# Class 12 Mathematics Sample Paper Term 1 With Solutions Set D

Please refer to Class 12 Mathematics Sample Paper Term 1 With Solutions Set D 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 1 CBSE Sample Papers for Mathematics in Standard 12.

## Sample Paper Term 1 Class 12 Mathematics With Solutions Set D

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 is
(a) π/4
(b) -π/4
(c) 3π/4
(d) None of these

C

2. If A =

(a) only ABis defined
(b) only BAis defined
(c) ABand BAboth are defined
(d) ABand BAboth are not defined

C

3. If √1+sin x + √1-sin x/√1+ sin x – √1-sin x = 0 then the value of x is
(a) cot -1 θ
(b) 2cot -1 θ
(c) sin-1 θ
(d) cos-1 θ

B

4. If product of rows and colums of matrix is 8, then number of possible different ordered matrices are
(a) 4
(b) 3
(c) 1
(d) 2

A

5. The interval of increase of the function f(x) = x-ex + tan (2π/7) is
(a) (-∞, 0)
(b) (0,∞)
(c) (1, ∞)
(d) (-∞, 1)

A

6. If A =

then which of the following is defined?
(a) A+ B
(b) B+ C
(c) C + D
(d) B+ D

D

7. If y = sin x/1+sin x , then dy/dx at x = π/2 is equal to
(a) 1
(b) 0
(c) 2
(d) 3

B

8. If

then x is equal to
(a) 6
(b) ± 6
(c) – 6
(d) 0

B

9. If f(x) =

is continuous at x = 0, then the value of α is
(a) 1
(b) 4
(c) 3
(d) -1

C

10. If f(x) = 1-cos x/x2 is continuous at x = 0, then f (0) is equal to
(a) 1
(b) 1/2
(c) 3/2
(d) 4

B

11. If y = sin3 2x, then dy/dx at x = π/2 is equal to
(a) 0
(b) 1
(c) -1
(d) 3

A

12. If the area of a ΔABC, with vertices A(1, 3), B(0, 0) and C(k, 0) is 3 sq units, then the value of k/2 is
(a) ±2
(b) ±1
(c) 4
(d) 5

B

13. The value of tan-1[2sin(2cos-1 √3/2)] is
(a) π/3
(b) 2π/3
(c) -π/3
(d) π/6

A

14. The value of cos-1[cos(13π/6)] is
(a) 13π/6
(b) π/6
(c) π/3
(d) 2π/3

B

15. The minor of a32 of the matrix

(a) 5
(b) -5
(c) 7
(d) 8

B

16. If the points (2, – 3),(k, – 1) and (0, 4) are collinear, then the value of k is
(a) 10/7
(b) 7/140
(c) 47
(d) 40/7

A

17. If y = (1+x1/6)(1+x1/3)(1-x1/6) , then dy/dx at x = 1 is equal to
(a) 2/3
(b) -2/3
(c) 3
(d) -4/3

B

18. The conditions x ≥ 0, y ≥ 0 are called
(a) restrictions only
(b) negative restrictions
(c) non-negative restrictions
(d) None of these

C

19. The sum of minor of 6 and cofactor of 4 respectively in the determinant Δ=

(a) 0
(b) 1
(c) -1
(d) 4

A

20. Let S be any set and P(S) be its power set. We define a relation R on P(S) by ARB which mean A⊆ B∀A, B∈P(S). Then, R is
(a) equivalence relation
(b) only reflexive and transitive
(c) only reflexive and symmetric
(d) None of the above

B

Section B

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

21. f :N → N where f(x) =

(a) one-one and into
(b) many-one and into
(c) one-one and onto
(d) many-one and onto

C

22. If y = logxx , then the value of dy/dx is
(a) xx (1 + logx)
(b) log(ex)
(c) log e/x
(d) log (x/e)

B

23. If y = √sin 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

A

24. The set of points, where the function f given by f (x) =|2x – 1|sin x is differentiable, is
(a) R
(b) R-{1/2}
(c) (0 , ∞)
(d) None of these

B

25. If A =

then A-1 exists, if
(a) λ = 2
(b) λ ¹ 2
(c) λ ≠ -2
(d) None of these

D

26. If x = a secθ and y = a cotθ, then dy/dx at θ = π/4 is equal to
(a) – √2
(b) √2
(c) 1
(d) -1

A

27. Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is
(a) 9
(b) 27
(c) 81
(d) 512

D

28. If A and B are square matrices of the same order and AB = 3I , then A- 1 is equal to
(a) 3 B
(b) 1/3B
(c) 3B-1
(d) 1/3 B-1

B

29. The maximum value of Z = 2x + 4y, if the feasible region for an LPP is as shown below, is

(a) 56
(b) 50
(c) 36
(d) 55

A

30. The curve y = x1/5 has at (0, 0)
(a) a vertical tangent (parallel to Y-axis)
(b) a horizontal tangent (parallel to X-axis)
(c) an oblique tangent
(d) no tangent

A

31. The area of the triangle whose vertices (-2, 6), (3, – 6) and (1, 5) is
(a) 30 sq units
(b) 35 sq units
(c) 40 sq units
(d) 15.5 sq units

D

32. Which of the given values of x and ymake the following pair of matrices equal ?

(a) x = -1/3 and y = 7
(b) not possible to find
(c) y = 7 and x = -2/3
(d) x = -1/3 and y = -2/3

B

33. If y = cos-1 x, then the value of d2y/dx2 in terms of y alone is
(a) – cot y cosec y2
(b) cosec y cot y2
(c) – cot y cosec y
(d) None of these

A

34. The interval in which the function f (x) = 2x3 + 9x2 + 12x – 1 is decreasing, is
(a) [- 1, ∞)
(b) [- 2, – 1]
(c) (- ∞, – 2]
(d) [- 1, 1]

B

35. Let R be the relation on the set R of real numbers defined by R = {(a, b)|1 + ab > 0}.
Then, R is
(a) reflexive, symmetric but not transitive
(b) reflexive, transitive but not symmetric
(c) transitive but not symmetric and reflexive
(d) an equivalence relation

A

36. If f is a function from the set of natural numbers to the set of even natural numbers given by f (x) = 2x. Then, f is
(a) one-one but not onto
(b) onto but not one-one
(c) Both one-one and onto
(d) Neither one-one nor onto

C

37. Corner points of the feasible region for an LPP are (0, 5), (6, 0), (6, 8), (0,2), (3, 0). Let Z = 2x + 3y be the objective function. The minimum value of Z occurs at
(a) only (0, 2)
(b) only (3, 0)
(c) the mid-point of the line segment joining the points (0, 2) and (3, 0)
(d) any point on the line joining the points (0, 2) and (3, 0)

D

38. If y + sin y = cos x, then dy/dx is equal to

C

39. If y = 1 + cos2(x2) , then dy/dx at x = √π/2 is equal to
(a) π
(b) -π
(c) π
(d) – π

D

40. If A =

such that A + A’ = I , then the value of α is
(a) π/6
(b) π/3
(c) π
(d) 3π/2

B

Section C

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

41. The feasible region for an LPP is shown in the following figure. Then, the minimum value of Z = 11x + 7y is

(a) 21
(b) 47
(c) 20
(d) 31

A

42. The tangent to the curve y = e2x at the point (0, 1) meets X-axis at
(a) (0, 1)
(b) (-1/2 , 2)
(c) (2, 0)
(d) (0, 2)

B

43. The function f (x) = 4 sin3 x – 6 sin2 x + 12 sin x + 100 is strictly
(a) increasing in (π,3π/2)
(b) decreasing in (π/2 , π)
(c) decreasing in [-π/2 , π/2]
(d) decreasing in [0,π/2]

B

44. The function f : R → R defined by f(x) = 4x +4|x| is
(a) one-one and into
(b) many-one and into
(c) one-one and onto
(d) many-one and onto

A

45. An optimisation problem may involve finding
(a) maximum profit
(b) minimum cost
(c) minimum use of resources
(d) All of these

D

CASE STUDY

P(x) = -6x2 + 120x + 25000 (in ₹) is the total profit function of a company where x denotes the production of the company.

Based on the above information, answer the following questions.

46. When the profit is maximum, production will be
(a) 8
(b) -8
(c) 10
(d) -10

C

47. The interval in which the profit is strictly increasing in
(a) (0, 10)
(b) (0, 12)
(c) (10, ∞)
(d) (12, ∞)

A

48. The maximum profit is
(a) ₹ 25450
(b) ₹ 25500
(c) ₹ 25550
(d) ₹ 25600

D

49. Value of P'(5) is
(a) 40
(b) 60
(c) 80
(d) 100