255.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image256.png\" \/>) and Area OAM (<img decoding=\"async\" style=\"height: 24px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image255.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image257.png\" \/>)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 66\" style=\"height: 157px; width: 233px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image258.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image035.png\" \/>\u00a0Required area = Area OBN + Area OAM<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image259.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 59px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image260.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image261.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image262.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image254.png\" \/>\u00a0sq. units<\/p>\n<p style=\"text-align: justify;\">Therefore, option (D) is correct,<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"17Choose_the_correct_answer\"><\/span><strong>17.Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>The area bounded by the curve <img decoding=\"async\" style=\"height: 27px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image263.png\" \/>axis and the ordinates <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image264.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image015.png\" \/>\u00a0is given by:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) 0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image265.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image266.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image267.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the curve is<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 67\" style=\"height: 188px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image268.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 27px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image269.png\" \/>\u00a0if <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image205.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 27px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image270.png\" \/>\u00a0if <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image271.png\" \/>\u00a0\u2026\u2026\u2026..(ii)<\/p>\n<p style=\"text-align: justify;\">Required area = Area ONBO + Area OAMO<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image272.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 59px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image273.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image274.png\" \/>\u00a0sq. units<\/p>\n<p style=\"text-align: justify;\">Therefore, option (C) is correct.<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"18Choose_the_correct_answer\"><\/span><strong>18.Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>The area of the circle <img decoding=\"async\" style=\"height: 24px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image275.png\" \/>\u00a0exterior to the parabola <img decoding=\"async\" style=\"height: 24px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image276.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image277.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image278.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image279.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image280.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Equation of the circle is <img decoding=\"async\" style=\"height: 24px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image275.png\" \/>\u00a0\u2026..(i)<\/p>\n<p style=\"text-align: justify;\">This circle is symmetrical about <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image002.png\" \/>axis and <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image142.png\" \/>\u00a0axis.<\/p>\n<p style=\"text-align: justify;\">Here two points of intersection are B<img decoding=\"async\" style=\"height: 31px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image281.png\" \/>\u00a0and B\u2019<img decoding=\"async\" style=\"height: 31px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image282.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 68\" style=\"height: 175px; width: 186px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image283.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Required area = Area of circle \u2013 Area of circle interior to the parabola<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 21px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image284.png\" \/>\u00a0Area OBAB\u2019O<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image285.png\" \/>\u00a02 x Area OBACO<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image286.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image285.png\" \/>2[Area OBCO + Area BACB]\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 54px; width: 235px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image287.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 319px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image288.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 308px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image289.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image290.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 215px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image291.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image292.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image293.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image294.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image295.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image296.png\" \/><\/p>\n<p style=\"text-align: justify;\">=\u00a0 <img decoding=\"async\" style=\"height: 48px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image297.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image279.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"19Choose_the_correct_answer\"><\/span><strong>19.Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>The area bounded by the <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image142.png\" \/>axis, <img decoding=\"async\" style=\"height: 17px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image298.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image087.png\" \/>\u00a0when <img decoding=\"async\" style=\"height: 41px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image299.png\" \/>\u00a0is:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 31px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image300.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 23px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image301.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 23px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image302.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image303.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Here both graphs intersect at the point B<img decoding=\"async\" style=\"height: 48px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image304.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 69\" style=\"height: 198px; width: 233px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image305.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\">Required shaded area = Area OABC \u2013 Area OBC<\/p>\n<p style=\"text-align: justify;\">= Area OABC \u2013 (Area OBM + Area BCM)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 66px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image306.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 40px; width: 236px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image307.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 337px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image308.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image309.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image310.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image311.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 31px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/08%20Misc\/image312.png\" \/>\u00a0sq. units<\/p>\n<p style=\"text-align: justify;\">Therefore, option (B) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Miscellaneous-9\"><\/span>NCERT Solutions class 12 Maths Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Class_12\"><\/span>CBSE App for Class 12<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Miscellaneous Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths &#8230; <a title=\"NCERT Solutions class 12 Maths Miscellaneous\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-miscellaneous-5\/\" aria-label=\"More on NCERT Solutions class 12 Maths Miscellaneous\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4502","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Miscellaneous | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Miscellaneous in PDF format for free download. 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