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

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

3. If

(A) 0
(B) 2
(C) –1
(D) 3

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

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 :
(A) 1/10 radian/sec
(B) 1/20/radian/sec
(C) 20 radian/sec
(D) 10 radian/sec

6. If A =

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

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

8. The additive inverse of matrix A =

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)

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

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

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

13. If A =

(A) 14
(B) 10
(C) 0
(D) –10

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

15. For matrix A =

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)

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

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

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)

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

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

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

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

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

25. If 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

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

28. The value of x, if

(A) ±1
(B) ±2
(C) ±3
(D) ±4

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)

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

31. If the function f(x) =

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

32. If 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)

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

35. If

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

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

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

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

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

40. If A =

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

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

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

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

45. If the matrix A =

(A) 0
(B) 3
(C) –1
(D) 4

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

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

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

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

50. The combined expense of men in family A and children in family C is _______.
(A) 600
(B) 700
(C) 800
(D) 900