{"id":4482,"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-3-2\/"},"modified":"2018-05-08T09:55:53","modified_gmt":"2018-05-08T04:25:53","slug":"ncert-solutions-class-12-maths-exercise-3-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-2\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 3.2"},"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-3-2\/#NCERT_Solutions_class_12_Maths_Matrices\" >NCERT Solutions class 12 Maths Matrices\u00a0<\/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-3-2\/#5_If_A_and_B_then_compute_3A_%E2%80%93_5B\" >5. If A = \u00a0and B = \u00a0then compute 3A \u2013 5B.<\/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-3-2\/#7_Find_X_and_Y_if\" >7. Find X and Y, if:<\/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-3-2\/#8_Fin_X_if_Y_and_2X_Y\" >8. Fin X if Y = \u00a0and 2X + Y = \u00a0<\/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-3-2\/#9_Find_and_if\" >9. Find \u00a0and \u00a0if \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-2\/#10_Solve_the_equation_for_and_if\" >10. Solve the equation for \u00a0and \u00a0if \u00a0<\/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-3-2\/#11_If_find_the_values_of_and\" >11. If \u00a0find the values of \u00a0and \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-3-2\/#12_Given_find_the_values_of_and\" >12. Given: \u00a0find the values of \u00a0and<\/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-3-2\/#13_If_show_that\" >13. If \u00a0show that \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-2\/#14_Show_that\" >14. Show that:<\/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-3-2\/#15_Find_A2_%E2%80%93_5A_6I_if_A\" >15. Find A2 \u2013 5A + 6I if A = .<\/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-3-2\/#16_If_A_prove_that_A3_%E2%80%93_6A2_7A_2I_0\" >16. If A = \u00a0prove that A3 \u2013 6A2 + 7A + 2I = 0.<\/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-3-2\/#17_If_A_and_I_find_so_that\" >17. If A = \u00a0and I = \u00a0find \u00a0so that \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-3-2\/#NCERT_Solutions_class_12_Maths_Exercise_32\" >NCERT Solutions class 12 Maths Exercise 3.2<\/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-3-2\/#18_If_A_and_I_is_the_identity_matrix_of_order_2_show_that\" >18. If A = \u00a0and I is the identity matrix of order 2, show that\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-3-2\/#19_A_trust_fund_has_30000_that_must_be_invested_in_two_different_types_of_bond_The_first_bond_pays_5_interest_per_year_and_the_second_bond_pays_7_interest_per_year_Using_matrix_multiplication_determine_how_to_divide_30000_in_two_types_of_bonds_if_the_trust_fund_must_obtain_an_annual_interest_of_a_1800_b_2000\" >19. A trust fund has ` 30,000 that must be invested in two different types of bond. The first bond pays 5% interest per year and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide ` 30,000 in two types of bonds, if the trust fund must obtain an annual interest of (a) ` 1800, (b) ` 2000.<\/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-3-2\/#NCERT_Solutions_class_12_Maths_Exercise_32-2\" >NCERT Solutions class 12 Maths Exercise 3.2<\/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-3-2\/#20_The_bookshop_of_a_particular_school_has_10_dozen_chemistry_books_8_dozen_physics_books_10_dozen_economics_books_Their_selling_prices_are_80_60_and_40_each_respectively_Find_the_total_amount_the_bookshop_will_receive_from_selling_all_the_books_using_matrix_algebra\" >20. The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are ` 80, ` 60 and ` 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.<\/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-3-2\/#NCERT_Solutions_class_12_Maths_Exercise_32-3\" >NCERT Solutions class 12 Maths Exercise 3.2<\/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-3-2\/#21_The_restriction_on_and_so_that_PY_WY_will_be_define_are\" >21. The restriction on \u00a0and \u00a0so that PY + WY will be define are:<\/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-3-2\/#NCERT_Solutions_class_12_Maths_Exercise_32-4\" >NCERT Solutions class 12 Maths Exercise 3.2<\/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-3-2\/#22_If_then_order_of_matrix_7X_%E2%80%93_5Z_is\" >22. If \u00a0then order of matrix 7X \u2013 5Z is:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-2\/#NCERT_Solutions_class_12_Maths_Exercise_32-5\" >NCERT Solutions class 12 Maths Exercise 3.2<\/a><\/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-3-2\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 3.2 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-matrices\/1287\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Matrices\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%20pic.jpg\" alt=\"NCERT Solutions class 12 Maths Exercise 3.2\" width=\"187\" height=\"243\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Matrices\"><\/span>NCERT Solutions class 12 Maths Matrices<strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><strong>1. Let A = <img decoding=\"async\" style=\"height: 49px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image001.png\" \/>\u00a0B = <img decoding=\"async\" style=\"height: 49px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image002.png\" \/>\u00a0C = <img decoding=\"async\" style=\"height: 49px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image003.png\" \/>. Find each of the following:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) A + B<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) A \u2013 B<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) 3A \u2013 C<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) AB<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) BA<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> A + B = <img decoding=\"async\" style=\"height: 49px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image004.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> A \u2013 B = <img decoding=\"async\" style=\"height: 49px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image006.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> 3A \u2013 C = <img decoding=\"async\" style=\"height: 49px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image008.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 288px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> AB = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 264px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image011.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> BA = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image012.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 273px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image013.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>2. Compute the following:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 49px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image014.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 53px; width: 248px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image015.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 75px; width: 182px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image016.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <img decoding=\"async\" style=\"height: 53px; width: 243px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image017.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong><img decoding=\"async\" style=\"height: 49px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image014.png\" \/>\u00a0\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image018.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 53px; width: 248px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 60px; width: 358px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 75px; width: 182px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image016.png\" \/>\u00a0\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 276px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image020.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 53px; width: 243px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image017.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 279px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image021.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>3. Compute the indicated products:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 49px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image022.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 75px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image023.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 49px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image024.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <img decoding=\"async\" style=\"height: 75px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image025.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) <img decoding=\"async\" style=\"height: 75px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image026.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vi) <img decoding=\"async\" style=\"height: 75px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image027.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> <img decoding=\"async\" style=\"height: 49px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image022.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 372px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 75px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image023.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 83px; width: 224px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 49px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image024.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 385px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 75px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 83px; width: 412px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 = <img decoding=\"async\" style=\"height: 75px; width: 394px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> <img decoding=\"async\" style=\"height: 75px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 83px; width: 384px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image033.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(vi)<\/strong> <img decoding=\"async\" style=\"height: 75px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 232px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image034.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>4. If A = <img decoding=\"async\" style=\"height: 75px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image035.png\" \/>\u00a0B = <img decoding=\"async\" style=\"height: 75px; width: 86px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image036.png\" \/>\u00a0and C = <img decoding=\"async\" style=\"height: 75px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image037.png\" \/>\u00a0then compute (A + B) and (B \u2013 C). Also, verify that A + (B \u2013 C) = (A + B) \u2013 C.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>A + B = <img decoding=\"async\" style=\"height: 75px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image038.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image039.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\">B \u2013 C = <img decoding=\"async\" style=\"height: 75px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image041.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image042.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now, A + (B \u2013 C) = (A + B) \u2013 C<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 75px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image045.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 75px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image047.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 75px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image049.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0L.H.S. = R.H.S.\u00a0\u00a0Proved.<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_If_A_and_B_then_compute_3A_%E2%80%93_5B\"><\/span><strong>5. If A = <img decoding=\"async\" style=\"height: 101px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image050.png\" \/>\u00a0and B = <img decoding=\"async\" style=\"height: 101px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image051.png\" \/>\u00a0then compute 3A \u2013 5B.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>3A \u2013 5B = <img decoding=\"async\" style=\"height: 101px; width: 275px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 228px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image054.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>6. Simplify: <img decoding=\"async\" style=\"height: 49px; width: 300px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image055.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 49px; width: 300px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 53px; width: 377px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image057.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Find_X_and_Y_if\"><\/span><strong>7. Find X and Y, if:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(i) X + Y = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image058.png\" \/>\u00a0and X \u2013 Y = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image059.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) 2X + 3Y = <img decoding=\"async\" style=\"height: 49px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image060.png\" \/>\u00a0and 3X + 2Y = <img decoding=\"async\" style=\"height: 49px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image061.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Given: X + Y = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image058.png\" \/>\u00a0\u00a0\u2026..(i)<\/p>\n<p style=\"text-align: justify;\">and X \u2013 Y = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image059.png\" \/>\u00a0\u00a0\u2026..(ii)<\/p>\n<p style=\"text-align: justify;\">Adding eq. (i) and (ii), we get<\/p>\n<p style=\"text-align: justify;\">\u00a0 2X = <img decoding=\"async\" style=\"height: 49px; width: 273px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image062.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 X = <img decoding=\"async\" style=\"height: 49px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\">Subtracting eq. (i) and (ii), we get<\/p>\n<p style=\"text-align: justify;\">\u00a0 2Y = <img decoding=\"async\" style=\"height: 49px; width: 263px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image064.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 Y = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Given: 2X + 3Y = <img decoding=\"async\" style=\"height: 49px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image060.png\" \/>\u00a0\u00a0\u2026..(i)<\/p>\n<p style=\"text-align: justify;\">\u00a0and 3X + 2Y = <img decoding=\"async\" style=\"height: 49px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image066.png\" \/>\u00a0\u00a0\u2026..(ii)<\/p>\n<p style=\"text-align: justify;\">Multiplying eq. (i) by 2, 4X + 6Y = <img decoding=\"async\" style=\"height: 49px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image067.png\" \/>\u00a0\u00a0\u00a0\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Multiplying eq. (ii) by 3, 9X + 6Y = <img decoding=\"async\" style=\"height: 49px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image068.png\" \/>\u00a0\u00a0\u00a0\u2026\u2026\u2026(iv)<\/p>\n<p style=\"text-align: justify;\">Eq. (iv) \u2013 Eq. (iii) = 5X = <img decoding=\"async\" style=\"height: 49px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image069.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image070.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0X = <img decoding=\"async\" style=\"height: 49px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image071.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now, From eq. (i),\u00a0 3Y = <img decoding=\"async\" style=\"height: 49px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image072.png\" \/>\u00a02X = <img decoding=\"async\" style=\"height: 49px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image073.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 3Y = <img decoding=\"async\" style=\"height: 49px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image074.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image075.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 Y = <img decoding=\"async\" style=\"height: 49px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image076.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_Fin_X_if_Y_and_2X_Y\"><\/span><strong>8. Fin X if Y = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image077.png\" \/>\u00a0and 2X + Y = <img decoding=\"async\" style=\"height: 49px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image078.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>2X + Y = <img decoding=\"async\" style=\"height: 49px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image079.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a02X = <img decoding=\"async\" style=\"height: 49px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image079.png\" \/>\u00a0\u2013 Y<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a02X = <img decoding=\"async\" style=\"height: 49px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a02X = <img decoding=\"async\" style=\"height: 49px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image081.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0X = <img decoding=\"async\" style=\"height: 49px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image082.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image083.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_Find_and_if\"><\/span><strong>9. Find <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image084.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image085.png\" \/>\u00a0if <img decoding=\"async\" style=\"height: 49px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image086.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 49px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image087.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image088.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image089.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equating corresponding entries, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image090.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image091.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image092.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image093.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image094.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image095.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image094.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image096.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_Solve_the_equation_for_and_if\"><\/span><strong>10. Solve the equation for <img decoding=\"async\" style=\"height: 17px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image097.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 9px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image098.png\" \/>\u00a0if <img decoding=\"async\" style=\"height: 49px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image099.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 49px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image100.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image101.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image102.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equating corresponding entries, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image103.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image104.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image105.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 19px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image106.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image107.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image108.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image109.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 21px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image110.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image111.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 19px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image112.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image113.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image114.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image115.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image096.png\" \/>, <img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image111.png\" \/>, <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image109.png\" \/>, <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image115.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_If_find_the_values_of_and\"><\/span><strong>11. If <img decoding=\"async\" style=\"height: 49px; width: 142px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image117.png\" \/>\u00a0find the values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image084.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image118.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 49px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image119.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image120.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image121.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equating corresponding entries, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image122.png\" \/>\u00a0\u2026\u2026\u2026.(i) and <img decoding=\"async\" style=\"height: 21px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image123.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Adding eq. (i) and (ii), we have <img decoding=\"async\" style=\"height: 19px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image124.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image096.png\" \/>\u00a0in eq. (ii),\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image125.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image126.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_Given_find_the_values_of_and\"><\/span><strong>12. Given: <img decoding=\"async\" style=\"height: 49px; width: 258px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image127.png\" \/>\u00a0find the values of <img decoding=\"async\" style=\"height: 17px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image097.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image128.png\" \/><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 49px; width: 253px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image129.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 236px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image130.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equating corresponding entries, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image131.png\" \/>\u00a0\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image132.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image133.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 21px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image134.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image135.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image136.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image137.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 19px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image138.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image139.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 19px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image140.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image141.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting <img decoding=\"async\" style=\"height: 19px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image141.png\" \/>\u00a0in eq. (i),\u00a0\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image142.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 17px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image143.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 17px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image144.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image133.png\" \/>, <img decoding=\"async\" style=\"height: 21px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image137.png\" \/>, <img decoding=\"async\" style=\"height: 17px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image144.png\" \/>, <img decoding=\"async\" style=\"height: 19px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image141.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_If_show_that\"><\/span><strong>13. If <img decoding=\"async\" style=\"height: 75px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image145.png\" \/>\u00a0show that <img decoding=\"async\" style=\"height: 27px; width: 146px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image146.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 75px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image147.png\" \/>\u00a0\u00a0\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Changing <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image084.png\" \/>\u00a0to <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image148.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 75px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image149.png\" \/><\/p>\n<p style=\"text-align: justify;\">L.H.S. = <img decoding=\"async\" style=\"height: 75px; width: 268px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image150.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 440px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image151.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 83px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image152.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image153.png\" \/><\/p>\n<p style=\"text-align: justify;\">= R.H.S. [changing <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image084.png\" \/>\u00a0to <img decoding=\"async\" style=\"height: 27px; width: 50px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image154.png\" \/>\u00a0in eq. (i)]\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_Show_that\"><\/span><strong>14. Show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 49px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image155.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 75px; width: 324px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image156.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> L.H.S. = <img decoding=\"async\" style=\"height: 49px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image157.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image158.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image159.png\" \/><\/p>\n<p style=\"text-align: justify;\">R.H.S. = <img decoding=\"async\" style=\"height: 49px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image160.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 185px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image161.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image162.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 L.H.S. <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image163.png\" \/>\u00a0R.H.S.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> L.H.S. = <img decoding=\"async\" style=\"height: 75px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image164.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 83px; width: 395px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image165.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image166.png\" \/><\/p>\n<p style=\"text-align: justify;\">R.H.S. = <img decoding=\"async\" style=\"height: 75px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image167.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 83px; width: 416px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image168.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image169.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 L.H.S. <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image163.png\" \/>\u00a0R.H.S.<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_Find_A2_%E2%80%93_5A_6I_if_A\"><\/span><strong>15. Find A<sup>2<\/sup> \u2013 5A + 6I if A = <img decoding=\"async\" style=\"height: 75px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image170.png\" \/>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>A<sup>2<\/sup> \u2013 5A + 6I = <img decoding=\"async\" style=\"height: 75px; width: 351px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image171.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 391px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image172.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 283px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image173.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 242px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image174.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image175.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_If_A_prove_that_A3_%E2%80%93_6A2_7A_2I_0\"><\/span><strong>16. If A = <img decoding=\"async\" style=\"height: 75px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image176.png\" \/>\u00a0prove that A<sup>3<\/sup> \u2013 6A<sup>2<\/sup> + 7A + 2I = 0.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = A<sup>3<\/sup> \u2013 6A<sup>2<\/sup> + 7A + 2I<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 517px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image177.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 652px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image178.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 484px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image179.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 281px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image180.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 267px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image181.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 213px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image182.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 232px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image183.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image184.png\" \/>\u00a0= 0 (Zero matrix)<\/p>\n<p style=\"text-align: justify;\">= R.H.S.\u00a0\u00a0\u00a0\u00a0\u00a0 Proved.<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"17_If_A_and_I_find_so_that\"><\/span><strong>17. If A = <img decoding=\"async\" style=\"height: 49px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image185.png\" \/>\u00a0and I = <img decoding=\"async\" style=\"height: 49px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image186.png\" \/>\u00a0find <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image187.png\" \/>\u00a0so that <img decoding=\"async\" style=\"height: 21px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image188.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: \u00a0A = <img decoding=\"async\" style=\"height: 49px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image185.png\" \/>\u00a0and I = <img decoding=\"async\" style=\"height: 49px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 86px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image189.png\" \/>\u00a0\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 49px; width: 279px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image190.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 268px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image191.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 197px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image192.png\" \/><\/p>\n<p style=\"text-align: justify;\">Equating corresponding entries, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 19px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image193.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image194.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image195.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image196.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image195.png\" \/>\u00a0\u00a0\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image197.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image198.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image195.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image195.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_32\"><\/span>NCERT Solutions class 12 Maths Exercise 3.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"18_If_A_and_I_is_the_identity_matrix_of_order_2_show_that\"><\/span><strong>18. If A = <img decoding=\"async\" style=\"height: 88px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image199.png\" \/>\u00a0and I is the identity matrix of order 2, show that<img decoding=\"async\" style=\"height: 49px; width: 220px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image200.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = I + A = <img decoding=\"async\" style=\"height: 88px; width: 347px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image201.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now, I \u2013 A = <img decoding=\"async\" style=\"height: 88px; width: 333px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image202.png\" \/><\/p>\n<p style=\"text-align: justify;\">R.H.S. = <img decoding=\"async\" style=\"height: 49px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image203.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 88px; width: 244px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image204.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 88px; width: 308px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image205.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 162px; width: 315px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image206.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 162px; width: 385px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image207.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 171px; width: 228px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image208.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 162px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image209.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 88px; width: 142px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image210.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 L.H.S. = R.H.S.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Proved.<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"19_A_trust_fund_has_30000_that_must_be_invested_in_two_different_types_of_bond_The_first_bond_pays_5_interest_per_year_and_the_second_bond_pays_7_interest_per_year_Using_matrix_multiplication_determine_how_to_divide_30000_in_two_types_of_bonds_if_the_trust_fund_must_obtain_an_annual_interest_of_a_1800_b_2000\"><\/span><strong>19. A trust fund has ` 30,000 that must be invested in two different types of bond. The first bond pays 5% interest per year and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide ` 30,000 in two types of bonds, if the trust fund must obtain an annual interest of (a) ` 1800, (b) ` 2000.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let the investment in first bond be ` <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image084.png\" \/>, then the investment in the second bond = `<img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image211.png\" \/><\/p>\n<p style=\"text-align: justify;\">Interest paid by first bond = 5% = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image212.png\" \/>\u00a0per rupee and interest paid by second bond = 5% = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image213.png\" \/>\u00a0per rupee.<\/p>\n<p style=\"text-align: justify;\">Matrix of investment is A = <img decoding=\"async\" style=\"height: 27px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image214.png\" \/><\/p>\n<p style=\"text-align: justify;\">Matrix of annual interest per rupee B = <img decoding=\"async\" style=\"height: 68px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image215.png\" \/><\/p>\n<p style=\"text-align: justify;\">Matrix of total annual interest is AB = <img decoding=\"async\" style=\"height: 66px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image216.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image217.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image218.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image219.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 Total annual interest = ` <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image220.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(a)<\/strong> According to question, <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image221.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 146px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image222.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image223.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, Investment in first bond = ` 15,000<\/p>\n<p style=\"text-align: justify;\">And Investment in second bond = ` (30000 \u2013 15000) = ` 15,000<\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong> According to question, <img decoding=\"async\" style=\"height: 41px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image224.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image225.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image226.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, Investment in first bond = ` 5,000<\/p>\n<p style=\"text-align: justify;\">And Investment in second bond = ` (30000 \u2013 15000) = ` 25,000<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_32-2\"><\/span>NCERT Solutions class 12 Maths Exercise 3.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"20_The_bookshop_of_a_particular_school_has_10_dozen_chemistry_books_8_dozen_physics_books_10_dozen_economics_books_Their_selling_prices_are_80_60_and_40_each_respectively_Find_the_total_amount_the_bookshop_will_receive_from_selling_all_the_books_using_matrix_algebra\"><\/span><strong>20. The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are ` 80, ` 60 and ` 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let the number of books as a 1 x 3 matrix B = <img decoding=\"async\" style=\"height: 49px; width: 338px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image227.png\" \/><\/p>\n<p style=\"text-align: justify;\">Let the selling prices of each book as a 3 x 1 matrix S = <img decoding=\"async\" style=\"height: 75px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image228.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 Total amount received by selling all books = BS = <img decoding=\"async\" style=\"height: 75px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image229.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 30px; width: 197px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image230.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 205px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image231.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, Total amount received by selling all the books = ` 20160<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_32-3\"><\/span>NCERT Solutions class 12 Maths Exercise 3.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"21_The_restriction_on_and_so_that_PY_WY_will_be_define_are\"><\/span><strong>21. The restriction on <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image232.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image233.png\" \/>\u00a0so that PY + WY will be define are:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 21px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image234.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image187.png\" \/>\u00a0is arbitrary, <img decoding=\"async\" style=\"height: 21px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image235.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image233.png\" \/>\u00a0is arbitrary, <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image236.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 21px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image237.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 25px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image238.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now, <img decoding=\"async\" style=\"height: 25px; width: 212px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image239.png\" \/><\/p>\n<p style=\"text-align: justify;\">On comparing,\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image236.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image240.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, option (A) is correct.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_32-4\"><\/span>NCERT Solutions class 12 Maths Exercise 3.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"22_If_then_order_of_matrix_7X_%E2%80%93_5Z_is\"><\/span><strong>22. If <img decoding=\"async\" style=\"height: 17px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image241.png\" \/>\u00a0then order of matrix 7X \u2013 5Z is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 21px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image242.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image243.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image244.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 17px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image245.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Here <img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image246.png\" \/>\u00a0(given), the order of matrices X and Z are equal.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 7X \u2013 5Z is well defined and the order of 7X \u2013 5Z is same as the order of X and Z.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image116.png\" \/>\u00a0 The order of 7X \u2013 5Z is either equal to <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image243.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 21px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image247.png\" \/><\/p>\n<p style=\"text-align: justify;\">But it is given that <img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.2\/image246.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, the option (B) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_32-5\"><\/span>NCERT Solutions class 12 Maths Exercise 3.2<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 13 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_Students\"><\/span>CBSE App for Students<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 3.2 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 3.2\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-2\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 3.2\">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-4482","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 3.2 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 3.2 in PDF format for free download. 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