# CBSE Class 12 Mathematics Term 1 Sample Paper Set D

See below CBSE Class 12 Mathematics Term 1 Sample Paper Set D 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 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 branch of cosec–1 is …A… Here, A refers to
(a) (-π/2 , π/2)
(b) [-π/2 , π/2]
(c) [-π/2 , π/2] – {0}
(d) (-π/2 , π/2) – {0}

C

2. The value of sin{1/2 cot-1(tan cos-1√3/2)} is
(a) √3/2
(b) 1/√2
(c) 1/2
(d) None of these

C

3. If A is an invertible matrix of order 3 and|A|= 2, then the value of det (A -1) is
(a) -1/2
(b) 1/4
(c) 2/3
(d) 1/2

D

4. If aij = 1/2(3i + 2i) and A = [aij] 2×2 , then a21 + a22 is equal to
(a) 1
(b) 8
(c) 9
(d) -1

C

5. The points on the curve y = x3 at which the slope of the tangent is equal to the y-coordinate of the points, are
(a) (0, 0) and (27,3)
(b) (0, 0) and (3, 27)
(c) (2, 3) and (27, 14)
(d) (3 , 2) and (14, 27)

B

6. The region represented by the system of inequation x, y ≥ 0, x + 2y ≤ 2 and x + 2y ≤ 8 is
(b) unbounded in Ist and IInd quadrant
(d) None of the above

C

7. If A =

then k is equal to
(a) -1
(b) 0
(c) 2
(d) 1

D

8. If A =

then the value of det (AB) is
(a) 28
(b) 7
(c) – 28
(d) 4

C

9. The value of cos-1(cos 7π/6) is
(a) π/6
(b) -π/6
(c) 7π/6
(d) 5π/6

D

10. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} Choose the correct answer.
(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

11. The minimum value of Z, where Z = 2x + 3y, subject to constraints 2x + y ≥ 23, x + 3y ≤ 24 and x, y ≥ 0, is
(a) 10
(b) 23
(c) 33
(d) 48

B

12. The slope of the tangent to the curve y = x3 – x at x = 2 is
(a) 5
(b) 6
(c) 7
(d) 11

D

13. If A is any square matrix of order 3 x 3 such that|A|= 9, then the value of|adj A|is
(a) 3
(b) 81
(c) 9
(d) 27

B

14. Let f : Z → Z be a function given by f (x) = x + 2. Then, f (x) is
(a) one-one
(b) one-one and onto
(c) neither one-one nor onto
(d) None of these

B

15. The feasible region of a LPP is shown in following figure. Let Z = 3x – 2y be the objective function. Minimum of Z occurs at

(a) (4, 0)
(b) (0, 5)
(c) (5, 4)
(d) (0, 0)

B

16. If A’ is the transpose of a square matrix A, then
(a) |A|¹|A’|
(b) |A|=|A’|
(c) |A|+|A’|= 0
(d) |A|=|A’|only, when Ais symmetric

B

17. If y = log (tan x), then dy/dx at x = π/4 is equal to
(a) 1
(b) 2
(c) 3
(d) 4

B

18. If 2

then (x – y) is equal to
(a) 2
(b) -1
(c) 1
(d) 0

D

19. The feasible region for an LPP is shown in the following figure. Minimum of Z = 2x + y is

(a) 11
(b) 6
(c) 3
(d) 8

D

20. The equation of normal to the curve y = (x – 1)2 at (2, 1) is given by
(a) x +2y = -4
(b) x +2y = 4
(c) x -2y = 4
(d) None of these

B

Section B

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

21. If the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) :|a – b |< } 2 2 8 , then number of elements in R is
(a) 8
(b) 9
(c) 10
(d) 11

D

22. The value of k for which the following function is continuous at x = 3

(a) 1
(b) 3
(c) 4
(d) 12

A

23. If the following function f (x) is continuous at x = 0, then the value of k is

(a) 5/2
(b) 1/2
(c) 3/2
(d) 0

A

24. The principal value of sec-1 2 is ..A.. Here, A refers to
(a) π/3
(b) π/6
(c) -π/3
(d) 2π/3

A

25. The function given by f(x) = log x/x has maximum at
(a) x = e
(b) x = 1
(c) x = 2
(d) None of these

A

26. If the function f be given by f(x) = (x+2)e-x , then
(a) f is increasing in (- ∞, – 1]
(b) f is decreasing in [- 1, ∞)
(c) Both (a) and (b) are true
(d) Both (a) and (b) are false

C

27. The equation of the normal to the curve y = x (2 – x) at the point (2, 0) is
(a) x +2y = 2
(b) x -2y = 2
(c) 2x + y = 4
(d) None of the above

B

28. If the graphical form of an LPP is as follows

The coordinate of the corner point A of the feasible region of the LPP is
(a) (40, 15)
(b) (15, 15)
(c) (2, 70)
(d) None of these

A

29. The point on the curve x2 + y2 = a2 and y ≥ 0 at which the tangent is parallel to X-axis, is
(a) (0, a)
(b) (a , 0)
(c) (a/2 , √3/2 a)
(d) (- a, 0)

A

30. The feasible region of an LPP is given below

The square root of maximum of Z, where Z = x + 2y, is
(a) 20
(b) 21
(c) 24
(d) 25

A

31. If A =

then A2 – 4A is equal to
(a) 2 I3
(b) 3 I3
(c) 4I3
(d) 5I3

D

32. The line y = x + 1 is a tangent to the curve y2 = 4x , then the point of contact is
(a) (1, 2)
(b) (2, 1)
(c) (1, – 2)
(d) (- 1, 2)

A

33. If

then the value of x is
(a) 0
(b) 2/3
(c) 5/4
(d) -5/4

C

34. The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq units. Then, the value of k will be
(a) 9
(b) 3
(c) -9
(d) 6

B

35. 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) neither transitive nor reflexive but symmetric

B

36. Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? If g is described by g(x) = ax + b, then the value which should be assigned to a and b is
(a) g is a function and α = 2 and β = -1
(b) g is a function and α = -1 and β = 2
(c) g is a function and α = 1 and β = -1
(d) g is not a function

A

37. If a and b are positive numbers such that a > b, then the minimum value of a secθ – b tanθ, (0<θ < π/2) is
(a) √a2 – b2
(b) √a2 + b2
(c) 1/√a2 – b2
(d) 1/√a2 + b2

A

38. If 12 is divided into two parts such that the product of the square of one part and the fourth power of the second part is maximum, then its parts are
(a) 5 and 7
(b) 6 and 6
(c) 3 and 9
(d) 4 and 8

D

39. If y = sec (tan-1 x) , then dy/dx is equal to
(a) xy/1+x2
(b) xy√1+x2
(c) x/√1+x2
(d) None of these

A

40. If A = {1, 2, 3,K, n} and B = {a, b}. Then, the number of surjections from A into B is
(a) nP2
(b) 2n -2
(c) 2n -1
(d) None of these

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. If f : (-1, 1) → R be a differentiable function with f (0) = – 1 and f ‘ (0) = 1. Let g(x) = [ f(2f (x) + 2)] 2 . Then, g’ (0) is equal to
(a) 4
(b) -4
(c) 0
(d) -2

B

42. If x2/3 + y2/3 = a2/3 , then dy/dx is equal to
(a) -3√y/x
(b) 3√y/x
(c) y/x
(d) None of these

A

43. If B =

A

44. If f(x) =

is continuous at x = 0, then the value of k is
(a) 1
(b) -2
(c) 2
(d) 1/2

C

45. The maximum value of [x(x-1) + ]1/3 , where 0 ≤ x ≤ 1 is
(a) (1/3)1/3
(b) 1/2
(c) 1
(d) zero

C

CASE STUDY

If A = [aij ] be an m´ nmatrix, then the matrix obtained by interchanging the rows and columns of Ais called the transpose of A.
A square matrix A = [aij ] is said to be symmetric, if AT = A for all possible values of i and j.
A square matrix A = [aij ] is said to be skew-symmetric, if AT = -A for all possible values of i and j.
Based on above information, answer the following questions.

46. The transpose of matrix [1 – 2 – 5] is

A

47. (ABC)T is equal to
(a) CT BT AT
(b) AT BT
(c) AT BT C
(d) BT CT AT

A

48. For any square matrix A with real number entries
(a) A A+ T is skew-symmetric matrix
(b) A A+ T is symmetric matrix
(c) A A+ T is symmetric as well as skew-symmetric matrix
(d) None of the above

B

49. Any square matrix can be expressed as
(a) difference of a symmetric and a skew-symmetric matrix
(b) sum of two symmetric matrices
(c) sum of a symmetric and a skew-symmetric matrix
(d) sum of two skew-symmetric matrices