{"id":114098,"date":"2021-12-05T13:11:22","date_gmt":"2021-12-05T07:41:22","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=114098"},"modified":"2021-12-06T11:03:45","modified_gmt":"2021-12-06T05:33:45","slug":"class-12-maths-sample-question-paper-cbse-exam-2021-22-important-questions","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/education\/class-12-maths-sample-question-paper-cbse-exam-2021-22-important-questions","title":{"rendered":"Class 12 Maths Sample Question Paper | CBSE Exam 2021-22 Important Questions"},"content":{"rendered":"<h2>CBSE 2021-22, Maths board exam sample question paper for Class 12. Check the important questions which need to be focused on while preparing for the class 12 Maths board exam.<\/h2>\n<ul>\n<li>Subject Code &#8211; 041<\/li>\n<li>CLASS: XII<\/li>\n<li>Session: 2021-22<\/li>\n<li>Subject- Mathematics<\/li>\n<li>Term &#8211; 1<\/li>\n<li>Time Allowed: 90 minutes<\/li>\n<li>Maximum Marks: 40<\/li>\n<\/ul>\n<p><strong>General Instructions:<\/strong><br \/>\n1. This question paper contains three sections \u2013 A, B and C. Each part is compulsory.<br \/>\n2. Section &#8211; A has 20 MCQs, attempt any 16 out of 20. 3. Section &#8211; B has 20 MCQs, attempt any 16 out of 20.<br \/>\n4. Section &#8211; C has 10 MCQs, attempt any 8 out of 10.<br \/>\n5. All questions carry equal marks.<br \/>\n6. There is no negative marking.<\/p>\n<p><strong>SECTION \u2013 A<\/strong><br \/>\nIn this section, attempt any 16 questions out of Questions 1 \u2013 20.<br \/>\nEach Question is of 1 mark weightage.<\/p>\n<p>1. sin [ )] is equal to:<br \/>\na) b)<br \/>\nc) -1 d) 1<\/p>\n<h2>2. The value of k (k &lt; 0) for which the function defined as is continuous at \ud835\udc65 = 0 is:<\/h2>\n<p>a) \u00b11 b) 1 c) d) 1 2<\/p>\n<h2>3. If A = [aij] is a square matrix of order 2 such that aij , then A2 is:<\/h2>\n<h2>4. Value of <em>k<\/em>, for which A = is a singular matrix is:<\/h2>\n<p>a) 4 b) -4 c) \u00b14 d) 0<\/p>\n<h2>5. Find the intervals in which the function f given by f (x) = x 2 \u2013 4x + 6 is strictly increasing:<\/h2>\n<p>a) (\u2013 \u221e, 2) (2, \u221e) b) (2, \u221e) c) (\u2212\u221e, 2) d) (\u2013 \u221e, 2] (2, \u221e)<\/p>\n<h2>6. Given that A is a square matrix of order 3 and | A | = &#8211; 4, then | adj A | is equal to:<\/h2>\n<p>a) -4 b) 4 c) -16 d) 16<\/p>\n<h2>7. A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?<\/h2>\n<p>a) (1, 1) b) (1, 2) c) (2, 2) d) (3, 3)<\/p>\n<h2>8. If , then value of a + b c + 2d is:<\/h2>\n<p>a) 8 b) 10 c) 4 d) 8<\/p>\n<h2>9. The point at which the normal to the curve y = \ud835\udc65 + 1\/x, x &gt; 0 is perpendicular to the line 3x \u2013 4y \u2013 7 = 0 is:<\/h2>\n<p>a) (2, 5\/2) b) (\u00b12, 5\/2)<br \/>\nc) (- 1\/2, 5\/2) d) (1\/2, 5\/2)<\/p>\n<h2>10. sin (tan-1x), where |x| &lt; 1, is equal to:<\/h2>\n<p>11. Let the relation R in the set A =<br \/>\nb| is a multiple of 4}. Then [1], th<br \/>\nx Z e equi : 0 \u2264 x \u2264 12}, given by R = valence class containing 1 {(a, b) : |a \u2013 , is:<br \/>\na) {1, 5, 9} b) {0, 1, 2, 5}<br \/>\nc) d) A<\/p>\n<h2>12. If ex + ey = ex+y , then :<\/h2>\n<p>a) e y &#8211; x b) e x + y<br \/>\nc) \u2013 e y &#8211; x d) 2 e x &#8211; y<\/p>\n<h2>13. Given that matrices A and B are of order 3\u00d7n and m\u00d75 respectively, then the order of matrix C = 5A +3B is:<\/h2>\n<p>a) 3\u00d75 b) 5\u00d73<br \/>\nc) 3\u00d73 d) 5\u00d75<\/p>\n<h2>14. If y = 5 cos x \u2013 3 sin x, then is equal to:<\/h2>\n<p>a) &#8211; y b) y<br \/>\nc) 25y d) 9y<\/p>\n<h2>15. For matrix A = is equal to:<\/h2>\n<p>a) b)<\/p>\n<p>c) d)<\/p>\n<p>16. The points on the curve axis are:<br \/>\nat which the tangents are parallel to y- 1<\/p>\n<p>a) (0,\u00b14) b) (\u00b14,0)<br \/>\nc) (\u00b13,0) d) (0, \u00b13)<\/p>\n<h2>17. Given that A = [\ud835\udc4e\ud835\udc56\ud835\udc57] is a square matrix of order 3\u00d73 and |A| = 7, then the value of , where \ud835\udc34\ud835\udc56\ud835\udc57 denotes the cofactor of element \ud835\udc4e\ud835\udc56\ud835\udc57 is:<\/h2>\n<p>a) 7 b) -7<br \/>\nc) 0 d) 49<\/p>\n<h2>18. If y = log(cos\ud835\udc52\ud835\udc65), then \ud835\udc51\ud835\udc66\/\ud835\udc51\ud835\udc65 is:<\/h2>\n<p>a) cos\ud835\udc52\ud835\udc65\u22121 b) \ud835\udc52\u2212\ud835\udc65 cos\ud835\udc52\ud835\udc65<br \/>\nc) \ud835\udc52\ud835\udc65sin \ud835\udc52\ud835\udc65 d) \u2212 \ud835\udc52\ud835\udc65 tan \ud835\udc52\ud835\udc65<\/p>\n<h2>19. Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum?<\/h2>\n<p>a) Point B b) Point C<br \/>\nc) Point D d) every point on the line segment CD<\/p>\n<h2>20. The least value of the function \ud835\udc53(\ud835\udc65) = 2\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc65 + \ud835\udc65 in the closed interval [ is:<\/h2>\n<p>a) 2 b) \ud835\udf0b \u221a<br \/>\nc) d) The least value does not exist.<\/p>\n<p><strong>SECTION \u2013 B<\/strong><br \/>\nIn this section, attempt any 16 questions out of the Questions 21 &#8211; 40.<br \/>\nEach question is of 1 mark weightage.<\/p>\n<h2>21. The function: R R defined as \ud835\udc53(\ud835\udc65) = \ud835\udc653 is:<\/h2>\n<p>a) One-on but not onto b) Not one-one but onto<br \/>\nc) Neither one-one nor onto d) One-one and onto<\/p>\n<h2>23. In the given graph, the feasible region for a LPP is shaded. The objective function Z = 2x \u2013 3y, will be minimum at:<\/h2>\n<p>a) (4, 10) b) (6, 8)<br \/>\nc) (0, 8) d) (6, 5)<\/p>\n<h2>26. The real function f(x) = 2&#215;3 \u2013 3&#215;2 \u2013 36x + 7 is:<\/h2>\n<p>a) Strictly increasing in (\u2212\u221e, \u22122) and strictly decreasing in ( \u22122, \u221e)<br \/>\nb) Strictly decreasing in ( \u22122, 3)<br \/>\nc) Strictly decreasing in (\u2212\u221e, 3) and strictly increasing in (3, \u221e)<br \/>\nd) Strictly decreasing in (\u2212\u221e, \u22122) \u222a (3, \u221e)<\/p>\n<h2>28. Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:<\/h2>\n<p>a) b)<br \/>\nc) 64 d) 16<\/p>\n<h2>29. The value of for which the function \ud835\udc53 (\ud835\udc65) = \ud835\udc65 + \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc65 + \ud835\udc4f is strictly decreasing over R is:<\/h2>\n<p>a) \ud835\udc4f &lt; 1 b) No value of b exists c) \ud835\udc4f \u2264 1 d) \ud835\udc4f \u2265 1<\/p>\n<h2>30. Let R be the relation in the set N given by R = {(a, b) : a = b \u2013 2, b &gt; 6}, then:<\/h2>\n<p>a) (2,4) \u2208 R b) (3,8) \u2208 R<br \/>\nc) (6,8) \u2208 R d) (8,7) \u2208 R<\/p>\n<h2>31. The point(s), at which the function f gi ven by is continuous, is\/are:<\/h2>\n<p>a) \ud835\udc65\ud835\udf16R b) \ud835\udc65 = 0<br \/>\nc) \ud835\udc65\ud835\udf16 R {0} d) = \u22121and<\/p>\n<h2>32. If A = , then the values of \ud835\udc58, \ud835\udc4e and respectively are:<\/h2>\n<p>a) \u22126, \u221212, \u221218 b) \u22126, \u22124, \u22129<br \/>\nc) \u22126, 4, 9 d) \u22126, 12, 18<\/p>\n<p>33. A linear programming problem is as follows:<br \/>\n\ud835\udc40\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc5a\ud835\udc56\ud835\udc67\ud835\udc52 \ud835\udc4d = 30\ud835\udc65 + 50\ud835\udc66 subject to the constraints,<br \/>\n3\ud835\udc65 + 5\ud835\udc66 \u2265 15<br \/>\n2\ud835\udc65 + 3\ud835\udc66 \u2264 18<br \/>\n\ud835\udc65 \u2265 0, \ud835\udc66 \u2265 0<br \/>\nIn the feasible region, the minimum value of Z occurs at<br \/>\na) a unique point b) no point<\/p>\n<p>c) infinitely many points d) two points only<\/p>\n<p>34. The area of a trapezium is defined by function \ud835\udc53 and given by \ud835\udc53(\ud835\udc65) = (10 +<br \/>\n, then the area when it is maximised is:<br \/>\na) 75\ud835\udc50\ud835\udc5a2 b) 7\u221a3\ud835\udc50\ud835\udc5a2<br \/>\nc) 75\u221a3\ud835\udc50\ud835\udc5a2 d) 5\ud835\udc50\ud835\udc5a2<\/p>\n<h2>35. If A is square matrix such that A2 = A, then (I + A)\u00b3 \u2013 7 A is equal to:<\/h2>\n<p>a) A b) I + A<br \/>\nc) I A d) I<\/p>\n<h2>36. If tan-1 x = y, then:<\/h2>\n<p>a) \u22121 &lt; y &lt; 1 b) c) d) y<\/p>\n<h2>37. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let <em>f<\/em>= {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given infor mation, is best defined as:<\/h2>\n<p>a) Surjective function b) Injective function c) Bijective function d) function<\/p>\n<h2>38. For A = , then 14A-1 is given b y:<\/h2>\n<p>a) b) c) d)<\/p>\n<h2>39. The point(s) on the curve y = x 3 \u2013 11x + 5 at which the tangent is y = x \u2013 11 is\/are:<\/h2>\n<p>a) (-2,19) b) (2, &#8211; 9) c) (\u00b12, 19) d) (-2, 19) and (2, -9)<\/p>\n<h2>40. Given that A = and A 2 = 3 , then:<\/h2>\n<p>a) 1 + \ud835\udefc2 + \ud835\udefd\ud835\udefe = 0 b) 1 \u2212 \ud835\udefc2 \u2212 \ud835\udefd\ud835\udefe = 0 c) 3 \u2212 \ud835\udefc2 \u2212 \ud835\udefd\ud835\udefe = 0 d) 3 + \ud835\udefc2 + \ud835\udefd\ud835\udefe = 0<\/p>\n<p>SECTION \u2013 C In this section, attempt any 8 questions. Each question is of 1-mark weightage. Questions 46-50 are based on a Case-Study.<\/p>\n<h2>41. For an objective function \ud835\udc4d = \ud835\udc4e\ud835\udc65 + \ud835\udc4f\ud835\udc66, where \ud835\udc4e, \ud835\udc4f &gt; 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:<\/h2>\n<p>a) \ud835\udc4f \u2212 3\ud835\udc4e = 0 b) \ud835\udc4e = 3\ud835\udc4f<\/p>\n<p>c) \ud835\udc4e + 2\ud835\udc4f = 0 d) 2\ud835\udc4e \u2212 \ud835\udc4f = 0<\/p>\n<h2>42. For which value of m is the line y = mx + 1 a tangent to the curve y 2 = 4x?<\/h2>\n<p>a) b)<\/p>\n<p>c) d)<\/p>\n<h2>43. The maximum value of [\ud835\udc65( \ud835\udc65 \u2212 1 ) + 1]3, 0\u2264 \ud835\udc65 \u2264 1 is:<\/h2>\n<h2>44. In a linear programming problem, the constraints on the decision variables x and y are \u2212 3\ud835\udc66 \u2265 0, \ud835\udc66 \u2265 0, 0 \u2264 \ud835\udc65 \u2264 3. The feasible region<\/h2>\n<p>a) is not in the first quadrant b) is bounded in the first quadrant<br \/>\nc) is unbounded in the first quadrant d) does not exist<\/p>\n<h2>45. Let A = , where 0 \u2264 \u03b1 \u2264 2\u03c0, then:<\/h2>\n<p>a) |A|=0 b) |A| \ud835\udf16(2, \u221e)<br \/>\nc) |A| \ud835\udf16(2,4) d) |A| \ud835\udf16[2,4]<\/p>\n<p><strong>CASE STUDY<\/strong><br \/>\nThe fuel cost per hour for running a train is proportional to the square of the speed it generates in km per hour. If the fuel costs \u20b9 48 per hour at speed 16 km per hour and the fixed charges to run the train amount to \u20b9 1200 per hour.<br \/>\nAssume the speed of the train as \ud835\udc63 km\/h.<\/p>\n<p>Based on the given information, answer the following questions.<\/p>\n<h2>46. Given that the fuel cost per hour is times the square of the speed the train generates in km\/h, the value of is:<\/h2>\n<p>a) 16\/3 b) 1\/3<br \/>\nc) 3 d) 3\/16<\/p>\n<h2>47. If the train has travelled a distance of 500km, then the total cost of running the train is given by function:<\/h2>\n<h2>48. The most economical speed to run the train is:<\/h2>\n<p>a) 18km\/h b) 5km\/h<br \/>\nc) 80km\/h d) 40km\/h<\/p>\n<h2>49. The fuel cost for the train to travel 500km at the most economical speed is:<\/h2>\n<p>a) \u20b9 3750 b) \u20b9 750<br \/>\nc) \u20b9 7500 d) \u20b9 75000<\/p>\n<h2>50. The total cost of the train to travel 500km at the most economical speed is:<\/h2>\n<p>a) \u20b9 3750 b) \u20b9 75000<br \/>\nc) \u20b9 7500 d) \u20b9 15000<\/p>\n<ul>\n<li><a href=\"https:\/\/www.mapsofindia.com\/ci-moi-images\/my-india\/2021\/12\/12TH-Maths-SQP.pdf\">Download CBSE Class 12 Maths Sample Question Paper<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE 2021-22, Maths board exam sample question paper for Class 12. Check the important questions which need to be focused on while preparing for the class 12 Maths board exam. Subject Code &#8211; 041 CLASS: XII Session: 2021-22 Subject- Mathematics Term &#8211; 1 Time Allowed: 90 minutes Maximum Marks: 40 General Instructions: 1. This question [&hellip;]<\/p>\n","protected":false},"author":21814,"featured_media":114101,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":{"0":"post-114098","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-education"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/114098","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21814"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=114098"}],"version-history":[{"count":3,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/114098\/revisions"}],"predecessor-version":[{"id":114113,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/114098\/revisions\/114113"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/114101"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=114098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=114098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=114098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}