# Class 12 Mathematics Sample Paper Term 1 Set F

Section A

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

1. If y = log x2 , then dy/dx at x = 2 is equal to
(a) 1
(b) 2
(c) 3
(d) 0

A

2. If A =

then 2x equals
(a) 2
(b) 1/2
(c) 1
(d) 1/2

C

3. The value of cos-1(cos 7π/6) is
(a) 7π/6
(b) π/6
(c) 5π/6
(d) None of these

C

4. The relation ‘has the same father as’ over the set of children is
(a) only reflexive
(b) only symmetric
(c) only transitive
(d) an equivalence relation

D

5. The elements aij of a 3 x 3 matrix are given by aij = 1/2 |-3i + j| , then 2/7 a32 is equal to
(a) 0
(b) 1
(c) 2
(d) 3

B

6. If y = 3e2x + e-x and d2y/dx2 – y = ke2x , then k is equal to
(a) 1
(b) 2
(c) 9
(d) 8

C

7. Consider the linear programming problem.
Maximise Z = x + 3y ; Subject to the constraints x + y ≤ 40, x + y ≤ 90 and x, y ≥ 0, then maximum value of Z is
(a) 0
(b) 50
(c) 90
(d) does not exists

A

8. The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 20), (10, 20), (30, 10), (30, 0). The objective function is Z = 2x + 3y. Compare the quantity in Column A and Column B.

(a) The quantity in column A is greater
(b) The quantity in column B is greater
(c) The two quantities are equal
(d) The relationship cannot be determined on the basis of information supplied

A

9. If x = (t – 1)(t2+1+t) and y = (1-t)(1+t) , then dy/dx at t = -2/3 is equal to
(a) 0
(b) 5
(c) 1
(d) -2

C

10. If ay2 + bx2 + c = 0 , then dy/dx at (a, b) is equal to
(a) 2
(b) 3
(c) 0
(d) -1

D

11. If

then the value of x2+1/2 is
(a) 10
(b) 20
(c) 15
(d) 1

A

12. The matrix

(a) diagonal matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) scalar matrix

C

13. If A =

then AA’ is equal to

D

14. Let X = {0, 1, 2, 3, 4, 5} and Y = {-4, – 1, 0, 1, 4, 9, 16, 25} and f :X → Y defined by y = x2 , is
(a) one one onto
(b) one one into
(c) many one onto
(d) many one into

B

15. The function f : R → R given by f (x) = x3 + 1 is
(a) one-one but not onto
(b) onto but not one-one
(c) bijection
(d) neither one-one nor onto

C

16. If A =

then which of the following result is true
(a) A2 = I
(b) A2 = -I
(c) A2 = 2 I
(d) None of these

B

17. If Δ =

then Δ is equal to
(a) a2 + b2 + c2 + d2
(b) a2 – b2 – c2 – d2
(c) a2 – b2 + c2 – d2
(d) a2 – b2 – c2 +d2

A

18. Corner points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0) and (0, 5).
Let Z = 3x + 2y be the objective function. Then, MaximumZ -MinimumZ is equal to
(a) 20
(b) 16
(c) 14
(d) 18

C

19. The minimum value of y = x4 + 1 is
(a) 1
(b) 0
(c) – 1
(d) None of these

A

20. If A =

(a) 13
(b) 12
(c) 26
(d) 0

A

Section B

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

21. If y = √x2 + 1 + 1/√x+1 , then dy/dx at x = 1 is equal to
(a) 3/√2
(b) 3/4√2
(c) 4/3
(d) None of these

B

22. The feasible solution for a LPP is shown in following figure. Let Z = 3x + y be the objective function. Maximum of Z occurs at

(a) (7, 4)
(b) (5, 3)
(c) (0, 4)
(d) (3, 6)

A

23. If matrix A =

and A2 = λ/2 A , then the value of λ is
(a) 12
(b) 10
(c) 11
(d) 14

A

24. The relation R defined on the set N of natural number xRy ⇔ 2x2 – 3xy + y2 = 0 is
(a) symmetric but not reflexive
(b) only symmetric
(c) not symmetric but reflexive
(d) None of these

C

25. If

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

B

26. If A + B =

then B is equal to

A

27. If A =

then the value of|2A|- 4|A|is equal to
(a) – 1
(b) 2
(c) 1
(d) 0

D

28. The value of x for which matrix

is singular are
(a) 4, 1
(b) – 4, 1
(c) 2, 1
(d) None of these

B

29. If the points (0, 2), (1, x) and (3, 1) are collinear, then the value of x is
(a) 3/5
(b) 5/3
(c) 1
(d) 0

B

30. A and B are invertible matrices of the same order such that|(AB)-1 |= 8, if|A|= 2, then |B|is
(a) 16
(b) 4
(c) 6
(d) 1/16

D

31. If A =

then the determinant value of A2 – 2A is
(a) 15
(b) 25
(c) 10
(d) 14

B

32. If A is a non-singular matrix of order 3 and|A|= – 8, then the value of|adj A|is
(a) – 8
(b) 64
(c) – 64
(d) 24

B

33. If A =

then A-1 is equal to

A

34. If the function f(x) =

is continuous at x = 2, then the value of k is
(a) 1
(b) 2
(c) 3
(d) 4

C

35. If y = log x, then d3y/dx3 is equal to
(a) 3/x2
(b) 2/x
(c) 2/x3
(d) 1

C

36. Let f(x) =

then at x = 1
(a) LHL = RHL
(b) LHL ≠ RHL
(c) LHL = f (1)
(d) None of these

B

37. Let f : R → R be a function such that f (x) = x3 + 3x2 + 5x + sin x , then f (x) is
(a) an increasing function
(b) decreasing function
(c) neither increasing nor decreasing function
(d) None of these

A

38. The function f (x) = log(cos x) on the interval (0,π/2) is
(a) Increasing
(b) Strictly decreasing
(c) Strictly increasing
(d) None of these

B

39. The slope of the normal to the curve y = 2x2 + 3x sin at x = 0 is
(a) 3
(b) 1/3
(c) – 3
(d) -1/3

D

40. The slope of the normal to the curve x = 1 – a sinq, y = b cos2 θ at θ = π/2 is
(a) a/2b
(b) -a/2b
(c) b/2a
(d) -b/2a

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. Let r be the relation on the set R of all real numbers defined by setting arb iff |a – b|≤ 1/2 .
Then, ρ is
(a) reflexive and symmetric but not transitive
(b) symmertic and transitive but not reflexive
(c) transitive but neither reflexive nor symmetric
(d) None of the above

A

42. If A2 + A + I = 0 then A-1 is equal to
(a) A- I
(b) I – A
(c) – (A+ I)
(d) None of these

C

43. If the function f(x) =

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

C

44. The function f (x) = 2x3 – 3x2 – 36x + 7 is strictly decreasing in the interval
(a) (- ∞, – 2)
(b) (- 2, 3)
(c) (3, ∞)
(d) None of these

B

45. The point on the curve y = (x – 3)2 , where the tangent is parallel to the chord joining (3, 0) and (4, 1) is
(a) (-7/2 , 1/4)
(b) (5/2 , 1/4)
(c) (-5/2 , 1/4)
(d) (7/2 , 1/4)

D

CASE STUDY

Ronit and Aman, two friends are standing on either side of a tower of 30 m high. They observe its top at the angle of elevation α and β respectively. (as shown in the figure below).
The distance between Ronit and Aman is 40√3 m and distance between Ronit and tower is 30 √3 m.

Based on the above information, answer the following questions.

46. ∠ART = α is equal to
(a) cos-1(4/5)
(b) cos-1(√3/2)
(c) cos-1(2/5)
(d) cos-1(1/5)

B

47. ∠ART = α is equal to
(a) sin-1(1/2)
(b) sin-1 2
(c) sin-1(√3/2)
(d) sin-1(2/√3)

A

48. ∠TAR = β is equal to
(a) tan-1(√3)
(b) tan-1(1/2)
(c) tan-1(2)
(d) tan-1(1/3)

A

49. ∠ATR is equal to
(a) π/2
(b) π/3
(c) π/4
(d) π/6