# CBSE Class 12 Mathematics Term 1 Sample Paper Set B

See below CBSE Class 12 Mathematics Term 1 Sample Paper Set B 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 B

SECTION-A

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

1. What is the principal value of sin-1(1/2) ?
(A) π/8
(B) π/6
(C) π/12
(D) π/3

B

2. What is dy/dx of the given function where y = ex log(sec x) ?
(A) y = excotx
(B) y = ex (cotx + log secx)
(C) y = ex (cotx + log secx)
(D) ex (log (secx) + tanx)

D

3. If A = [aij]3×3 is a square matrix so that aij = i2 – j2 then A is:
(A) Unit matrix
(B) Symmetric matric
(C) Skew symmetric matrix
(D) Orthogonal matrix

C

4. Calculate the value of the given equation 2C11 + C12 – C13 where Cij is the cofactor of the aij element of the matrix A =

(A) Determinant of the given matrix
(B) 0
(C) 10
(D) None of the above

B

5. Find the slope of tangent at y = 7x3 – 3x – 5 sinx at x = 0 ?
(A) 0
(B) –2
(C) –4
(D) –8

D

6. All square matrices are invertible, that is the inverse of all the square matrices exist. Is the statement correct?
(A) Yes
(B) No
(C) No, all matrices has inverse
(D) None of the above

B

7. Total number of equivalence relations defined in the set S = {1,2} is
(A) 2
(B) 3!
(C) 23
(D) 33

A

8. If A =

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

A

9. What is the local maximum value of the function in the interval y = 2sin2x – 2x ∈ (0,π/2) ?
(A) No local maximum value in the given interval
(B) 0
(C) 1
(D) 2

A

10. What is the principal value of cos-1(1/2) ?
(A) π/8
(B) π/6
(C) π/12
(D) π/3

D

11. Let us define a relation R in R as aRb if a > b. Then R is
(A) an equivalence relation
(B) reflexive, transitive but not symmetric
(C) symmetric, transitive but not reflexive
(D) transitive relation

D

12. If y = 2cos2 θ/sin2 θ – cos2 θ , then dy/dx will be
(A) y = 2 cos θ /sin θ – cos2 θ
(B) y = sin θ/sin2 θ – tan θ
(C) 0
(D) y = cosθ tanθ/sin2 θ – cos 2θ

C

13. The given matrix is A =

, find the numbers a and b such that A2 + aA + bI = 0
(A) 2, 4
(B) 1, 9
(C) –4, 1
(D) 3, 3

C

14. If y = 5e5x – 3 then which of the following is true?
(A) d2y/dx2 – 25y = 0
(B) d2y/dx2 + 25y = 0
(C) d2y/dx2 + 625y = 0
(D) d2y/dx2 – 125y = 0

D

15. If A and B are two matrices such that AB exists, then
(A) may or may not exist
(B) always exist
(C) Exist
(D) None of these

A

16. Which of the following functions are increasing in the interval (1,1000)
(A) logx
(B) cosx
(C) sinx
(D) 1/ x

A

17. The area of a triangle formed by the coordinates (1, –1), (2, 1) and (4, 5) is :
(A) 5 units
(B) 15 units
(C) 10 units
(D) 0 units

A

18. Which of the following is the following is not continuous in R?
(A) ex
(B) cosx
(C) f–1(x)
(D) All are continuous

D

19. A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 15 units of carbohydrate, at least 17 units of protein and at most6 units of fat. The nutrient contents of 1kg food is given below:

1 kg of food X costs `16 and 1 kg of food Y cost`20. Find the least cost of the mixture which will
produce the required diet.

(A) 100
(B) 128
(C) 110
(D) 99

A

20. Find the absolute maximum of the given function x3 – 2x in the interval [1, 3] ?
(A) 25
(B) 23
(C) 22
(D) 21

D

SECTION-B

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

21. Let a function f : N → N given by f(x) = 2x, then f(x) is
(A) noto
(B) one-one and onto
(C) one-one
(D) None of these

C

22. The derivative of cos–1(2x2 – 1) w.r.t. cos–1x is
(A) 2
(B) -1/2√1-x2
(C) 2/x
(D) 1 – x2

A

23. In which of the following, the constraints of a linear function has to be maximized or minimized according to a set of given conditions
(A) Constraints
(B) Objective functions
(C) Decision variables
(D) Feasible solutions

B

24. If y = loge(x2/e2) , then d2y/dx2 equal to
(A) -1/x
(B) -1/x2
(C) 2/x2
(D) -2/x2

D

25. Given A =

(A) 2A–1 = 9I – A
(B) 2A–1 = 9I + A
(C) 2A–1 = 9I – 2A
(D) None of these

A

26. Find the point at which slope of the tangent to the curve y = x2 – 1 become parallel to a line with inclination 45° with positive x-axis?
(A) x = 1/2
(B) x = 1
(C) y = -1/2
(D) x = 2

A

27. Range of sin–1x is ….
(A) [–3π/2, –π/2]
(B) [–π/2, π/2]
(C) [π/2, 3π/2]
(D) All of the above

D

28. Let A be a non-singular square matrix of order 3 × 3. Then |adj A| is equal to
(A) |A|
(B) |A|2
(C) |A|3
(D) 3|A|

B

29. If f (x) = 3x + x3 – 1/8 sin2x , then the Function in (0.5, 3)
(A) Increasing
(B) Decreasing
(C) Constant
(D) Neither increasing nor decreasing

A

30. Let A be set of 50 files placed in a rack. Let f : A → N be a function defined by f(x) = Code number mentioned on the file The given function is
(A) one-one
(B) onto
(C) one-one and onto
(D) onto but not one-one

A

31. If

(A) Continuous
(B) Discontinuous
(C) Limit does not exist
(D) Differentiable

B

32. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is :
(A) 27
(B) 18
(C) 81
(D) 512

D

33. The restrictions on the variables of linear programming problems are called
(A) Optimization problem
(B) Feasible region
(C) Infeasible region
(D) Constraints

D

34. The equation of tangent to the curve y = sin x at the point (0, 0) is
(A) y = – x
(B) y = 2x
(C) y = x
(D) y = 1/2 x

C

35. Assume X, Y, Z, W and P are matrices of order 2 × π, 3 × k, 2 × p, π × 3 and p × k, respectively. The restriction on n, k and p so that PY + WY will be defined are :
(A) k = 3, p = n
(B) k is arbitrary, p = 2
(C) p is arbitrary, k = 3
(D) k = 2, p = 3

A

36. The domain of sin–1x is
(A) [1, 2]
(B) [–1, 1]
(C) [1, ∞]
(D) [–∞, 1]

B

37. Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is
(A) 1
(B) 2
(C) 3
(D) 4

A

38. If A is an invertible matrix of order 2, then det (A–1) is equal to
(A) det(A)
(B) 1/det(A)
(C) -1/3
(D) 3

B

39. The slope of normal to the curve x2 + 2y + y2 = 0 at (– 1, 2) is
(A) – 3
(B) 1/3
(C) -1/3
(D) 3

B

40. Consider the system of equations: x + y + z = 2; 2x + y – z = 3 and 3x + 2y + kz = 4. The system of equations has unique solution if
(A) k ≠ 1
(B) k ≠ –1
(C) k ≠ 0
(D) k ≠ 2

C

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. The objective function in a LPP is always
(B) Linear
(C) Constant
(D) Cubic

B

42. The function f(x) = x3 – 3x2 + 6x – 100 is the set of real numbers.
(A) Increasing
(B) Strictly increasing
(C) Neither increasing
(D) Strictly decreasing

B

43. Consider the function f(x) = sin4x + cos4x. f(x) is decreasing in

B

44. Z = 30×1 + 30x2, subject to x1 > 0, x2 > 0, x1 + 3x2 < 6, 4x1 + 8x2 > 16, x1 + x2 < 4. The minimum value of Z occurs at
(A) (3, 0)
(B) (2, 1)
(C) (0, 2)
(D) (4, 0)

C

45. If the matrix P =

is a symmetric matrix, then the value of a and b.
(A) a = -2/3 , b = 1/2
(B) a = -1/2 , b = 2/3
(C) a = -2/3 , b = 3/2
(D) a = 1/3 , b = -2/3

C

CASE-STUDY

Raj’s father wanted to construct a fence around the rectangular garden with one side open. The total area of fencing needed in 300 sq ft. Based on the information furnished above answer the following problem.

46. In order to construct the garden with 300 sq ft of fencing what should be maximized
(A) Volume
(B) Area
(C) Perimeter
(D) Length of the side

B

47. If the length of the side of the garden which is perpendicular to the wall is x and y denotes the parallel side then the total amount of fence wire can be represented mathematically as:
(A) x + 2y = 150
(B) x + 2y = 100
(C) x + 2y = 200
(D) 2x + y = 300

D

48. The area when represented in terms of x will have the value of
(A) 300 – x2
(B) 300 + x2
(C) 300 – 2x2
(D) None of the above

C

49. The maximum value of the area is calculated as:
(A) 10000 sq ft
(B) 12000 sq ft
(C) 11250 sq ft
(D) 10500 sq ft