{"id":33316,"date":"2018-12-07T11:47:36","date_gmt":"2018-12-07T11:47:36","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=33316"},"modified":"2020-12-02T16:12:05","modified_gmt":"2020-12-02T10:42:05","slug":"cbse-sample-papers-for-class-12-maths-paper-4","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/cbse-sample-papers-for-class-12-maths-paper-4\/","title":{"rendered":"CBSE Sample Papers for Class 12 Maths Paper 4"},"content":{"rendered":"<p>CBSE Sample Papers for Class 12 Maths Paper 4 are part of <a href=\"https:\/\/cbselibrary.com\/cbse-sample-papers-for-class-12-maths\/\">CBSE Sample Papers for Class 12 Maths<\/a>. Here we have given CBSE Sample Papers for Class 12 Maths Paper 4.<\/p>\n<h2>CBSE Sample Papers for Class 12 Maths Paper 4<\/h2>\n<table>\n<tbody>\n<tr>\n<td width=\"122\"><strong>Board<\/strong><\/td>\n<td width=\"122\">CBSE<\/td>\n<\/tr>\n<tr>\n<td width=\"122\"><strong>Class<\/strong><\/td>\n<td width=\"122\">XII<\/td>\n<\/tr>\n<tr>\n<td width=\"122\"><strong>Subject<\/strong><\/td>\n<td width=\"122\">Maths<\/td>\n<\/tr>\n<tr>\n<td width=\"122\"><strong>Sample Paper Set<\/strong><\/td>\n<td width=\"122\">Paper 4<\/td>\n<\/tr>\n<tr>\n<td width=\"122\"><strong>Category<\/strong><\/td>\n<td width=\"122\"><a href=\"https:\/\/cbselibrary.com\/cbse-sample-papers\/\">CBSE Sample Papers<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 4 of Solved CBSE Sample Paper for Class 12 Maths is given below with free PDF download solutions.<\/p>\n<p style=\"text-align: left;\"><strong>Time: 3 Hours<\/strong><br \/>\n<strong>Maximum Marks: 100<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>General Instructions:<\/strong><\/p>\n<ul>\n<li>All questions are compulsory.<\/li>\n<li>Questions 1-4 in section A are very short answer type questions carrying 1 mark each.<\/li>\n<li>Questions 5-12 in section B are short answer type questions carrying 2 marks each.<\/li>\n<li>Questions 13-23 in section C are long answer I type questions carrying 4 marks each.<\/li>\n<li>Questions 24-29 in section D are long answer II type questions carrying 6 marks each.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><strong>SECTION A<\/strong><\/p>\n<p>Question 1.<br \/>\nIf A is a skew symmetric matrix of order 3 x 3 then prove that |A| = 0<\/p>\n<p>Question 2.<br \/>\nCheck the continuity of the function<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119649\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-1.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 1\" width=\"235\" height=\"59\" \/><\/p>\n<p>Question 3.<br \/>\nFind the anti derivative of sin 2x by the method of inspection<\/p>\n<p>Question 4.<br \/>\nIf the line \\(\\frac { x-1 }{ 2 } =\\frac { y+4 }{ 1 } =\\frac { z-7 }{ 2 }\\) is parallel to the plane 3x &#8211; 2y + cz = 14 then find the value of c.<\/p>\n<p style=\"text-align: center;\"><strong>SECTION B<\/strong><\/p>\n<p>Question 5.<br \/>\nDetermine the value of x for which the matrix<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119651\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-2.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 2\" width=\"303\" height=\"93\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-2.png 303w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-2-300x92.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119652\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-3.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 3\" width=\"392\" height=\"65\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-3.png 392w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-3-300x50.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 7.<br \/>\nVerify Mean Value Theorem for f(x) = (x &#8211; 1) (x &#8211; 2) (x &#8211; 3) in [1, 4]<\/p>\n<p>Question 8.<br \/>\nFind the approximate value of f(3.01) when f(x) = 3x<sup>2<\/sup> + 5x + 4.<\/p>\n<p>Question 9.<br \/>\nFind the angle between the pair of lines<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119653\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-4.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 4\" width=\"315\" height=\"72\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-4.png 315w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-4-300x69.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p>Question 10.<br \/>\nEvaluate P(A \u222a B) if 2P(A) = P(B) = \\(\\frac { 5 }{ 13 }\\) and P(A|B) = \\(\\frac { 2 }{ 5 }\\)<\/p>\n<p>Question 11.<br \/>\nReshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain atleast 8 units of vitamin A and 11 units of vitamin B. Food P costs \u20b9 60\/kg and food Q costs \u20b9 80\/kg. Food P contains 3 units\/ kg of vitamin A and 5 units\/kg of vitamin B while food Q contains 4 units\/kg of vitamin A and 2 units\/kg of vitamin B. Formulate the L.P.P for minimum cost of the mixture.<\/p>\n<p>Question 12.<br \/>\nEvaluate \\(\\int _{ 0 }^{ 2 }{ \\left( x-\\left[ x \\right] \\right) } dx\\)<\/p>\n<p style=\"text-align: center;\"><strong>SECTION C<\/strong><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119655\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-5.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 5\" width=\"535\" height=\"167\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-5.png 535w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-5-300x94.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119657\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-6.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 6\" width=\"510\" height=\"240\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-6.png 510w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-6-300x141.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119658\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-7.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 7\" width=\"522\" height=\"58\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-7.png 522w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-7-300x33.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119659\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-8.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 8\" width=\"255\" height=\"98\" \/><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119662\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-9.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 9\" width=\"241\" height=\"62\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119663\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-10.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 10\" width=\"182\" height=\"60\" \/><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119664\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-11.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 11\" width=\"666\" height=\"38\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-11.png 666w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-11-300x17.png 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119665\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-12.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 12\" width=\"687\" height=\"77\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-12.png 687w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-12-300x34.png 300w\" sizes=\"(max-width: 687px) 100vw, 687px\" \/><\/p>\n<p>Question 21.<br \/>\n40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostellers got A grade while from outside students, only 30% got A grade in the examination. At the end of year, a student of the college was choosen at random and was found to get A grade. What is the probability that the selected student was a hosteller ?<\/p>\n<p>Question 22.<br \/>\nThree distinguishable balls are distributed in three cells. Find the conditional probability that all the three occupy the same cell given that atleast two of them are in the same cell. Which values are reflected from tricolour of our national flag?<\/p>\n<p>Question 23.<br \/>\nSolve the following L.P.P. graphically.<br \/>\nMaximise Z = 8000 x + 12000 y<br \/>\nSubject to constraints are<br \/>\n9x + 12y \u2264 180<br \/>\nx + 3y \u2264 30<br \/>\nx, y \u2265 0<\/p>\n<p style=\"text-align: center;\"><strong>SECTION D<\/strong><\/p>\n<p>Question 24.<br \/>\nLet A = {1, 2, 3, &#8230; 9} and R be the relation in A x A defined by (a, b) R (c, d). If a + d = b + c for a, b, c, d \u2208 A, prove that R is an equivalence relation. Also obtain the equivalence class (2, 5).<br \/>\n<strong>OR<\/strong><br \/>\nLet A = R &#8211; {3} and B = R &#8211; {1}. Let f : A \u2192 B defined by f(x) = \\(\\frac { x-2 }{ x-3 }\\) for all x \u2208 A. Then show that f is bijective. Hence find f<sup>-1<\/sup>(x). Also find the value of f<sup>-1<\/sup>(17).<\/p>\n<p>Question 25.<br \/>\nFind the area of the region bounded by the curves y = tan x, the tangent drawn to the curve y = tan x at x = \\(\\frac { \\pi }{ 4 }\\) and the x-axis using integration.<br \/>\n<strong>OR<\/strong><br \/>\nFind the area enclosed by the curves y = |x &#8211; 1| and y = 1 &#8211; |x &#8211; 1| using integration.<\/p>\n<p>Question 26.<br \/>\nShow that the four points (0, -1, -1), (-4, 4, 4), (4, 5, 1) and (3, 9, 4) are coplanar. Find the equation of the plane containing them.<br \/>\n<strong>OR<\/strong><br \/>\nFind the angle between the tangents to the parabolas y<sup>2<\/sup> = 4ax and x<sup>2<\/sup> = 4by at their point of intersection other than the origin.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119666\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-13.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 13\" width=\"686\" height=\"80\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-13.png 686w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-13-300x35.png 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119668\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-14.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 14\" width=\"539\" height=\"156\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-14.png 539w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-14-300x87.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 29.<br \/>\nA plot is in the form of a rectangle with a semicircular plot along one of the shorter sides. The perimeter of the total plot is 100 m. A farmer wants to use the maximum area for growing the grass. Find the dimensions of the plot so that maximum grass can be planted.<\/p>\n<p style=\"text-align: center;\"><strong>Solutions<\/strong><\/p>\n<p>Solution 1.<br \/>\nA is a skew symmetric matrix, so A&#8217; = -A<br \/>\n|A&#8217;| =|-A| \u21d2 |A| = -|A|<br \/>\n|A| =0<\/p>\n<p>Solution 2.<br \/>\nAt x = 1,<br \/>\nL.H.L = 1<br \/>\nR.H.L = 5<br \/>\nL.H.L \u2260 R.H.L, so f(x) is discontinuous at x = 1<\/p>\n<p>Solution 3.<br \/>\n\\(\\frac { -1 }{ 2 }\\) cos 2x<\/p>\n<p>Solution 4.<br \/>\n2(3) + 1 (-2) + 2c = 0<br \/>\n\u21d2 c = -2<\/p>\n<p>Solution 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119669\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-15.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 15\" width=\"594\" height=\"197\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-15.png 594w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-15-300x99.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Solution 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119670\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-16.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 16\" width=\"399\" height=\"109\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-16.png 399w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-16-300x82.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Solution 7.<br \/>\nf(x) is continuous in [1, 4]<br \/>\nf(x) is differentiable in ]1, 4[<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119671\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-17.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 17\" width=\"323\" height=\"146\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-17.png 323w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-17-300x136.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Solution 8.<br \/>\nx + \u2206x = 3.01, x = 3<br \/>\n\u2206x = 0.01<br \/>\nf(x + \u2206x) =f(x) + f'(x) \u2206x<br \/>\nf(3.01) =f(3) + f'(3) (0.01) = 46 + 23 (0.01) = 46.23<\/p>\n<p>Solution 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119672\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-18.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 18\" width=\"297\" height=\"181\" \/><\/p>\n<p>Solution 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119674\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-19.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 19\" width=\"339\" height=\"95\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-19.png 339w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-19-300x84.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Solution 11.<br \/>\nLet food P consist x kg and food Q consist y kg in mixture.<br \/>\nObjective function is minimise cost Z = 60x + 80y<br \/>\nSubject to constraints are<br \/>\n3x + 4y \u2265 8<br \/>\n5x + 2y \u2265 11<br \/>\nx, y \u2265 0<\/p>\n<p>Solution 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119675\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-20.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 20\" width=\"428\" height=\"69\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-20.png 428w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-20-300x48.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Solution 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119676\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-21.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 21\" width=\"386\" height=\"203\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-21.png 386w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-21-300x158.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><\/p>\n<p>Solution 14.<br \/>\nTaking a, b, c common from C<sub>1<\/sub>, C<sub>2<\/sub>, C<sub>3<\/sub><br \/>\nafter that R<sub>1<\/sub> \u2192 R<sub>1<\/sub> &#8211; R<sub>2<\/sub> &#8211; R<sub>3<\/sub><br \/>\nafter this C<sub>1<\/sub> \u2192 C<sub>1<\/sub> &#8211; C<sub>2<\/sub> and expand<br \/>\n<strong>OR<\/strong><br \/>\nR<sub>1<\/sub> \u2192 R<sub>1<\/sub> &#8211; R<sub>2<\/sub>, R<sub>2<\/sub> \u2192 R<sub>2<\/sub> &#8211; R<sub>3<\/sub><br \/>\nTaking (x &#8211; y),(y &#8211; z) common from R<sub>1<\/sub> and R<sub>2<\/sub><br \/>\nThen R<sub>1<\/sub> \u2192 R<sub>1<\/sub> &#8211; R<sub>2<\/sub>, R<sub>3<\/sub> \u2192 R<sub>3<\/sub> &#8211; zR<sub>2<\/sub><br \/>\nThen taking (x &#8211; z) common from R<sub>1<\/sub> and expand.<\/p>\n<p>Solution 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119677\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-22.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 22\" width=\"412\" height=\"216\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-22.png 412w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-22-300x157.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><\/p>\n<p>Solution 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119678\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-23.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 23\" width=\"504\" height=\"233\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-23.png 504w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-23-300x139.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Solution 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119680\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-24.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 24\" width=\"540\" height=\"228\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-24.png 540w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-24-300x127.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Solution 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119681\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-25.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 25\" width=\"395\" height=\"148\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-25.png 395w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-25-300x112.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Solution 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119682\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-26.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 26\" width=\"462\" height=\"155\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-26.png 462w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-26-300x101.png 300w\" sizes=\"(max-width: 462px) 100vw, 462px\" \/><\/p>\n<p>Solution 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119684\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-27.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 27\" width=\"443\" height=\"224\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-27.png 443w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-27-300x152.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Solution 21.<br \/>\nE<sub>1<\/sub>: student of a college reside in Hostel<br \/>\nE<sub>2<\/sub>: student of a college reside outside<br \/>\nA: student got A grade<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119685\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-28.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 28\" width=\"383\" height=\"168\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-28.png 383w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-28-300x132.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Solution 22.<br \/>\nE<sub>1<\/sub>: All the three balls are in the same cell.<br \/>\nE<sub>2<\/sub>: At least two balls are in the same cell.<br \/>\nSince each ball can be place in a cell in 3 ways, so three distinct balls can be place in three cells by 3 x 3 x 3 = 27 ways.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119688\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-29.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 29\" width=\"358\" height=\"186\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-29.png 358w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-29-300x156.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><br \/>\nIn tricolour:<br \/>\nOrange &#8211; strength and courage<br \/>\nWhite &#8211; peace and truth<br \/>\nGreen &#8211; growth and fertility<\/p>\n<p>Solution 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119690\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-30.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 30\" width=\"335\" height=\"145\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-30.png 335w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-30-300x130.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Solution 24.<br \/>\nProve reflexive, Prove symmetric, Prove transitive<br \/>\nR is reflexive, symmetric and transitive, so R is an equivalence relation.<br \/>\nEquivalence class (2, 5) is (p, q) \u21d2 2 + q = 5 + p<br \/>\nSo (1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)<br \/>\n<strong>OR<\/strong><br \/>\nProve one-one, Prove onto<br \/>\nf is one-one and onto, so it is bijective<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119691\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-31.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 31\" width=\"429\" height=\"58\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-31.png 429w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-31-300x41.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/p>\n<p>Solution 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119692\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-32.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 32\" width=\"621\" height=\"417\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-32.png 621w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-32-300x201.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119695\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-33.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 33\" width=\"587\" height=\"301\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-33.png 587w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-33-300x154.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119696\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-34.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 34\" width=\"613\" height=\"67\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-34.png 613w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-34-300x33.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/p>\n<p>Solution 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119698\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-35.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 35\" width=\"684\" height=\"245\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-35.png 684w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-35-300x107.png 300w\" sizes=\"(max-width: 684px) 100vw, 684px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119700\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-36.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 36\" width=\"575\" height=\"508\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-36.png 575w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-36-300x265.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Solution 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119701\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-37.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 37\" width=\"248\" height=\"165\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119703\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-38.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 38\" width=\"365\" height=\"210\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-38.png 365w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-38-300x173.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><\/p>\n<p>Solution 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119704\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-39.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 39\" width=\"559\" height=\"369\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-39.png 559w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-39-300x198.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Solution 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119706\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-40.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 40\" width=\"223\" height=\"109\" \/><br \/>\nLet length of rectangular plot = x m<br \/>\nbreadth of rectangular plot = 2r m<br \/>\nradius of semicircle = r m<br \/>\nx + x + 2r + \u03c0r = 100<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119708\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-41.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 41\" width=\"461\" height=\"308\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-41.png 461w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-41-300x200.png 300w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-119710\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-42.png\" alt=\"CBSE Sample Papers for Class 12 Maths Paper 4 42\" width=\"502\" height=\"263\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-42.png 502w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/CBSE-Sample-Papers-for-Class-12-Maths-Paper-4-42-300x157.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>We hope the CBSE Sample Papers for Class 12 Maths Paper 4 help you. If you have any query regarding CBSE Sample Papers for Class 12 Maths Paper 4, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Sample Papers for Class 12 Maths Paper 4 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 4. CBSE Sample Papers for Class 12 Maths Paper 4 Board CBSE Class XII Subject Maths Sample Paper Set Paper 4 Category CBSE Sample &#8230; <a title=\"CBSE Sample Papers for Class 12 Maths Paper 4\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/cbse-sample-papers-for-class-12-maths-paper-4\/\" aria-label=\"More on CBSE Sample Papers for Class 12 Maths Paper 4\">Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>CBSE Sample Papers for Class 12 Maths Paper 4 - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/cbse-sample-papers-for-class-12-maths-paper-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"CBSE Sample Papers for Class 12 Maths Paper 4\" \/>\n<meta property=\"og:description\" content=\"CBSE Sample Papers for Class 12 Maths Paper 4 are part of CBSE Sample Papers for Class 12 Maths. 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