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

Please refer to Class 12 Mathematics Sample Paper Term 1 With Solutions Set C 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 C

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-1(√5/3)] is
(A) 3+√5/2
(B) 3-√5/2
(C) -3+√5/2
(D) -3 – √5/2

B

2. 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

3. If A = [1 –3 5], B =

(A) 
(B) 
(C) 28
(D) 24

B

4. If A is skew symmetric matrix of order 2, then the value of |A| is
(A) 3
(B) 9
(C) 0
(D) 27

C

5. For the curve y = 10x – 2x3, if x increases at the rate of 3 units/sec, then at x = 2 the slope of curve is changing aunits/sec.
(A) 0
(B) –72
(C) 24
(D) 48

B

6. If A is any square matrix of order 3 × 3 such that |A| = 2, then the value of |adj A| is:
(A) 3
(B) 1/3
(C) 4
(D) 27

C

7. The maximum number of equivalence relations on the set A = {6, 7, 8} are
(A) 1
(B) 2
(C) 5
(D) 5

C

8. Which of the given values of x and y make the following pair of matrices equal

(A) x = -1/3 , y = 7
(B) Not possible to find
(C) y = 7 , x = -2/3
(D) x = -1/3 , y = -2/3

C

9. If the curve ay + 2x2 = 8 and 2x3 = y, cut orthogonally at (2, 2), then the value of a is :
(A) 151
(B) 0
(C) 183
(D) 192

D

10. The value of cos -1(cos 3π/2) is
(A) π/2
(B) 3π/2
(C) 5π/2
(D) 7π/2

A

11. Let A = {1, 2, 3, …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

12. If y = loge(x3/e3) , then d2y/dx2 will be
(A) -1/x
(B) -2/x2
(C) 3/x2
(D) -3/x2

D

13. If A =

(A) 0
(B) I
(C) 2I
(D) aI

A

14. If y = log(1 -x4/1 +x4) , then dy/dx is equal to
(A) 4x3/1 – x8
(B) -8x3/1 – x8
(C) 1/4 – x8
(D) -4x3/1 – x8

B

15. If A =

(A) -1/21
(B) 1/21
(C) 1/20
(D) Can’t be determined

B

16. The points at which the tangents to the curve y = x3 – 27x + 20 are parallel to x-axis are :
(A) (2, –2), (–2, –34)
(C) (2, 34), (–2, 0)
(B) (0, 34), (–2, 0)
(D) (3, –34), (–3, 74)

D

17. If A =

C

18. If y = ettant, x = et then dy/dx will be
(A) sec2t + tant
(B) sec2t – tant
(C) sec2t
(D) sect + tant

A

19. Z = 10x + 23y, subject to x + y ≥ 3, x + 5y ≥ 4, 3x + 3y ≥ 4, x ≥ 0, y ≥ 0. The minimum value of Z occurs at
(A) (2.56, 3.56)
(B) (28, 8)
(C) (2.75, 0.25)
(D) (0, 1)

C

20. Maximum slope of the curve y = –x3 + 3x2 + 10x – 32 is :
(A) 0
(B) 13
(C) 16
(D) 32

B

SECTION-B

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

21. If A = {2, 3, 4}, B = {5, 6, 7, 8} and f = {(2, 5), (3, 6), (4, 7)} is a function from A to B, then f(x) is:
(A) One-one function
(B) Many one function
(C) Onto function
(D) None

A

22. Find y1 = dy/dx if xy5 + 2y + 5x = 0 ?
(A) y1 = -(y5+5)/5xy4 + 2
(B) y1 = (y5+5)/5xy4 + 2
(C) y1 = y5+5/5xy4 – 2
(D) y1 = -y5+5/-5xy4 + 2

A

23. The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 20), (10, 20), (30, 20), (40, 0). The objective function is Z = 3x + 4y.
Compare the quantity in Column A and Column B

(A) The quantity in column A is smaller
(B) The quantity in column B is smaller
(C) The two quantities are equal
(D) The relationship cannot be determined On the basis of the information supplied

C

24. If xy = 1, then dy/dx + y2 is equal to :
(A) 1/x
(B) 0
(C) -1/x2
(D) y/x

B

25. The inverse of the matrix

B

26. The equation of the normal to the curve y = 3x2 + 7 sin x at x = 0 is :
(A) x – 7y = 0
(B) 7x + y = 0
(C) x + 7y = 0
(D) x – 7y = 0

C

27. What is the value of sec2 (tan–12) ?
(A) 1
(B) 4
(C) 5
(D) 3

C

28. If

(A) -1/2 , 3
(B) -1/2 , 3
(C) 1/2 , 3
(D) 1/2 , -3

D

29. The radius of a balloon is increasing at the rate of 12 cm/sec. At what rate is the surface area of the balloon increasing when the radius is 10 cm ?
(A) 960 cm2/sec
(B) 960 p cm2/sec
(C) 980 cm2/sec
(D) 980 p cm2/sec

B

30. The function f : R → R, f(x) = x2 is :
(A) One-one
(B) Onto
(C) Not one-one
(D) None

C

31. If the function f(x) =

is continuous at x = 2, then the value of k is :
(A) 1
(B) 2
(C) 3
(D) 4

D

32. If

(A) -3/2 , -3/2
(B) 1/2 , -3/2
(C) 3/2 , -3/2
(D) -3/2 , 1/2

C

33. The main criterion of the objective function of the linear programming is
(A) It should be a constraint
(B) It should be a function that can be optimized
(C) A relation between the variables
(D) None of these

B

34. Slope of the tangent to the curve y = 2x2 – 3x + 8 at (2, 0) is :
(A) 5
(B) 7
(C) 10
(D) 8

A

35. If

(A) 2
(B) –2
(C) 3
(D) 1

D

36. The value of expression 2sec 2+sin-1(1/2) is
(A) π/6
(B) 5π/6
(C) 7π/6
(D) 1

B

37. Which of the following functions from Ζ into Ζ are bijections?
(A) f(x) = x3
(B) f(x) = x + 2
(C) f(x) = 2x + 1
(D) f(x) = x2 + 1

B

38. If A =

D

39. For the curve y = 8x – 3x3 , if x in creases at the rate of 2 units/sec, then at x = 4, the slope of curve is :
(A) Decreasing by 144 unit/sec
(B) Increasing by 144 unit/sec
(C) 144 unit/sec
(D) 72 unit/sec

A

40. If A =

(A) 21/7
(B) 23/7
(C) 29/7
(D) 31/7

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. Maximize Z = 3x + 5y, subject to x ≤ 1, x + y ≤ 4, 2x – y ≤ 2, x ≥ 0, y ≥ 0
(A) 12 at (2, 2)
(B) 14.03 at (22, 15)
(C) 16 at (2, 1)
(D) 20 at (0,4)

D

42. The line y = 3x + 5 is a tangent to the curve y2 = 12x at the point :
(A) (1/3 , 2)
(B) (2 , 1/3)
(C) (-1/3 , 2)
(D) (1/3 , -2/)

A

43. The maximum value of 65 – 70x – 35x2 is :
(A) 70
(B) 80
(C) 90
(D) 100

D

44. A L.P.P. is as follows :
Maximize Z = 50x + 15y subject to, 5x + y ≤ 100, x + y ≤ 60, x, y > 0 The coordinates of the corner points of the feasible region are (0, 0), (20, 0), (10, 50) and (0, 60). The maximum value of Z is :
(A) 1050
(B) 1150
(C) 1250
(D) 1200

C

45. If A =

, then the value of |A – 4I| is :
(A) 18
(B) –18
(C) 20
(D) –20

B

CASE-STUDY

II. Read the following text and answer the following questions, on the basis of the same:
An architect designs a building for a multi-national company. The floor consists of a rectangular region with semicircular ends having a perimeter of 200 m as shown below:

46. If x and y represents the length and breadth of the rectangular region, then the relation between the variables is :
(A) x + πy = 100
(B) 2x + πy = 200
(C) πx + y = 50
(D) x + y = 100

B

47. The area of the rectangular region A expressed as a function of x is :
(A) 2/π (100x – x2)
(B) 1/π (100x – x2)
(C) x/π (100x – x)
(D) πy2 + 2/π (100x – x2)

A

48. The maximum value of area A is :
(A) π/3200 m2
(B) 3200/π m2
(C) 5000/π m2
(D) 1000/π m2

C

49. The CEO of the multi-national company is interested in maximizing the area of the whole floor including the semi-circular ends. For this to happen the value of x should be
(A) 0 m
(B) 30 m
(C) 50 m
(D) 80 m