# Class 12 Mathematics Sample Paper Term 2 With Solutions Set B

Please refer to Class 12 Mathematics Sample Paper Term 2 With Solutions Set B below. These Class 12 Mathematics Sample Papers will help you to get more understanding of the type of questions expected in the upcoming exams. All sample guess papers for Mathematics Class 12 have been designed as per the latest examination pattern issued by CBSE. Please practice all Term 2 CBSE Sample Papers for Mathematics in Standard 12.

## Sample Paper Term 2 Class 12 Mathematics With Solutions Set B

SECTION-A

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

1. The value of tan-1[2 cos(2 sin-1 1/2)] is:
(A) π/3
(B) π/4
(C) π/2
(D) 3π/4

B

2. If y = Ae5x + Be–5x, then d2y/dx2 is equal to
(A) 25y
(B) 5y
(C) – 25y
(D) 15y

A

3. If

(A) 0
(B) 2
(C) –1
(D) 3

D

4. If A is a square matrix of order 3, such that A(adj A) = 8I, then |adj A| is equal to
(A) 1
(B) 8
(C) 64
(D) 8I

C

5. A ladder, 5 metre long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metre from the wall is :

D

6. If A =

(A) λ = 2
(B) λ ≠ 2
(C) λ ≠ –1
(D) None of these

C

7. Let R be the relation in the set {p, q, r} given by R = {(p, p), (q, q), (r, r), (p, q)}. Then
(A) R is reflexive and symmetric but not transitive
(B) R is reflexive and transitive but not symmetric
(C) R is symmetric and transitive but not reflexive
(D) R is an equivalence relation

B

8. The additive inverse of matrix A =

B

9. A particle moves along the curve x2 = 3y. The point at which, ordinate increases at the same rate as the abscissa is ________
(A) (3, 2)
(B) (3/4 , 3/2)
(C) (3/2) , (3/2)
(D) (3/2) , (3/4)

D

10. The value of sin-1(cos 3π/5) is
(A) π/10
(B) 3π//5
(C) -π/10
(D) -3π/5

C

11. Consider the set A = {1, 3, 5}. The number of reflexive relations on set A is:
(A) 25
(B) 26
(C) 28
(D) 29

B

12. If (2x + 3)5 then dy/dx is equal to
(A) 10(2x + 3)4
(B) 6(2x + 3)4
(C) 3(2x + 3)4
(D) 2(2x + 3)4

A

13. If A =

(A) 14
(B) 10
(C) 0
(D) –10

B

14. If x = t2 and y = t3 then d2y/dx2 is
(A) 3/2
(B) 3/4t
(C) 3/2t
(D) 3/4

B

15. For matrix A =

B

16. The tangent to the curve y = e4x at the point (0, 5) meets x-axis at :
(A) (0, 5)
(B) (-5/4 , 0)
(C) (5, 0)
(D) (0, –5)

B

17. If A is a square matrix such that A2 = A, then (I + A)2 – 3A is:
(A) 2I
(B) 3I
(C) I
(D) 4I

C

18. If y = (x3 + cot x), then d2y/dx2 is:
(A) 6x + 2cosec2x cotx
(B) 6 + 2cosec2x cotx
(C) 6x + 2cosecx cotx
(D) 6x2 + 2cosecx cotx

A

19. The feasible solution for a LPP is shown in given figure. Let Z = 3x – 4y be the objective function maximum of Z occurs at

(A) (0, 0)
(B) (0, 8)
(C) (5, 0)
(D) (4, 10)

C

20. The total revenue received from the sale of x units of a product is given by R(x) = 4x2 + 28x + 13 in rupees. The marginal revenue when x = 4 is:
(A) 66
(B) 60
(C) 64
(D) 68

B

SECTION-B

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

21. Let f : R → R be defined as f(x) = x4. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto

D

22. If y = 3e2x + 2e3x, then d2y/dx2 + 6y is:
(A) 1
(B) 6(e2x + e3x)
(C) 0
(D) 6(2e2x + 3e3x)

C

23. The feasible region for an LPP is shown in the given Figure. Let F = 3x – 4y be the objective function.

minimum value of F is
(A) 0
(B) 8
(C) –16
(D) –18

C

24. If y = cot-1(√1 + x2 + x , then dy/dx is:
(A) 1/2(1+x2)
(B) -1/2(1+x2)
(C) -1/1+x2
(D) 1/1+x2

B

25. If A =

A

26. A man is walking at the rate of 6.5 km/hr towards the foot of a tower 120 m high. At what rate is he approaching the top of the tower when he is 50 m away from the tower?
(A) 2 km/h
(B) 3 km/hr
(C) 2.5 km/hr
(D) 3.5 km/hr

C

27. The value of sin-1 [cos(66π/5)] is
(A) 3π/5
(B) -7π/5
(C) π/10
(D) -π/10

D

28. The value of x, if

(A) ±1
(B) ±2
(C) ±3
(D) ±4

D

29. The point on the curve y = 2x2 – 6x – 4 at which the tangent is parallel to the x-axis; is:
(A) (3 , -17/2)
(B) (3/2 , -17)
(C) (3, –17)
(D) (3/2 , -17/2)

D

30. If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5), (3, 6)} is a function from A to B.
(A) onto function
(B) one-one function
(C) many one
(D) None of these

B

31. If the function f(x) =

(A) 4
(B) 5
(C) 6
(D) 8

C

32. If A =

A

33. Z = 25x1 + 20x2, subject to x1 ≥ 0, x2 ≥ 0, x1 + x2 ≥ 8, x1 + 2x2 ≥ 12, 5x1 + 2x2 ≥ 15. The minimum value of Z occurs at
(A) (8, 0)
(B) (52,154)
(C) (72,94)
(D) (0, 8)

D

34. The equation of the normal to the curve y = 2×2 + 5sin x at x = 0, is:
(A) x + 6y = 0
(B) x + 5y = 0
(C) x + 8y = 0
(D) x + 10y = 0

B

35. If

(A) 2
(B) 4
(C) 0
(D) 1

A

36. The value of sin-1(1/2) + cos-1 (0) + 3tan -1 (1) will be:
(A) 12π/23
(B) π/2
(C) 23π/12
(D) 12 π/31

C

37. What is the Principal value of cot-1(-1/√3) ?
(A) π/3
(B) 2π/3
(C) π/6
(D) 3π/2

B

38. Let A be a 2 × 2 matrix. Then |adj A|=
(A) A
(B) A2
(C) |A|
(D) None of these

C

39. The side of a square sheet is increasing at the rate of 4 cm/min. At what rate is the area increasing when the side is 8 cm long?
(A) 80 cm2/min
(B) 84 cm2/min
(C) 64 cm2/min
(D) None of these

C

40. If A =

D

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. Corner points of the feasible region for an LPP are (3, 0), (6, 0), (6, 8) and (0, 5) and F = 4x + 6y be the objective function. The difference of the maximum and minimum value of F is
(A) 84
(B) 12
(C) 72
(D) 60

D

42. The equation of tangent to the curve y = 2 + sin x at the point (0, 0) is:
(A) 2x + y = 0
(B) 2x – y = 0
(C) x + y = 0
(D) y – x = 0

A

43. Equation of tangent to the curve y = –6x2 + 5x + 8 at the point (0, 0) is:
(A) y = 5x
(B) y = –5x
(C) x = 5y
(D) x = –5y

A

44. In LPP objective function is given by Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≤ 0, y ≥ 0. And corner points of feasible region are (3, 0), (7, 0) and (0,5), the minimum value of Z is:
(A) 21
(B) 49
(C) 6
(D) 5

D

45. If the matrix A =

(A) 0
(B) 3
(C) –1
(D) 4

C

CASE-STUDY

There are three families A, B and C. The number of members in these families are given in the table below.

The daily expenses of each man, woman and child are respectively ₹ 200, ₹100 and ₹50.

46. The total daily expense of family A is _______.
(A) 850
(B) 900
(C) 1,200
(D) 2,950

A

47. The total daily expense of family C is _______.
(A) 850
(B) 900
(C) 1,200
(D) 2,950

C

48. The combined daily expense of all the women is _______.
(A) 850
(B) 900
(C) 1,200
(D) 2,950

B

49. The family with highest expense is _______.
(A) A
(B) B
(C) C
(D) All have same expense