{"id":37042,"date":"2022-02-18T14:23:13","date_gmt":"2022-02-18T08:53:13","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=37042"},"modified":"2022-02-28T13:19:16","modified_gmt":"2022-02-28T07:49:16","slug":"cbse-previous-year-question-papers-class-12-maths-2016-delhi","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/cbse\/class-12\/maths\/cbse-previous-year-question-papers-class-12-maths-2016-delhi\/","title":{"rendered":"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/cbse\/class-12\/maths\/cbse-previous-year-question-papers-class-12-maths-2016-delhi\/#CBSE_Previous_Year_Question_Papers_Class_12_Maths_2016_Delhi\" title=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi\">CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi<\/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:\/\/infinitylearn.com\/surge\/cbse\/class-12\/maths\/cbse-previous-year-question-papers-class-12-maths-2016-delhi\/#CBSE_Previous_Year_Question_Papers_Class_12_Maths_2016_Delhi_Set_I\" title=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi Set I\">CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi Set I<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Previous_Year_Question_Papers_Class_12_Maths_2016_Delhi\"><\/span>CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Time allowed: 3 hours<br \/>\nMaximum marks : 100<\/p>\n<p>General Instructions:<\/p>\n<ul>\n<li>All questions are compulsory.<\/li>\n<li>The question paper consists of 29 questions divided into four sections A, B, C and D. Section A comprises of 4 questions of one mark each, Section B comprises of 8 questions of two marks each, Section C comprises of 11 questions of four marks each and Section D comprises of 6 questions of six marks 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 1 question of Section A, 3 questions of Section B, 3 questions of Section C and 3 questions of Section D. You have to attempt only one of the alternatives in all such questions.<\/li>\n<li>Use of calculators is not permitted. You may ask for logarithmic tables, if required.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"CBSE_Previous_Year_Question_Papers_Class_12_Maths_2016_Delhi_Set_I\"><\/span>CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi Set I<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Section \u2013 A<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the maximum value of [1]\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129626\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-1.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 1\" width=\"176\" height=\"78\" \/><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129627\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-2.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 2\" width=\"363\" height=\"420\" \/><\/p>\n<p>Question 2.<br \/>\nIf A is a square matrix such that A<sup>2<\/sup> = I, then find the simplified value of (A \u2013 I)<sup>3<\/sup> + (A + I)<sup>3<\/sup> \u2013 7A. [1]\nSolution:<br \/>\nGiven,<br \/>\n(A \u2013 I)<sup>3<\/sup> + (A + I)<sup>3<\/sup> \u2013 7A<br \/>\n= A<sup>3<\/sup> \u2013 I<sup>3<\/sup> \u2013 3A<sup>2<\/sup>I + 3AI<sup>2<\/sup> + A<sup>3<\/sup> + I<sup>3<\/sup> + 3A<sup>2<\/sup>I<br \/>\n= 2A<sup>3<\/sup> + 6AI<sup>2<\/sup> \u2013 7A<br \/>\n= 2A.A<sup>2<\/sup> + 6AI<sup>2<\/sup> \u2013 7A<br \/>\n= 2AI + 6AI \u2013 7A<br \/>\n= 8A \u2013 7A = A<\/p>\n<p>Question 3.<br \/>\nMatrix A = \\(\\left[\\begin{array}{rrr}{0} &amp; {2 b} &amp; {-2} \\\\ {3} &amp; {1} &amp; {3} \\\\ {3 a} &amp; {3} &amp; {-1}\\end{array}\\right]\\) is given to be symmetric, find values of a and b. [1]\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129629\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-3.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 3\" width=\"308\" height=\"428\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129630\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-4.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 4\" width=\"277\" height=\"51\" \/><\/p>\n<p>Question 4.<br \/>\nFind the position vector of a point which divides the join of points with position vectors \\(\\vec{a}-2 \\vec{b}\\) and \\(2 \\vec{a}+\\vec{b}\\) externally in the ratio 2 : 1. [1]\nSolution:<br \/>\nLet A and B be the given points with<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129631\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-5.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 5\" width=\"366\" height=\"231\" \/><\/p>\n<p>Question 5.<br \/>\nThe two vectors \\(\\hat{j}+\\hat{k} \\text { and } 3 \\hat{i}-\\hat{j}+4 \\hat{k}\\) represent the two sides AB and AC, respectively of a \u2206ABC. Find the length of the median through A. [1]\nSolution:<br \/>\nIn \u2206ABC,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129632\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-6.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 6\" width=\"372\" height=\"506\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129633\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-7.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 7\" width=\"367\" height=\"136\" \/><\/p>\n<p>Question 6.<br \/>\nFind the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is \\(2 \\hat{i}-3 \\hat{j}+6 \\hat{k}\\). [1]\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129634\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-8.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 8\" width=\"371\" height=\"277\" \/><\/p>\n<p><strong>Section \u2013 B<\/strong><\/p>\n<p>Question 7.<br \/>\nProve that: [4]\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129635\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-9.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 9\" width=\"302\" height=\"48\" \/><br \/>\nSolution:<br \/>\nLHS =<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129636\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-10.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 10\" width=\"370\" height=\"492\" \/><br \/>\nOR<br \/>\nSolve for x : 2 tan<sup>-1<\/sup>(cos x) = tan<sup>-1<\/sup>(2 cosec x)<br \/>\nSolution:<br \/>\nGiven, 2 tan<sup>-1<\/sup>(cos x) = tan<sup>-1<\/sup>(2 cosec x)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129637\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-11.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 11\" width=\"303\" height=\"53\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129638\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-12.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 12\" width=\"362\" height=\"203\" \/><\/p>\n<p>Question 8.<br \/>\nThe monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves \u20b9 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value ? [4]\nSolution:<br \/>\nLet the monthly incomes of Aryan and Babban be 3x and 4x respectively.<br \/>\nSuppose their monthly expenditures are 5y and 7y respectively.<br \/>\nSince each saves \u20b9 15,000 per month.<br \/>\nMonthly saving of Aryan : 3x \u2013 5y = 15,000<br \/>\nMonthly saving of Babban : 4 x \u2013 7y = 15,000<br \/>\nThe above system of equations can be written in the matrix form as follows:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129639\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-13.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 13\" width=\"369\" height=\"526\" \/><br \/>\n\u21d2 x = 30,000 and y = 15,000<br \/>\nTherefore,<br \/>\nMonthly income of Aryan = 3 \u00d7 30,000 = \u20b9 90,000<br \/>\nMonthly income of Babban = 4 \u00d7 30,000 = \u20b9 1,20,000<br \/>\nValue : Saving in good time helps us to survive in bad times.<\/p>\n<p>Question 9.<br \/>\nIf x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 \u2013 cos 2t), find the values of \\(\\frac{d y}{d x} \\text { at } t=\\frac{\\pi}{4} \\text { and } t=\\frac{\\pi}{3}\\). [4]\nSolution:<br \/>\nWe have, x = a sin 2t (1 + cos 2t)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129640\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-14.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 14\" width=\"373\" height=\"564\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129641\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-15.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 15\" width=\"167\" height=\"167\" \/><br \/>\nOR<br \/>\nIf y = x<sup>x<\/sup> prove that \\(\\frac{d^{2} y}{d x^{2}}-\\frac{1}{y}\\left(\\frac{d y}{d x}\\right)^{2}-\\frac{y}{x}=0\\).<br \/>\nSolution:<br \/>\nGiven, y = x<sup>x<\/sup><br \/>\nTaking log on both sides, we get<br \/>\nlog y = log(x<sup>x<\/sup>)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129642\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-16.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 16\" width=\"366\" height=\"491\" \/><\/p>\n<p>Question 10.<br \/>\nFind the values of p ans q for which [4]\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129643\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-17.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 17\" width=\"325\" height=\"173\" \/><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129644\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-18.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 18\" width=\"377\" height=\"448\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129645\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-19.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 19\" width=\"370\" height=\"481\" \/><\/p>\n<p>Question 11.<br \/>\nShow that the equation of normal at any point on the curve x = 3 cos t \u2013 cos<sup>3<\/sup> t and y = 3 sin t- sin<sup>3<\/sup> is 4(y cos<sup>3<\/sup> t \u2013 x sin<sup>3<\/sup>t) = 3 sin 4 t. \u2013 sin<sup>3<\/sup> t is [4]\nSolution:<br \/>\nGiven,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129646\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-20.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 20\" width=\"378\" height=\"556\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129647\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-21.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 21\" width=\"369\" height=\"273\" \/><\/p>\n<p>Question 12.<br \/>\nFimd: [4]\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129648\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-22.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 22\" width=\"168\" height=\"54\" \/><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129649\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-23.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 23\" width=\"367\" height=\"549\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129650\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-24.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 24\" width=\"358\" height=\"90\" \/><br \/>\nOR<br \/>\nEvaluate<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129651\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-25.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 25\" width=\"156\" height=\"51\" \/><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129652\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-26.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 26\" width=\"202\" height=\"52\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129653\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-27.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 27\" width=\"394\" height=\"477\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129654\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-28.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 28\" width=\"171\" height=\"126\" \/><\/p>\n<p>Question 13.<br \/>\nFind: [4]\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129655\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-29.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 29\" width=\"110\" height=\"59\" \/><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129656\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-30.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 30\" width=\"302\" height=\"386\" \/><\/p>\n<p>Question 14.<br \/>\nEvaluate : [4]\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129657\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-31.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 31\" width=\"118\" height=\"47\" \/><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129658\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-32.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 32\" width=\"196\" height=\"44\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129659\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-33.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 33\" width=\"370\" height=\"538\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129660\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-34.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 34\" width=\"93\" height=\"92\" \/><\/p>\n<p>Question 15.<br \/>\nFind the particular solution of the differential equation (1 \u2013 y<sup>2<\/sup>) (1 + logx) dx + 2xy dy=0, given that y = 0 when x = 1. [4]\nSolution:<br \/>\nThe given differential equation is,<br \/>\n(1 \u2013 y<sup>2<\/sup>) (1 + log x).dx + 2xy dy = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129661\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-35.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 35\" width=\"268\" height=\"375\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129662\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-36.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 36\" width=\"284\" height=\"281\" \/><\/p>\n<p>Question 16.<br \/>\nFind the general solution of the following differential equation: [4]\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129663\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-37.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 37\" width=\"222\" height=\"45\" \/><br \/>\nSolution:<br \/>\nThe given differential equation is,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129664\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-38.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 38\" width=\"319\" height=\"567\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129665\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-39.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 39\" width=\"322\" height=\"102\" \/><\/p>\n<p>Question 17.<br \/>\nShow that the vectors \\(\\vec{a}, \\vec{b} \\text { and } \\vec{c}\\) are coplanar if \\(\\vec{a}+\\vec{b}, \\vec{b}+\\vec{c} \\text { and } \\vec{c}+\\vec{a}\\) are coplanar. [4]\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129666\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-40.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 40\" width=\"370\" height=\"543\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129667\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-41.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 41\" width=\"370\" height=\"176\" \/><\/p>\n<p>Question 18.<br \/>\nFind the vector and cartesian equations of the line through the point (1, 2, \u2013 4) and perpendicular to the two lines.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129668\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-42.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 42\" width=\"308\" height=\"78\" \/><br \/>\nSolution:<br \/>\nThe equations of the given lines are<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129669\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-43.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 43\" width=\"371\" height=\"239\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129670\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-44.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 44\" width=\"376\" height=\"365\" \/><\/p>\n<p>Question 19.<br \/>\nThree persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1 : 2 : 4. The probabilities that A, B and C can introduce changes to improve profits of the company are 0.8, 0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C. [4]\nSolution:<br \/>\nLet E<sub>1<\/sub>, E<sub>2<\/sub> and E<sub>3<\/sub> be the events denoting the selection of A, B and C as managers respectively.<br \/>\nP(E<sub>1<\/sub>) = Probability of selection of A = \\(\\frac{1}{7}\\)<br \/>\nP(E<sub>2<\/sub>) = Probability of selection of B = \\(\\frac{2}{7}\\)<br \/>\nP(E<sub>3<\/sub>) = Probability of selection of C = \\(\\frac{4}{7}\\)<br \/>\nLet A be the event denoting the change not taking place.<br \/>\nP(A\/E<sub>1<\/sub>) = Probability that A does not introduce change = 0.2<br \/>\nP(A\/E<sub>2<\/sub>) = Probability that B does not introduce change = 0.5<br \/>\nP(A\/E<sub>3<\/sub>) = Probability that C does not introduce change 0.7 .<br \/>\n\u2234 Required probability = P(E<sub>3<\/sub>\/A)<br \/>\nBy Bayes\u2019 theorem, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129671\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-45.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 45\" width=\"377\" height=\"174\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129672\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-46.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 46\" width=\"110\" height=\"102\" \/><br \/>\nOR<br \/>\nA and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.<br \/>\nSolution:<br \/>\nTotal of 7 on the dice can be obtained in the following ways :<br \/>\n(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129673\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-47.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 47\" width=\"372\" height=\"513\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129674\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-48.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 48\" width=\"372\" height=\"327\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129675\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-49.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 49\" width=\"371\" height=\"284\" \/><\/p>\n<p><strong>Section \u2013 C<\/strong><\/p>\n<p>Question 20.<br \/>\nLet f : N \u2192 N be a function defined as f(x) = 9x<sup>2<\/sup> + 6x \u2013 5. Show that f : N \u2192 S, where S is the range off, is invertible. Find the inverse of f and hence find f<sup>-1<\/sup> (43) and f<sup>-1<\/sup> (163). [6]\nSolution:<br \/>\nGiven,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129676\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-50.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 50\" width=\"376\" height=\"570\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129677\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-51.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 51\" width=\"366\" height=\"128\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129678\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-52.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 52\" width=\"283\" height=\"110\" \/><\/p>\n<p>Question 21.<br \/>\nProve that \\(\\left|\\begin{array}{lll}{y z-x^{2}} &amp; {z x-y^{2}} &amp; {x y-z^{2}} \\\\ {z x-y^{2}} &amp; {x y-z^{2}} &amp; {y z-x^{2}} \\\\ {x y-z^{2}} &amp; {y z-x^{2}} &amp; {z x-y^{2}}\\end{array}\\right|\\) is visible by (x + y + z) and hence find the quotient. [6]\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129679\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-53.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 53\" width=\"371\" height=\"533\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129680\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-54.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 54\" width=\"398\" height=\"352\" \/><br \/>\nOR<br \/>\nUsing elementary transformations, find the inverse of the matrix A = \\(\\left[\\begin{array}{lll}{8} &amp; {4} &amp; {3} \\\\ {2} &amp; {1} &amp; {1} \\\\ {1} &amp; {2} &amp; {2}\\end{array}\\right]\\) and use it to solve the following system of linear equations:<br \/>\n8x + 4y + 3z = 19<br \/>\n2x + y + z = 5<br \/>\nx + 2y + 2z = 7<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129681\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-55.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 55\" width=\"362\" height=\"523\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129682\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-56.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 56\" width=\"297\" height=\"386\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129683\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-57.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 57\" width=\"309\" height=\"532\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129684\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-58.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 58\" width=\"374\" height=\"398\" \/><\/p>\n<p>Question 22.<br \/>\nShow that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is \\(\\frac{4 r}{3}\\). Also find maximum volume in terms of volume of the sphere. [6]\nSolution:<br \/>\nA sphere of fixed radius (r) is given. Let R and h be the radius and the height of the cone respectively.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129685\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-59.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 59\" width=\"374\" height=\"535\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129686\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-60.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 60\" width=\"321\" height=\"510\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129687\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-61.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 61\" width=\"365\" height=\"78\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129688\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-62.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 62\" width=\"375\" height=\"568\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129689\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-63.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 63\" width=\"374\" height=\"182\" \/><br \/>\nOR<br \/>\nFind the intervals in which f(x) = sin 3x \u2013 cos 3x, 0 &lt; x &lt; \u03c0, is strictly increasing or strictly decreasing.<br \/>\nSolution:<br \/>\nConsider the function<br \/>\nf(x) = sin 3x \u2013 cos 3x<br \/>\n\u21d2 f'(x) = 3 cos 3x + 3 sin 3x<br \/>\n= 3 (sin 3x + cos 3x)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129690\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-64.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 64\" width=\"349\" height=\"192\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129691\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-65.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 65\" width=\"369\" height=\"544\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129692\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-66.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 66\" width=\"369\" height=\"477\" \/><\/p>\n<p>Question 23.<br \/>\nUsing integration find the area of the region {(x, y) : x<sup>2<\/sup> + y<sup>2<\/sup> \u2264 2ax, y<sup>2<\/sup> \u2265 ax, x, y \u2265 0} [6]\nSolution:<br \/>\nWe have, {(x, y) : x<sup>2<\/sup> + y<sup>2<\/sup> \u2264 2ax, y<sup>2<\/sup> \u2265 ax, x, y \u2265 0}<br \/>\nConsider x<sup>2<\/sup> + y<sup>2<\/sup> = 2ax<br \/>\ny<sup>2<\/sup> = ax \u20269ii)<br \/>\nx = 0, y = 0<br \/>\nSolving equation (i) and (ii), we get<br \/>\nx<sup>2<\/sup> + ax = 2ax<br \/>\n\u21d2 x<sup>2<\/sup> \u2013 ax = 0<br \/>\n\u21d2 x(x \u2013 a) = 0<br \/>\n\u2234 x = 0, a<br \/>\nSo, points of intersections of (i) and (ii) are (0, 0) and (a, \u00b1 a). Also, equation (i) can be written as, (x \u2013 a)<sup>2<\/sup> + (y \u2013 0)<sup>2<\/sup> = a<sup>2<\/sup> whose centre is at (a, 0) and radius is of \u2018a\u2019 units.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129693\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-67.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 67\" width=\"361\" height=\"572\" \/><\/p>\n<p>Question 24.<br \/>\nFind the coordinate of the point P where the line through A(3, -4, -5) and B (2, \u2013 3, 1) crosses the plane passing through three points L (2, 2, 1), M (3, 0, 1) and N (4, \u2013 1, 0). Also, find the ratio in which P divides the line segment AB. [6]\nSolution:<br \/>\nThe equation of the plane passing through three given points can be given by<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129694\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-68.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 68\" width=\"298\" height=\"133\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129695\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-69.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 69\" width=\"379\" height=\"532\" \/><br \/>\nAt the point of intersection, these points satisfy the equation of the plane 2x + y + z \u2013 7 = 0<br \/>\nPutting the values of x, y and z in the equation of the plane, we get the value of \u03bb<br \/>\n2(-\u03bb + 3) + (\u03bb \u2013 4) + (6\u03bb \u2013 5) \u2013 7 = 0<br \/>\n\u21d2 -2\u03bb + 6 + \u03bb \u2013 4 + 6\u03bb \u2013 5 \u2013 7 = 0<br \/>\n\u21d2 5\u03bb =10<br \/>\n\u21d2 \u03bb = 2<br \/>\nThus, the point of intersection is P (1, \u2013 2, 7). Now, let P divide the line AB in the ratio m : n.<br \/>\nBy the section formula, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129696\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-70.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 70\" width=\"231\" height=\"144\" \/><br \/>\nHence, P divides externally the line segment AB in the ratio 2 : 1.<\/p>\n<p>Question 25.<br \/>\nAn urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and variance of the distribution. [6]\nSolution:<br \/>\nLet X denote the total number of red balls when four balls are drawn one by one with replacement.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129697\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-71.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 71\" width=\"398\" height=\"546\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129698\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-72.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 72\" width=\"377\" height=\"364\" \/><\/p>\n<p>Question 26.<br \/>\nA manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at \u20b9 7 profit and B at a profit of \u20b9 4. Find the production level per day for maximum profit graphically.<br \/>\nSolution:<br \/>\nLet the numbers of units of products A and B to be produced be x and y, respectively.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129699\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-73.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 73\" width=\"374\" height=\"338\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-129700\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/CBSE-Previous-Year-Question-Papers-Class-12-Maths-2016-Delhi-74.png\" alt=\"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi 74\" width=\"383\" height=\"464\" \/><br \/>\nTherefore, the manufacturer has to produce 2 units of product A and 3 units of product B for the maximum profit of \u20b9 26.<\/p>\n<p>All questions are same in Outside Delhi Set II and Set III<\/p>\n<h4><\/h4>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi Time allowed: 3 hours Maximum marks : 100 General Instructions: [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"CBSE Previous Year Question Papers Class 12 Maths 2016 Delhi","custom_permalink":"cbse\/class-12\/maths\/cbse-previous-year-question-papers-class-12-maths-2016-delhi\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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