{"id":17667,"date":"2018-06-29T14:34:38","date_gmt":"2018-06-29T09:04:38","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=17667"},"modified":"2019-01-18T17:15:48","modified_gmt":"2019-01-18T11:45:48","slug":"cbse-question-paper-2018-class-12-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/cbse-question-paper-2018-class-12-mathematics\/","title":{"rendered":"CBSE Question Paper 2018 class 12 Mathematics"},"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\/cbse-question-paper-2018-class-12-mathematics\/#Previous_Year_Question_Papers_%E2%80%93_Download_Free_PDF\" >Previous Year Question Papers &#8211; Download Free PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-question-paper-2018-class-12-mathematics\/#Class_12_Mathematics_list_of_chapters\" >Class 12 Mathematics list of chapters<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-question-paper-2018-class-12-mathematics\/#CBSE_Question_Paper_2018_class_12_Mathematics\" >CBSE Question Paper 2018 class 12 Mathematics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-question-paper-2018-class-12-mathematics\/#Mathematics_Question_Paper_2018_with_solution\" >Mathematics Question Paper 2018 with solution<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-question-paper-2018-class-12-mathematics\/#CBSE_Question_Paper_2018\" >CBSE Question Paper 2018<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"title\"><span class=\"ez-toc-section\" id=\"Previous_Year_Question_Papers_%E2%80%93_Download_Free_PDF\"><\/span>Previous Year Question Papers &#8211; Download Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>CBSE Question Paper 2018 class 12 Mathematics<\/strong>\u00a0conducted by Central Board of Secondary Education, New Delhi in the month of March 2018. CBSE previous year question papers with solution are available in myCBSEguide mobile app and cbse guide website. The Best CBSE App for students and teachers is myCBSEguide which provides complete study material and practice papers to cbse schools in India and abroad.<\/p>\n<p style=\"text-align: center;\"><strong>Question Paper 2018 class 12 Maths\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-last-year-papers\/3\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20pic.jpg\" alt=\"CBSE Question Paper 2018 class 12 Mathematics\" width=\"118\" height=\"154\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Class_12_Mathematics_list_of_chapters\"><\/span>Class 12 Mathematics list of chapters<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol>\n<li>Relations and Functions<\/li>\n<li>Inverse Trigonometric Functions<\/li>\n<li>Matrices<\/li>\n<li>Determinants<\/li>\n<li>Continuity and Differentiability<\/li>\n<li>Application of Derivatives<\/li>\n<li>Integrals<\/li>\n<li>Application of Integrals<\/li>\n<li>Differential Equations<\/li>\n<li>Vector Algebra<\/li>\n<li>Three Dimensional Geometry<\/li>\n<li>Linear Programming<\/li>\n<li>Probability<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Question_Paper_2018_class_12_Mathematics\"><\/span>CBSE Question Paper 2018 class 12 Mathematics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Time allowed : 3 hours<\/strong><br \/>\n<strong>Maximum Marks: 100<\/strong><\/p>\n<p><strong>General Instructions :<\/strong><\/p>\n<ol start=\"1\">\n<li><strong>All<\/strong> questions are compulsory.<\/li>\n<li>The question paper consists of <strong>29<\/strong> questions divided into four sections A, B, C and D. Section A comprises of 4 questions of <strong>one mark<\/strong> each, Section B comprises of <strong>8<\/strong> questions of <strong>two marks<\/strong> each, Section C comprises of <strong>11 <\/strong>questions of <strong>four marks<\/strong> each and Section D comprises of <strong>6<\/strong> questions of <strong>six marks<\/strong> each.<\/li>\n<li>All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.<\/li>\n<li>There is no overall choice. However, internal choice has been provided in 3 questions of four marks each and 3 questions of six marks each. You have to attempt only one of the alternatives in all such questions.<\/li>\n<li>Use of calculators is <strong>not<\/strong> permitted. You may ask for logarithmic tables if required.<\/li>\n<\/ol>\n<hr \/>\n<p style=\"text-align: center;\"><strong> SECTION A<\/strong><\/p>\n<p><strong>Question numbers 1 to 4 carry 1 mark each.<\/strong><\/p>\n<ol>\n<li>Find the value of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"47\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%7B%5C%5Ctan%20%5E%7B%20-%201%7D%7D%5C%5Csqrt%203%20-%20%7B%5C%5Ccot%20%5E%7B%20-%201%7D%7D%5C%5Cleft(%20%7B%20-%20%5C%5Csqrt%203%20%7D%20%5C%5Cright)%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\tan ^{ - 1}}\\sqrt 3 - {\\cot ^{ - 1}}\\left( { - \\sqrt 3 } \\right)\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>.<\/li>\n<li>If the matrix <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"46\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7DA%20%3D%20%5C%5Cleft%5B%20%7B%5C%5Cbegin%7Barray%7D%7B*%7B20%7D%7Bc%7D%7D%200%26a%26%7B%20-%203%7D%20%5C%5C%5C%5C%202%260%26%7B%20-%201%7D%20%5C%5C%5C%5C%20b%261%260%20%5C%5Cend%7Barray%7D%7D%20%5C%5Cright%5D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?A = \\left[ {\\begin{array}{*{20}{c}} 0&amp;amp;a&amp;amp;{ - 3} \\\\ 2&amp;amp;0&amp;amp;{ - 1} \\\\ b&amp;amp;1&amp;amp;0 \\end{array}} \\right]\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is skew-symmetric, find the values of &#8216;a&#8217; and &#8216;b&#8217;.<\/li>\n<li>Find the magnitude of each of the two vectors\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"45\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20a%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec a\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"44\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20b%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec b\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>, having the same magnitude such that the angle between them is 60\u00b0 and their scalar product is.<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"43\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7B9%7D%7B2%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{9}{2}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<li>If a <sub>*<\/sub> b denotes the larger of \u2018a\u2019 and \u2018b\u2019 and if a <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"42\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ccirc%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\circ\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> b = (a <sub>*<\/sub> b) + 3, then write the value of (5) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"41\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ccirc%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\circ\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> (10), where <sub>*<\/sub> and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"40\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ccirc%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\circ\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> are binary operations.<\/li>\n<\/ol>\n<p><strong>SECTION B<\/strong><\/p>\n<p><strong>Question numbers 5 to 12 carry 2 marks each.<\/strong><\/p>\n<ol start=\"5\">\n<li>Prove that:\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"39\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D3%20%5C%5C%3B%20%7B%5C%5Csin%20%5E%7B%20-%201%7D%7Dx%20%3D%20%7B%5C%5Csin%20%5E%7B%20-%201%7D%7D(3x%20-%204%7Bx%5E3%7D)%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?3 \\; {\\sin ^{ - 1}}x = {\\sin ^{ - 1}}(3x - 4{x^3})\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>, <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"38\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dx%20%5C%5Cin%20%5C%5Cleft%5B%20%7B%5C%5Cfrac%7B%7B%20-%201%7D%7D%7B2%7D%2C%5C%5C%3B%5C%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5Cright%5D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x \\in \\left[ {\\frac{{ - 1}}{2},\\;\\frac{1}{2}} \\right]\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<li>Given <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"37\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7DA%20%3D%20%5C%5Cleft%5B%20%7B%5C%5Cbegin%7Barray%7D%7B*%7B20%7D%7Bc%7D%7D%202%26%7B%20-%203%7D%20%5C%5C%5C%5C%20%7B%20-%204%7D%267%20%5C%5Cend%7Barray%7D%7D%20%5C%5Cright%5D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?A = \\left[ {\\begin{array}{*{20}{c}} 2&amp;amp;{ - 3} \\\\ { - 4}&amp;amp;7 \\end{array}} \\right]\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>, compute A<sup>-1<\/sup> and show that 2A<sup>-1<\/sup> = 9I &#8211; A.<\/li>\n<li>Differentiate <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"36\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%7B%5C%5Ctan%20%5E%7B%20-%201%7D%7D%5C%5Cleft(%20%7B%5C%5Cfrac%7B%7B1%20%2B%20%5C%5Ccos%20x%7D%7D%7B%7B%5C%5Csin%20x%7D%7D%7D%20%5C%5Cright)%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\tan ^{ - 1}}\\left( {\\frac{{1 + \\cos x}}{{\\sin x}}} \\right)\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> with respect to x.<\/li>\n<li>The total cost C(x) associated with the production of x units of an item is given by C(x) = 0\u00b7005x<sup>3<\/sup> &#8211; 0\u00b702x<sup>2<\/sup> + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.<\/li>\n<li>Evaluate : <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"35\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cint%20%7B%5C%5Cfrac%7B%7B%5C%5Ccos%202x%20%2B%202%7B%7B%5C%5Csin%20%7D%5E2%7Dx%7D%7D%7B%7B%7B%7B%5C%5Ccos%20%7D%5E2%7Dx%7D%7D%7D%20dx%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\int {\\frac{{\\cos 2x + 2{{\\sin }^2}x}}{{{{\\cos }^2}x}}} dx\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<li>Find the differential equation representing the family of curves y = a e<sup>bx+5<\/sup>, where a and b are arbitrary constants.<\/li>\n<li>If <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"34\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ctheta%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\theta\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is the angle between two vectors\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"33\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Chat%20i%20-%202%5C%5Chat%20j%20%2B%203%5C%5Chat%20k%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\hat i - 2\\hat j + 3\\hat k\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"32\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D3%5C%5Chat%20i%20-%202%5C%5Chat%20j%20%2B%20%5C%5Chat%20k%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?3\\hat i - 2\\hat j + \\hat k\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> find sin.<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"31\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ctheta%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\theta\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<li>A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><strong>SECTION C<\/strong><\/p>\n<p><strong>Question numbers 13 to 23 carry 4 marks each.<\/strong><\/p>\n<ol start=\"13\">\n<li>Using properties of determinants, prove that<br \/>\n<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"30\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cleft%7C%20%7B%5C%5Cbegin%7Barray%7D%7B*%7B20%7D%7Bc%7D%7D%201%261%26%7B1%20%2B%203x%7D%20%5C%5C%5C%5C%20%7B1%20%2B%203y%7D%261%261%20%5C%5C%5C%5C%201%26%7B1%20%2B%203z%7D%261%20%5C%5Cend%7Barray%7D%7D%20%5C%5Cright%7C%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left| {\\begin{array}{*{20}{c}} 1&amp;amp;1&amp;amp;{1 + 3x} \\\\ {1 + 3y}&amp;amp;1&amp;amp;1 \\\\ 1&amp;amp;{1 + 3z}&amp;amp;1 \\end{array}} \\right|\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> = 9 (3xyz + xy + yz + zx)<\/li>\n<li>If (x<sup>2<\/sup> + y<sup>2<\/sup>)<sup>2<\/sup> = xy, find <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"29\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7B%7Bdy%7D%7D%7B%7Bdx%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{{dy}}{{dx}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>.\n<div><strong>OR<\/strong><\/div>\n<p>If <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"28\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dx%20%3D%20a(2%5C%5Ctheta%20-%20%5C%5Csin%202%5C%5Ctheta%20)%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x = a(2\\theta - \\sin 2\\theta )\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"27\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dy%20%3D%20a(1%20-%20%5C%5Ccos%202%5C%5Ctheta%20)%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y = a(1 - \\cos 2\\theta )\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>, find <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"26\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7B%7Bdy%7D%7D%7B%7Bdx%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{{dy}}{{dx}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> when <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"25\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ctheta%20%3D%20%5C%5Cfrac%7B%5C%5Cpi%20%7D%7B3%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\theta = \\frac{\\pi }{3}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>.<\/li>\n<li>If y = sin (sin x), prove that <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"24\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7B%7B%7Bd%5E2%7Dy%7D%7D%7B%7Bd%7Bx%5E2%7D%7D%7D%20%2B%20%5C%5Ctan%20x%5C%5Cfrac%7B%7Bdy%7D%7D%7B%7Bdx%7D%7D%20%2B%20y%7B%5C%5Ccos%20%5E2%7Dx%20%3D%200%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{{{d^2}y}}{{d{x^2}}} + \\tan x\\frac{{dy}}{{dx}} + y{\\cos ^2}x = 0\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>.<\/li>\n<li>Find the equations of the tangent and the normal, to the curve 16x<sup>2<\/sup> + 9y<sup>2<\/sup> = 145 at the point (x<sub>1<\/sub>, y<sub>1<\/sub>), where x<sub>1<\/sub> = 2 and y<sub>1<\/sub> &gt; 0.\n<div>OR<\/div>\n<p>Find the intervals in which the function f(x) =\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"23\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7B%7B%7Bx%5E4%7D%7D%7D%7B4%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{{{x^4}}}{4}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> &#8211; x<sup>3<\/sup> \u2013 5x<sup>2<\/sup> + 24x + 12 is (a) strictly increasing, (b) strictly decreasing.<\/li>\n<li>An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of the tank is half of its width. If the cost is to be borne by nearby settled lower-income families, for whom water will be provided, what kind of value is hidden in this question?<\/li>\n<li>Find : <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"22\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cint%20%7B%5C%5Cfrac%7B%7B2%5C%5Ccos%20x%7D%7D%7B%7B(1%20-%20%5C%5Csin%20x)(1%20%2B%20%7B%7B%5C%5Csin%20%7D%5E2%7Dx)%7D%7D%7D%20dx%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\int {\\frac{{2\\cos x}}{{(1 - \\sin x)(1 + {{\\sin }^2}x)}}} dx\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<li>Find the particular solution of the differential equation e<sup>x<\/sup> tan y dx + (2 &#8211; e<sup>x<\/sup>) sec<sup>2<\/sup>y dy = 0, give that <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"21\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dy%20%3D%20%5C%5Cfrac%7B%5C%5Cpi%20%7D%7B4%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y = \\frac{\\pi }{4}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> when x = 0.\n<div><strong>OR<\/strong><\/div>\n<p>Find the particular solution of the differential equation <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"20\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7B%7Bdy%7D%7D%7B%7Bdx%7D%7D%20%2B%202y%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{{dy}}{{dx}} + 2y\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> tanx = sinx, given that y = 0 when.<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"19\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dx%20%3D%20%5C%5Cfrac%7B%5C%5Cpi%20%7D%7B3%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x = \\frac{\\pi }{3}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<li>Let <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"18\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20a%20%3D%204%5C%5Chat%20i%20%2B%205%5C%5Chat%20j%20-%20%5C%5Chat%20k%2C%5C%5C%3B%5C%5Cvec%20b%20%3D%20%5C%5Chat%20i%20-%204%5C%5Chat%20j%20%2B%205%5C%5Chat%20k%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec a = 4\\hat i + 5\\hat j - \\hat k,\\;\\vec b = \\hat i - 4\\hat j + 5\\hat k\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"17\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20c%20%3D%203%5C%5Chat%20i%20%2B%20%5C%5Chat%20j%20-%20%5C%5Chat%20k%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec c = 3\\hat i + \\hat j - \\hat k\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>. Find a vector\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"16\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20d%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec d\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> which is perpendicular to both\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"15\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20c%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec c\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"14\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20b%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec b\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"13\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cvec%20d%20%5C%5Ccdot%20%5C%5Cvec%20a%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\vec d \\cdot \\vec a\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> = 21.<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><strong>These are first 20 questions only.\u00a0<\/strong><b>To view and download complete question paper with solution<\/b><\/p>\n<p style=\"text-align: center;\"><b><strong><a class=\"button\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\">Download myCBSEguide App<\/a><\/strong><\/b><\/p>\n<p style=\"text-align: center;\"><b>the best CBSE App from google playstore\u00a0now or login to our Student Dashboard.<\/b><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mathematics_Question_Paper_2018_with_solution\"><\/span>Mathematics Question Paper 2018 with solution<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download class 12 Mathematics question paper with solution from best CBSE App the myCBSEguide. CBSE class 12 Mathematics question paper 2018 in PDF format with solution will help you to understand the latest question paper pattern and marking scheme of the CBSE board examination. You will get to know the difficulty level of the question paper. CBSE question papers 2018 for class 12 Mathematics have 29 questions with solution.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Question_Paper_2018\"><\/span>CBSE Question Paper 2018<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>CBSE question papers 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 209, 2008, 2007, 2006, 2005 and so on for all the subjects are available under this download link. Practicing real question paper certainly helps students to get confidence and improve performance in weak areas.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physics\/1251\/cbse-last-year-papers\/3\/\">Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-chemistry\/1267\/cbse-last-year-papers\/3\/\">Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-last-year-papers\/3\/\">Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-biology\/1298\/cbse-last-year-papers\/3\/\">Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-accountancy\/1315\/cbse-last-year-papers\/3\/\">Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-business-studies\/1727\/cbse-last-year-papers\/3\/\">Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-economics\/1327\/cbse-last-year-papers\/3\/\">Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-history\/1869\/cbse-last-year-papers\/3\/\">History<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-geography\/1863\/cbse-last-year-papers\/3\/\">Geography<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-political-science\/1879\/cbse-last-year-papers\/3\/\">Political Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physical-education\/1877\/cbse-last-year-papers\/3\/\">Physical Education<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-computer-science\/1851\/cbse-last-year-papers\/3\/\">Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-informatics-practices\/1873\/cbse-last-year-papers\/3\/\">Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-english-core\/1855\/cbse-last-year-papers\/3\/\">English Core<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-hindi-core\/1865\/cbse-last-year-papers\/3\/\">Hindi Core<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-hindi-elective\/1867\/cbse-last-year-papers\/3\/\">Hindi Elective<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12\/1250\/\">Other Subjects<\/a><\/li>\n<\/ul>\n<p>To download CBSE Question Paper 2018 class 12 Accountancy, Chemistry, Physics, 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>Previous Year Question Papers &#8211; Download Free PDF CBSE Question Paper 2018 class 12 Mathematics\u00a0conducted by Central Board of Secondary Education, New Delhi in the month of March 2018. CBSE previous year question papers with solution are available in myCBSEguide mobile app and cbse guide website. The Best CBSE App for students and teachers is &#8230; <a title=\"CBSE Question Paper 2018 class 12 Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-question-paper-2018-class-12-mathematics\/\" aria-label=\"More on CBSE Question Paper 2018 class 12 Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":-1,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1346,1014,1432],"tags":[1679,1643,1528,1342,321,1485,1591],"class_list":["post-17667","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","category-cbse-question-papers","category-mathematics-cbse-class-12","tag-cbse-last-year-question-paper","tag-cbse-previous-year","tag-cbse-question-paper-2018","tag-class-12","tag-mathematics","tag-maths","tag-ten-year-question-paper"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - 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