CBSE Class 12 Mathematics Term 1 Sample Paper Set C

See below CBSE Class 12 Mathematics Term 1 Sample Paper Set C with solutions. We have provided CBSE Sample Papers for Class 12 Mathematics as per the latest paper pattern issued by CBSE for the current academic year. All sample papers provided by our Class 12 Mathematics teachers are with answers. You can see the sample paper given below and use them for more practice for Class 12 Mathematics examination.

CBSE Sample Paper for Class 12 Mathematics Term 1 Set C

SECTION-A

In this section, attempt any 16 questions out of Questions 1 –20.
Each Question is of 1 mark weightage.

1. The principal value of cot-1 (-1/√3) is
(A) 3π/4
(B) 2π/3
(C) π/6
(D) π/3

2. The derivative of the function y =x^sin2x is

3. If A =

,then –A² + 6A is :

(B) 2I
(C) 3I
(D) 4I

4. The value of determinant

(A) – 81
(B) 0
(C) 79
(D) None of the above

5. Absolute maximum of the function 3x + 5 in [6, 12] is:
(A) 40
(B) 10
(C) 20
(D) 41

6. If x

, then the values of x and y are: 
(A) 5, 5/2
(B) -5, 5/2
(C) 5, -5/2
(D) -5, 5/2

7. Given set A = {2, 3, 5}. An identity relation in set A is:
(A) R= {(2, 3), (2, 5)}
(B) R= {(2, 2), (3, 3), (5, 5)}
(C) R= {(2, 2), (3, 3), (5, 5), (2, 5)}
(D) R= {(5, 2), (3, 2), (2, 2)}

8. The value of If A =

9. What is the absolute minimum of the function |x – 4| in the interval [6, 9] ?
(A) 5
(B) 4
(C) 6
(D) 8

10. The value of cos-1 (cos 7π/6) will be
(A) 7π/6
(B) 5π/6
(C) π/5
(D) π/6

11. Let R be relation from R to R the set of real numbers defined by R = {(x, y): x, y Î R and x – y + 5 is an irrational number}. Then, R is:
(A) Reflexive
(B) Transitive
(C) Symmetric
(D) An equivalence relation

12. If f(x) = x⁴, then f'(-1/2) =
(A) 1/2
(B) 3/2
(C) 0
(D) – 1/2

13. If all the elements of a matrix are zero, the matrix is called:
(A) Zero matrix
(B) Row matrix
(C) Scalar matrix
(D) Column matrix 

14. If y = cos x log x then the value of dy/dx is
(A) sin x log x – 1
(B) sin x /x + cos x log x
(C) cos x /x – sin x log x 
(D) 1/x + cos x log x

15. For Matrix A =

16. The slope of the perpendicular to the tangent to curve y = x² – 5 at x = 1 is :
(A) -1/2
(B) 2
(C) 1/2
(D) –2

17. The value of x such that

(A) 8.5
(B) –8.5
(C) 0
(D) No such value exist

18. If y = √cos x + y , then dy/dx is equal to
(A) cos x/2y – 1
(B) cos x/1 – 2y
(C) sin x/1 – 2y
(D) sin x/2y – 1

19. Z = x – 5y + 20 subject to x – y ³ 0, –x + 2y ³ 2, x ³ 3, y £ 4; x, y ³ 0 and the corner points of the feasible region are (3 , 5/2) , (6, 4), (4, 4), (3, 3). Then the minimum value of Z is :
(A) 8
(B) 4
(C) 6
(D) 3

20. Which of the following is true for the given function?

(A) Continuous at x = 0
(B) Not continuous at x = 0
(C) differentiable at x = 0
(D) None of the above

SECTION-B

In this section, attempt any 16 questions out of the Questions 21 -40.
Each Question is of 1 mark weightage.

21. Which of the following functions from Z into Z are bijections?
(A) f(x) = x⁵
(B) f(x) = x + 7
(C) f(x) = 6x + 5
(D) f(x) = x² + 9

22. If y = log (1-x³/1+x³) , then dy/dx is equal to
(A) 4x³/1-x⁶
(B) -6x²/1-62
(C) 1/4-x6
(D) -4x³/1-x⁶

23. A set of values of the variables x₁, x₂, x₃, ……….., xn satisfying the constraints of a L.P.P. is called a:
(A) Feasible solution of L.P.P.
(B) Solution of L.P.P.
(C) Both A and B
(D) None

24. If y = 2 sinx + 3 cosx, then y + d²y/dx² is :
(A) 2 sin x + 3 cos x
(B) 1
(C) 0
(D) none of these

25. If

(A) 5
(B) ± 5
(C) –5
(D) 0

26. The points on the curve y = x³ – 8x + 10 at which the tangent is y = x – 15 are :
(A) ( √3, √3 -15) and (- √3, – √3 -15)
(B) (3, – 12) and (–3, –18)
(C) (3, 12) and (–3, – 12)
(D) None of these

27. If R = {(1, 2), (2, 1)}, then R–1 is:
(A) {(2, 1), (2, 2)}
(B) {(1, 1), (2, 2)}
(C) {(1, 2), (1, 1)}
(D) {(2, 1), (1, 2)}

28. If

29. The tangent to the curve y = e3x at the point (0, 2) meets x-axis at :
(A) (0, 1)
(B) (-2/3 , 0)
(C) (2, 0)
(D) (0, 2)

30. Consider the set A = {3, 5, 7}. The number of reflexive relations on set A is :
(A) 2¹²
(B) 12²
(C) 2⁸
(D) 4²

31. If the equation of tangent at (2, 3) on the curve y² = ax³ + b is y = 4x – 5. Then the value of a is :
(A) 2
(B) –2
(C) ±2
(D) √2

32. If A =

33. A feasible solution of a L.P.P. is said to be:
(A) Constraints
(B) Optimal
(C) Variables
(D) None

34. The slope of tangent at y = 8x³ – 4x – 15 sinx at x = 0, is:
(A) 19
(B) –19
(C) –18
(D) 18

35. If A =

36. The principal value of sin -1(1/√2) is :
(A) π/3
(B) π/4
(C) 2π/3
(D) π/6

37. Let R be the relation in the set of integers Z given by R = {(a, b); 2 divides a – b}, then R is :
(A) Symmetric
(B) Transitive
(C) Reflexive
(D) None of these

38. The value of x for the given determinant

(A) 1/2 or -3
(B) 1/2 or 3
(C) -1/2 or 3
(B) -1/2 or 3

39. The point at which the tangents to the curve y = x⁴ – 32x + 37 are parallel to x-axis, is:
(A) (2, 11)
(B) (–2, 11)
(C) (–2, –11)
(D) (2, –11)

40. If matrix A = [3 4 5]. Then A A’ will be (‘where A’ is the transpose of matrix A).
(A) 4
(B) 21
(C) 50
(D) 28

SECTION-C

In this section, attempt any 8 questions. Each question is of 1-mark weightage.
Questions 46-50 are based on a Case-Study.

41. In LPP, if Z = 6x + 10y, subject to x + 2y ≥ 10, 2x + 2y ≥ 12, 3x + y ≥ 8, x ≥ 0, y ≥ 0.
Then the minimum value of Z occurs at :
(A) (10, 0)
(B) (1, 5)
(C) (0, 8)
(D) (2, 4)

42. Maximum slope of the curve y = –2x³ + x² + 8x – 25 is :
(A) 0
(B) 4
(C) 16
(D) 32

43. The slope of the normal to the curve y = 8x³ at x = 2; is
(A) -1/95
(B) -1/96
(C) 1/95
(D) -1/90

44. The corner points of the feasible region determined by the system of linear constraints are (40, 0), (20, 30), (60, 20), (60, 0). The objective function is Z = 5x + 3y.
Compare the quantity in Column A and Column B

(A) The quantity in column A is greater.
(B) The quantity in column B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined on the basis of the information supplied.

45. The value of x for determinant

(A) -1/2
(B) -1/4
(C) -1/3
(D) -1/5

CASE-STUDY

A right circular cylinder is inscribed in a cone.

S = Curved Surface Area of Cylinder.

46. r/r1 = ?
(A) h – h₁/h₁
(B) h₁ – h/h₁
(C) h – h₁/h₁
(D) h + h₁/h₁

47. The value of ‘S’ is:
(A) 2πr/h (h₁ – h)h
(B) 2πr/h₁(h₁ – h)h
(C) 2πr₁/h₁(h₁ – h)h
(D) 2πr₁/h₁(h₁+ h)h

48. The value of dS/dh is:
(A) 2πr₁/h (h₁ – 2h)
(B) 2πr₁/h₁(h – 2h₁)
(C) 2πr/h(h₁ – 2h)
(D) 2πr₁/h₁ (h₁ – 2h)

49. The value of d²s/dh² is:
(A) – 4πr₁/h₁
(B) – 4πr/h
(C) – 4πr₁/h
(D) 4πr₁/h

50. The relation between r1 and r is:
(A) r₁ = r/2
(B) 2r₁ = 3r
(C) r₁ = 2r
(D) r₁/2 = r/3