{"id":4496,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/"},"modified":"2018-05-04T14:55:56","modified_gmt":"2018-05-04T09:25:56","slug":"ncert-solutions-class-12-maths-exercise-8-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 8.1"},"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-exercise-8-1\/#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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#2_Find_the_area_of_the_region_bounded_by_and_the_axis_in_the_first_quadrant\" >2. Find the area of the region bounded by \u00a0and the axis in the first quadrant.<\/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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-2\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#3_Find_the_area_of_the_region_bounded_by_and_the_axis_in_the_first_quadrant\" >3. Find the area of the region bounded by \u00a0and the \u00a0axis in the first quadrant.<\/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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-3\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#4_Find_the_area_of_the_region_bounded_by_the_ellipse\" >4. Find the area of the region bounded by the ellipse \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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-4\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#5_Find_the_area_of_the_region_bounded_by_the_ellipse\" >5. Find the area of the region bounded by the ellipse<\/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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-5\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#6_Find_the_area_of_the_region_in_the_first_quadrant_enclosed_by_axis_line_and_the_circle\" >6. Find the area of the region in the first quadrant enclosed by axis, line \u00a0and the circle \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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-6\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#7_Find_the_area_of_the_smaller_part_of_the_circle_cut_off_by_the_line\" >7. Find the area of the smaller part of the circle \u00a0cut off by 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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-7\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#8_The_area_between_and_is_divided_into_two_equal_parts_by_the_line_find_the_value_of\" >8. The area between \u00a0and \u00a0is divided into two equal parts by the line \u00a0find the value of \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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-8\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#9_Find_the_area_of_the_region_bounded_by_the_parabola_and\" >9. Find the area of the region bounded by the parabola \u00a0and \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-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-9\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#10_Find_the_area_bounded_by_the_curve_and_the_line\" >10. Find the area bounded by the curve \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-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-10\" >NCERT Solutions class 12 Maths Exercise 8.1<\/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-exercise-8-1\/#11_Find_the_area_of_the_region_bounded_by_the_curve_and_the_line\" >11. Find the area of the region bounded by the curve \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-22\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/#12_Choose_the_correct_answer\" >12. 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-23\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/#13_Choose_the_correct_answer\" >13. 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-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/#NCERT_Solutions_class_12_Maths_Exercise_81-11\" >NCERT Solutions class 12 Maths Exercise 8.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/#CBSE_App_for_Class_12\" >CBSE App for Class 12<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 8.1 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 Exercise 8.1\" width=\"192\" height=\"246\" \/><\/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><strong>1. Find the area of the region bounded by the curve <\/strong><img decoding=\"async\" style=\"height: 24px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image001.png\" \/><strong>\u00a0and the lines <\/strong><img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image002.png\" \/><strong>\u00a0and the <\/strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/><strong>\u00a0axis.<\/strong><\/p>\n<p><strong>Ans. <\/strong>Equation of the curve (rightward parabola) is <img decoding=\"async\" style=\"height: 24px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image004.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 4\" style=\"height: 140px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image005.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image007.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>Required area (shaded region)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image008.png\" \/>\u00a0[From eq. (i)]\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image009.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 109px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image011.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image012.png\" \/>\u00a0=\u00a0 <img decoding=\"async\" style=\"height: 45px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image013.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image014.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"2_Find_the_area_of_the_region_bounded_by_and_the_axis_in_the_first_quadrant\"><\/span><strong>2. Find the area of the region bounded by <\/strong><img decoding=\"async\" style=\"height: 24px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image015.png\" \/><strong>\u00a0and the <\/strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/><strong>axis in the first quadrant.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equation of the curve (rightward parabola) is <img decoding=\"async\" style=\"height: 24px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image016.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image017.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" id=\"Picture 6\" style=\"height: 137px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image018.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>Required area (shaded region) bounded by curve <img decoding=\"async\" style=\"height: 24px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image019.png\" \/>\u00a0(vertical lines <img decoding=\"async\" style=\"height: 21px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image020.png\" \/>) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis in first quadrant.<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image021.png\" \/>\u00a0[From eq. (i)]\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image022.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 109px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image023.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image024.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image025.png\" \/><\/p>\n<p>=\u00a0 <img decoding=\"async\" style=\"height: 35px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image026.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 32px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image027.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-2\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"3_Find_the_area_of_the_region_bounded_by_and_the_axis_in_the_first_quadrant\"><\/span><strong>3. Find the area of the region bounded by <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image028.png\" \/><\/strong><strong>\u00a0and the <\/strong><strong><img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/><\/strong><strong>\u00a0axis in the first quadrant.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equation of curve (parabola) is <img decoding=\"async\" style=\"height: 24px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image030.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image031.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0Required (shaded) area bounded by curve <img decoding=\"async\" style=\"height: 24px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image032.png\" \/>\u00a0(Horizontal lines <img decoding=\"async\" style=\"height: 21px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image033.png\" \/>) and <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/>axis in first quadrant.<\/p>\n<p><img decoding=\"async\" id=\"Picture 10\" style=\"height: 129px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image034.jpg\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 205px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image035.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 109px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image036.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image037.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image038.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-3\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"4_Find_the_area_of_the_region_bounded_by_the_ellipse\"><\/span><strong>4. Find the area of the region bounded by the ellipse <\/strong><strong><img decoding=\"async\" style=\"height: 44px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image039.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><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\/Ex8.1\/image040.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" id=\"Picture 11\" style=\"height: 146px; width: 198px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image041.jpg\" \/><\/p>\n<p>Here <img decoding=\"async\" style=\"height: 27px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image042.png\" \/><\/p>\n<p>From eq. (i),<img decoding=\"async\" style=\"height: 44px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image043.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image045.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image046.png\" \/>\u2026\u2026\u2026.(ii)<\/p>\n<p>for arc of ellipse in first quadrant.<\/p>\n<p>Ellipse (i) ia symmetrical about <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis,<\/p>\n<p>(<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image047.png\" \/>\u00a0On changing <img decoding=\"async\" style=\"height: 17px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image048.png\" \/>\u00a0in eq. (i), it remains unchanged)<\/p>\n<p>Ellipse (i) ia symmetrical about <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/>axis,<\/p>\n<p>(<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image047.png\" \/>\u00a0On changing <img decoding=\"async\" style=\"height: 15px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image049.png\" \/>\u00a0in eq. (i), it remains unchanged)<\/p>\n<p><strong>Intersections of ellipse (i) with <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image050.png\" \/>\u00a0<\/strong><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image051.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 44px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image052.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image053.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image054.png\" \/><\/p>\n<p>Therefore, Intersections of ellipse (i) with <strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/><\/strong>axis are (0, 4) and <img decoding=\"async\" style=\"height: 27px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image055.png\" \/>.<\/p>\n<p><strong>Intersections of ellipse (i) with <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/>axis <img decoding=\"async\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image056.png\" \/>\u00a0<\/strong><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image057.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 44px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image058.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image060.png\" \/><\/p>\n<p>Therefore, Intersections of ellipse (i) with <strong><img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/><\/strong>axis are (0, 3) and <img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image061.png\" \/>.<\/p>\n<p>Now Area of region bounded by ellipse (i) = Total shaded area<\/p>\n<p>= 4 x Area OAB of ellipse in first quadrant<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image062.png\" \/>\u00a0[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image047.png\" \/>\u00a0At end B of arc AB of ellipse; <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image057.png\" \/>\u00a0and at end A of arc AB ; <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image063.png\" \/>]\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image064.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image065.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image066.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 51px; width: 279px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image067.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 253px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image068.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image069.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image070.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-4\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"5_Find_the_area_of_the_region_bounded_by_the_ellipse\"><\/span><strong>5. Find the area of the region bounded by the ellipse <\/strong><strong><img decoding=\"async\" style=\"height: 44px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image071.png\" \/><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><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\/Ex8.1\/image072.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 12\" style=\"height: 142px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image073.jpg\" \/><\/p>\n<p>Here <img decoding=\"async\" style=\"height: 27px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image074.png\" \/><\/p>\n<p>From eq. (i),<img decoding=\"async\" style=\"height: 44px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image075.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image076.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image077.png\" \/>\u2026\u2026\u2026.(ii)<\/p>\n<p>for arc of ellipse in first quadrant.<\/p>\n<p>Ellipse (i) ia symmetrical about <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis,<\/p>\n<p>(<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image047.png\" \/>\u00a0On changing <img decoding=\"async\" style=\"height: 17px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image048.png\" \/>\u00a0in eq. (i), it remains unchanged)<\/p>\n<p>Ellipse (i) ia symmetrical about <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/>axis,<\/p>\n<p>(<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image047.png\" \/>\u00a0On changing <img decoding=\"async\" style=\"height: 15px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image049.png\" \/>\u00a0in eq. (i), it remains unchanged)<\/p>\n<p><strong>Intersections of ellipse (i) with <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image050.png\" \/>\u00a0<\/strong><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image051.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 44px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image078.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image079.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image080.png\" \/><\/p>\n<p>Therefore, Intersections of ellipse (i) with <strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/><\/strong>axis are (0, 2) and <img decoding=\"async\" style=\"height: 27px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image081.png\" \/>.<\/p>\n<p><strong>Intersections of ellipse (i) with <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/>axis <img decoding=\"async\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image056.png\" \/>\u00a0<\/strong><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image057.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 44px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image058.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image060.png\" \/><\/p>\n<p>Therefore, Intersections of ellipse (i) with <strong><img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image029.png\" \/><\/strong>axis are (0, 3) and <img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image061.png\" \/>.<\/p>\n<p>Now Area of region bounded by ellipse (i) = Total shaded area<\/p>\n<p>= 4 x Area OAB of ellipse in first quadrant<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image082.png\" \/>\u00a0[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image047.png\" \/>\u00a0At end B of arc AB of ellipse; <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image057.png\" \/>\u00a0and at end A of arc AB ; <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image083.png\" \/>]\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image084.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image085.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image086.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 51px; width: 279px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image067.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 243px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image087.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image088.png\" \/>\u00a0\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-5\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"6_Find_the_area_of_the_region_in_the_first_quadrant_enclosed_by_axis_line_and_the_circle\"><\/span><strong>6. Find the area of the region in the first quadrant enclosed by <\/strong><strong><img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/><\/strong><strong>axis, line <\/strong><strong><img decoding=\"async\" style=\"height: 25px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image089.png\" \/><\/strong><strong>\u00a0and the circle <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image090.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong><strong>Step I<\/strong>. To draw the graphs and shade the region whose area we are to find.<\/p>\n<p><img decoding=\"async\" id=\"Picture 17\" style=\"height: 138px; width: 158px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image091.jpg\" \/><\/p>\n<p>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\/Ex8.1\/image092.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p>We know that eq. (i) represents a circle whose centre is (0, 0) and radius is 2.<\/p>\n<p>Equation of the given line is <img decoding=\"async\" style=\"height: 25px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image089.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 44px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image093.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p>We know that eq. (ii) being of the form <img decoding=\"async\" style=\"height: 17px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image094.png\" \/>\u00a0where <img decoding=\"async\" style=\"height: 44px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image095.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image096.png\" \/>\u00a0represents a straight line passing through the origin and making angle of <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image097.png\" \/>\u00a0with <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis.<\/p>\n<p><strong>Step II<\/strong>. To find values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image098.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image099.png\" \/>\u00a0Putting <img decoding=\"async\" style=\"height: 44px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image100.png\" \/>\u00a0from eq. (ii) in eq. (i),<\/p>\n<p><img decoding=\"async\" style=\"height: 44px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image101.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image102.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image103.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image104.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image105.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image105.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 44px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image100.png\" \/>,<img decoding=\"async\" style=\"height: 21px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image106.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image107.png\" \/><\/p>\n<p>Therefore, the two points of intersections of circle (i) and line (ii) are A<img decoding=\"async\" style=\"height: 32px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image108.png\" \/>\u00a0and D<img decoding=\"async\" style=\"height: 32px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image109.png\" \/>.<\/p>\n<p><strong>Step III<\/strong>. Now shaded area OAM between segment OA of line (ii) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 56px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image110.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image111.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 56px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image112.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 55px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image113.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image114.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 44px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image115.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image116.png\" \/>\u00a0sq. units\u2026\u2026\u2026.(iii)<\/p>\n<p><strong>Step IV<\/strong>. Now shaded area AMB between are AB of circle and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis.<\/p>\n<p>= = <img decoding=\"async\" style=\"height: 56px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image117.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image118.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 56px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image119.png\" \/>\u00a0From eq. (ii),<\/p>\n<p>= <img decoding=\"async\" style=\"height: 55px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image120.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 308px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image121.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image122.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image123.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image124.png\" \/>\u00a0\u00a0sq. units\u2026\u2026\u2026.(iv)<\/p>\n<p><strong>Step V<\/strong>. Required shaded area OAB = Area of OAM + Area of AMB<\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image125.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-6\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"7_Find_the_area_of_the_smaller_part_of_the_circle_cut_off_by_the_line\"><\/span><strong>7. Find the area of the smaller part of the circle <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image126.png\" \/><\/strong><strong>\u00a0cut off by the line <\/strong><strong><img decoding=\"async\" style=\"height: 44px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image127.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><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\/Ex8.1\/image126.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" id=\"Picture 18\" style=\"height: 148px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image128.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 24px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image129.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 28px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image130.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p>Here Area of smaller part of the circle <img decoding=\"async\" style=\"height: 24px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image126.png\" \/>\u00a0cut off by the line <img decoding=\"async\" style=\"height: 44px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image131.png\" \/>\u00a0= Area of ABMC = 2 x Area of ABM<\/p>\n<p>= <img decoding=\"async\" style=\"height: 77px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image132.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 77px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image133.png\" \/>[From eq. (ii)]\n<p>= <img decoding=\"async\" style=\"height: 63px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image134.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 93px; width: 345px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image135.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 56px; width: 253px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image136.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image137.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image138.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image139.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image140.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 47px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image141.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-7\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"8_The_area_between_and_is_divided_into_two_equal_parts_by_the_line_find_the_value_of\"><\/span><strong>8. The area between <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image142.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image063.png\" \/><\/strong><strong>\u00a0is divided into two equal parts by the line <\/strong><strong><img decoding=\"async\" style=\"height: 17px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image143.png\" \/><\/strong><strong>\u00a0find the value of <\/strong><strong><img decoding=\"async\" style=\"height: 15px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image144.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equation of the curve (parabola) is <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image142.png\" \/>\u00a0\u2026\u2026(i)<\/p>\n<p><img decoding=\"async\" id=\"Picture 20\" style=\"height: 173px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image145.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 25px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image007.png\" \/><\/p>\n<p>Now area bounded by parabola (i) and vertical line <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image063.png\" \/>\u00a0is divided into two equal parts by the vertical line <img decoding=\"async\" style=\"height: 15px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image146.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0Area OAMB = Area AMBDNC<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 51px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image147.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 51px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image148.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image149.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 93px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image150.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 93px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image151.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0\u00a0\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 51px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image152.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image153.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 32px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image154.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image155.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 32px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image156.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 32px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image157.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-8\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"9_Find_the_area_of_the_region_bounded_by_the_parabola_and\"><\/span><strong>9. Find the area of the region bounded by the parabola <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image158.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 27px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image159.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>The required area is the area included between the parabola <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image158.png\" \/>\u00a0and the modulus function <img decoding=\"async\" style=\"height: 48px; width: 163px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image160.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 21\" style=\"height: 131px; width: 174px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image161.jpg\" \/><\/p>\n<p>To find: Area between the parabola <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image158.png\" \/>\u00a0and the ray <img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image162.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image163.png\" \/><\/p>\n<p>Here, Limits of integration <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image162.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image164.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image165.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image166.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image167.png\" \/><\/p>\n<p>Now, for <img decoding=\"async\" style=\"height: 27px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image168.png\" \/>\u00a0, table of values,<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image162.png\" \/>\u00a0if <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image163.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 17px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image169.png\" \/>\u00a0if <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image170.png\" \/><\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image098.png\" \/><\/td>\n<td style=\"width: .4in;\">0<\/td>\n<td style=\"width: .4in;\">1<\/td>\n<td style=\"width: .4in;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image171.png\" \/><\/td>\n<td style=\"width: .4in;\">0<\/td>\n<td style=\"width: .4in;\">1<\/td>\n<td style=\"width: .4in;\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .4in;\">\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image098.png\" \/><\/td>\n<td style=\"width: .4in;\">0<\/td>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image172.png\" \/><\/td>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 17px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image173.png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image171.png\" \/><\/td>\n<td style=\"width: .4in;\">0<\/td>\n<td style=\"width: .4in;\">1<\/td>\n<td style=\"width: .4in;\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Now, Area between parabola <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image158.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis between limits <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image057.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image174.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 49px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image175.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image176.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image177.png\" \/>\u00a0\u2026\u2026\u2026..(i)<\/p>\n<p>And Area of ray <img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image162.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis,<\/p>\n<p>= <img decoding=\"async\" style=\"height: 49px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image175.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image178.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image179.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\/Ex8.1\/image006.png\" \/>\u00a0 Required shaded area in first quadrant = Area between ray <img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image162.png\" \/>\u00a0for <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image163.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis \u2013<\/p>\n<p>Area between parabola <img decoding=\"async\" style=\"height: 24px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image158.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis in first quadrant<\/p>\n<p>= Area given by eq. (ii) \u2013 Area given by eq. (i) = <img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image180.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-9\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"10_Find_the_area_bounded_by_the_curve_and_the_line\"><\/span><strong>10. Find the area bounded by the curve <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image181.png\" \/><\/strong><strong>\u00a0and the line <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image182.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong><strong>Step I. <\/strong>Graphs and region of<\/p>\n<p>Integration<\/p>\n<p><img decoding=\"async\" id=\"Picture 23\" style=\"height: 137px; width: 215px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image183.jpg\" \/><\/p>\n<p>Equation of the given curve is<\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image184.png\" \/>\u00a0\u2026\u2026..(i)<\/p>\n<p>Equation of the given line is<\/p>\n<p><img decoding=\"async\" style=\"height: 21px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image185.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image186.png\" \/><\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image098.png\" \/><\/td>\n<td style=\"width: .4in;\">0<\/td>\n<td style=\"width: .4in;\">1<\/td>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 17px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image173.png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image171.png\" \/><\/td>\n<td style=\"width: .4in;\">0<\/td>\n<td style=\"width: .4in;\"><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image187.png\" \/><\/td>\n<td style=\"width: .4in;\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Step II<\/strong>. Putting <img decoding=\"async\" style=\"height: 44px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image188.png\" \/>\u00a0from eq. (i) in eq. (ii),<\/p>\n<p><img decoding=\"async\" style=\"height: 44px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image189.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image190.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image191.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image192.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image193.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 27px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image194.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 27px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image195.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image083.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image196.png\" \/><\/p>\n<p>For <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image083.png\" \/>,from eq. (i),<img decoding=\"async\" style=\"height: 44px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image197.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0(2, 1)<\/p>\n<p>For <img decoding=\"async\" style=\"height: 21px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image198.png\" \/>\u00a0from eq. (i),<img decoding=\"async\" style=\"height: 44px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image199.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/><img decoding=\"async\" style=\"height: 45px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image200.png\" \/><\/p>\n<p>Therefore, the two points of intersection of parabola (i) and line (ii) are C<img decoding=\"async\" style=\"height: 45px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image200.png\" \/>\u00a0and D (2, 1).<\/p>\n<p><strong>Step III<\/strong>. Area CMOEDN between parabola (i) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis = <img decoding=\"async\" style=\"height: 51px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image201.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image202.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 67px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image203.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image204.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image205.png\" \/>\u00a0sq. units\u2026\u2026..(iii)<\/p>\n<p><strong>Step IV<\/strong>. Area of trapezium CMND between line (ii) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image003.png\" \/>axis = <img decoding=\"async\" style=\"height: 51px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image201.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image206.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image207.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 59px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image208.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 48px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image209.png\" \/>\u00a0=\u00a0 <img decoding=\"async\" style=\"height: 48px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image210.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image211.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image212.png\" \/>\u00a0sq. units\u2026\u2026\u2026.(iv)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image006.png\" \/>\u00a0Required shaded area = Area given by eq. (iv) \u2013 Area given by eq. (iii)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image213.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-10\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"11_Find_the_area_of_the_region_bounded_by_the_curve_and_the_line\"><\/span><strong>11. Find the area of the region bounded by the curve <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image214.png\" \/><\/strong><strong>\u00a0and the line <\/strong><strong><img decoding=\"async\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image215.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equation of the (parabola) curve is<\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image214.png\" \/>\u00a0\u2026\u2026\u2026(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 35px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image216.png\" \/>\u00a0\u2026\u2026\u2026(ii)<\/p>\n<p>Here required shaded area OAMB = 2 x Area OAM<\/p>\n<p><img decoding=\"async\" id=\"Picture 24\" style=\"height: 138px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image217.jpg\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image218.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image219.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 109px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image220.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image221.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image222.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 24px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image223.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3><span class=\"ez-toc-section\" id=\"12_Choose_the_correct_answer\"><\/span><strong>12. Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Area lying in the first quadrant and bounded by the circle <img decoding=\"async\" style=\"height: 24px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image224.png\" \/>\u00a0and the lines <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image057.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image083.png\" \/>\u00a0is<\/strong><\/p>\n<p><strong>(A) <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image225.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image226.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image227.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image228.png\" \/>\u00a0<\/strong><\/p>\n<p><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\/Ex8.1\/image092.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 28px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image229.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p><img decoding=\"async\" id=\"Picture 26\" style=\"height: 133px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image230.jpg\" \/><\/p>\n<p>Required area = <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image231.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image232.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 59px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image233.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image234.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image235.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image225.png\" \/>\u00a0sq. units<\/p>\n<p>Therefore, option (A) is correct.<\/p>\n<hr \/>\n<h3><span class=\"ez-toc-section\" id=\"13_Choose_the_correct_answer\"><\/span><strong>13. Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Area of the region bounded by the curve <img decoding=\"async\" style=\"height: 24px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image236.png\" \/>axis and the line <img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image237.png\" \/>\u00a0is:<\/strong><\/p>\n<p><strong>(A) 2<\/strong><\/p>\n<p><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image238.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image239.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image240.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong>Equation of the curve (parabola) is <img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image214.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 27\" style=\"height: 131px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image241.jpg\" \/><\/p>\n<p>Required area = Area OAM = <img decoding=\"async\" style=\"height: 51px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image242.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image243.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 59px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image244.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.1\/image245.png\" \/>\u00a0sq. units<\/p>\n<p>Therefore, option (B) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_81-11\"><\/span>NCERT Solutions class 12 Maths Exercise 8.1<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 Exercise 8.1 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 &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 8.1\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-1\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 8.1\">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-4496","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 Exercise 8.1 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 8.1 in PDF format for free download. 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