Class 12 Maths Sample Question Paper | CBSE Exam 2021-22 Important Questions

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 - 041
• CLASS: XII
• Session: 2021-22
• Subject- Mathematics
• Term - 1
• Time Allowed: 90 minutes
• Maximum Marks: 40

2. The value of k (k < 0) for which the function defined as is continuous at ? = 0 is:

3. If A = [aij] is a square matrix of order 2 such that aij , then A2 is:

4. Value of k, for which A = is a singular matrix is:

5. Find the intervals in which the function f given by f (x) = x 2 – 4x + 6 is strictly increasing:

6. Given that A is a square matrix of order 3 and | A | = - 4, then | adj A | is equal to:

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?

8. If , then value of a + b c + 2d is:

9. The point at which the normal to the curve y = ? + 1/x, x > 0 is perpendicular to the line 3x – 4y – 7 = 0 is:

10. sin (tan-1x), where |x| < 1, is equal to:

12. If ex + ey = ex+y , then :

13. Given that matrices A and B are of order 3×n and m×5 respectively, then the order of matrix C = 5A +3B is:

14. If y = 5 cos x – 3 sin x, then is equal to:

15. For matrix A = is equal to:

17. Given that A = [???] is a square matrix of order 3×3 and |A| = 7, then the value of , where ??? denotes the cofactor of element ??? is:

18. If y = log(cos??), then ??/?? is:

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?

20. The least value of the function ?(?) = 2???? + ? in the closed interval [ is:

21. The function: R R defined as ?(?) = ?3 is:

23. In the given graph, the feasible region for a LPP is shaded. The objective function Z = 2x – 3y, will be minimum at:

26. The real function f(x) = 2x3 – 3x2 – 36x + 7 is:

28. Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:

29. The value of for which the function ? (?) = ? + ???? + ? is strictly decreasing over R is:

30. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}, then:

31. The point(s), at which the function f gi ven by is continuous, is/are:

32. If A = , then the values of ?, ? and respectively are:

35. If A is square matrix such that A2 = A, then (I + A)³ – 7 A is equal to:

36. If tan-1 x = y, then:

37. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f= {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given infor mation, is best defined as:

38. For A = , then 14A-1 is given b y:

39. The point(s) on the curve y = x 3 – 11x + 5 at which the tangent is y = x – 11 is/are:

40. Given that A = and A 2 = 3 , then:

41. For an objective function ? = ?? + ??, where ?, ? > 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:

42. For which value of m is the line y = mx + 1 a tangent to the curve y 2 = 4x?

43. The maximum value of [?( ? − 1 ) + 1]3, 0≤ ? ≤ 1 is:

44. In a linear programming problem, the constraints on the decision variables x and y are − 3? ≥ 0, ? ≥ 0, 0 ≤ ? ≤ 3. The feasible region

45. Let A = , where 0 ≤ α ≤ 2π, then:

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:

47. If the train has travelled a distance of 500km, then the total cost of running the train is given by function:

48. The most economical speed to run the train is:

49. The fuel cost for the train to travel 500km at the most economical speed is:

50. The total cost of the train to travel 500km at the most economical speed is:

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