# CBSE Class 12 Mathematics Term 1 Sample Paper Set F

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

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(tan 3π/4) is
(a) 3π/4
(b) π/4
(c) 5π/4
(d) -π/4

D

2. If A is an invertible matrix of order 3 and|A|= 5, then |adi A|/|A| is equal to
(a) 5
(b) 25
(c) 1
(d) 0

A

3. The value of √1+cos x/1-cos x is y, then the value of x in terms of y is
(a) tan-1 y
(b) 2tan-1 y
(c) 2 cot-1 y
(d) cot-1 y

C

4. Let N be the set of natural numbers and f :N → N be a function given by f (x) = x + 1 for x ∈ N. Which one of the following is correct?
(a) f is one-one and onto
(b) f is one-one but not onto
(c) f is only onto
(d) f is neither one-one nor onto

B

5. If f be given by f (x) = x + 2, x ∈ (0, 1), then
(a) the function f has not a local maximum value
(b) the function f has not a local minimum value
(c) Both (a) and (b) are true
(d) Both (a) and (b) are false

C

6. If A is a non-singular matrix of order 3 and |adjA|= |A|α , then the value of α/2 is
(a) 0
(b) 1
(c) 2
(d) 3

B

7. The principal value of cot-1(-1/√3) is
(a) -π/4
(b) 5π/6
(c) 2π/3
(d) None of these

B

8. If x = a cos3 θ and y = a sin3 θ, then dy/dx at θ = π/4 is equal to
(a) 1
(b) – 1
(c) 0
(d) 4

B

9. If A =

and A = AT , then x/y is equal to
(a) 0
(b) 1
(c) 2
(d) – 1

B

10. The adjoint of the matrix

B

11. How many tangents are parallel to X-axis for the curve y = x2 – 4x + 3 ?
(a) 1
(b) 2
(c) 3
(d) No tangent is parallel to X-axis

D

12. The graph of inequations is given below.

The feasible region consists the corner point
(a) (20, 40)
(b) (200, 0)
(c) (20, 60)
(d) (20, 80)

D

13. If Δ =

then the difference of minor of the element a23 and minor of element a32 is
(a) 10
(b) 15
(c) 18
(d) 20

C

14. If AT =

then find AT + BT is equal to

A

15. Let D be the domain of the real valued function f defined by f (x) =√25-x2 . Then, D is equal to
(a) [-5, 5]
(b) [-2.5, 2.5]
(c) [-25, 25]
(d) [-0.5, 0.5]

A

16. Suppose P and Q are two different matrices of order 4 x n and n x p, then the order of the matrix P ´Q is
(a) 4 x p
(b) p x 4
(c) n x n
(d) 4 x 4

A

17. Let A = {a, b, c } and the relation R be defined on A as follows R = {(a, a), (b, c), (a, b)}Then, minimum number of ordered pairs to be added in R to make R reflexive and transitive is
(a) 1
(b) 2
(c) 3
(d) 4

C

18. If

is a symmetric matrix, then the value of 3x is
(a) 10
(b) 15
(c) 8
(d) 6

B

19. The principle value of cosec-1(-√2) is
(a) π/4
(b) π/2
|(c) – π/4
(d) 0

C

20. The number of all possible matrices of order 3 x 3 with each entry 3 or 4 is
(a) 27
(b) 18
(c) 81
(d) 512

D

Section B

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

21. Divide 20 into two parts such that the product of one part and the cube of the other is maximum, then the two parts are
(a) {10, 10}
(b) {12, 8}
(c) {15, 5}
(d) {5, 10}

C

22. The graphical representation of an LPP is the following

If Z = 100x + 170y, then the (MaximumZ – MinimumZ/100 ) is equals to
(a) 1200
(b) 1386
(c) 756
(d) 1400

B

23. LetT be the set of all triangles in the Euclidean plane and let a relation R onT be defined as aRb, if a is congruent to b, ∀ a, b ∈ T. Then, R is
(a) reflexive but not transitive
(b) transitive but not symmetric
(c) equivalence relation
(d) None of these

C

24. If the set P contains 3 elements and the set Q contains 4 elements, then the number of one-one and onto mappings from P to Q is
(a) 160
(b) 80
(c) 0
(d) None of these

C

25. The function f(x) = loge(x3 + √x6 + 1) is
(a) even
(b) odd
(c) decreasing
(d) None of these

B

26. The graph of inequations is shown below

If Z = x – 7y + 190, then Zmaximum – Zminimum is equal to
(a) 40
(b) 50
(c) 60
(d) 70

A

27. The graph of inequations is shown below

If Z = 7x + 4y, then the value of Z|atC + Z|atB is
(a) 10
(b) 30
(c) 50
(d) 70

C

28. If the function f is given by f (x) = x3 – 3x2 + 4x , x ∈ R , then
(a) f is strictly increasing on R
(b) f is decreasing on R
(c) f is neither increasing nor decreasing on R
(d) f is strictly decreasing on R

A

29. If (x – a)2 + (y – b)2 = c2 for some c > 0, then the value of [1+(dy/dx)2]3/2 is
(a) c3/(y-b)3
(b) c/(y-b)
(c) c2/(y-b)2
(d) c/(y-b)2

A

30. Graph of inequations is given below

If Z = 9x – 5y, then the value of Z at point B is
(a) 102
(b) 144
(c) 94
(d) 104

D

31. The coordinates of the point on the curve √x + √y = 4 at which tangent is equally inclined to the axes is
(a) (2, 2)
(b) (2,4)
(c) (3, 4)
(d) (4, 4)

D

32. If f(x) = x4/4 – x3 – 5x2 + 24x + 12 , then the critical numbers are
(a) -3, 2 and 4
(b) 2, 3 and 4
(c) -3, -2 and 4
(d) -3, 3 and 4

A

33. If 2

then x, y, z and t are respectively
(a) 3, 6, 9 and 6
(b) 3, 9, 6 and 6
(c) 3, 6, 6 and 9
(d) 6, 9, 3 and 6

A

34. If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is
(a) 1
(b) 0
(c) – 6
(d) 6

D

35. The bookshop of a particular school has 10 dozen Chemistry books, 8 dozen Physics books, 10 dozen Economics books. Their selling prices are ₹ 80, ₹ 60 and ₹ 40 each respectively. The total amount, the bookshop will receive from selling all the books using matrix algebra, is
(a) ₹ 21160
(b) ₹ 20610
(c) ₹ 26100
(d) ₹ 20160

D

36. If y = x + √x2 + a2 , then dy/dx is equal to
(a) y/√x2 + a2
(b) x/√x2 + a2
(c) x/√x + a
(d) y/√x + a

A

37. If y =(tan-1 x)2 , then the value of (x2+1)2 y2 + 2x (x2+1) y1 is
(a) 2
(b) 3
(c) 4
(d) None of these

A

38. If A =

satisfies the equation A’A = I , then the values of x, y and z are

D

39. A point on the curve y = (x – 2)2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4) is
(a) (2, 1)
(b) (3, 1)
(c) (4, 1)
(d) (1, 2)

B

40. The graph of inequations is drawn below

If Z = 8000x + 12000y, then Z|at A + Z| atB – Z| atC is
(a) 168000
(b) 198000
(c) 200000
(d) 208000

D

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 angle of intersection of the curves y = 4 – x2 and y = x2 is
(a) tan-1(4√2/7)
(b) tan-1(√2/7)
(c) tan-1(4/7)
(d) tan-1(4√2)

A

42. If x = a(cos t + log tan t/2) and y = a sin t, then dy/dx is equal to
(a) cot t
(b) tan t
(c) sec t
(d) cosec t

B

43. Let f : R → R be the function defined by f(x) = 1/2-cos x , ∀ x ∈ R. Then, the range of f is
(a) [1/2 , 1]
(b) [1/3 , 2]
(c) [1/2 , 2]
(d) [1/3 , 1]

D

44. If y = (1+x)(1+x2)(1+x4)…….(1+x2n) , then the value of dy/dx at x = 0 is
(a) 0
(b) -1
(c) 1
(d) None of these

C

45. The derivative of (esec2x + 3cos-1 x) is valid in
(a) [1, 1] – {0}
(b) (-1, 1)
(c) (-1, 1) – {0}
(d) None of these

B

CASE STUDY

Sometimes, x and y are given as functions of one another variable, say x = f(t), y = y(t) are two functions and t is a variable. In such a case, x and y are called parametric functions or parametric equations and t is called the parameter.
To find the derivatives of parametric functions, we use following steps I. First, write the given parametric functions, Suppose x = f (t) and y = g(t), where t is a parameter.
II. Differentiate both functions separately with respect to parameter t by using suitable formula, i.e. find dx/dt and dy/dt .
III. Divide the derivative of one function w.r.t. parameter by the derivative of second function w.r.t parameter, to get required value, i.e. dy/dt .
Thus, dy/dx = dy/dt/dx/dt = 8′(t)/f'(t)’ where f ‘ (t) ≠ 0.
Based on above information, answer the following questions.

46. If x = log t and y = cos t, then dy/dx is equal to
(a) – t sin t
(b) t sin t
(c) – t cos t
(d) t cos t

A

47. If x = cos t + sin t and y = sin t – cos t, then dy/dx at t = π/2 is equal to
(a) 1
(b) 0
(c) – 1
(d) 2

C

48. If x = at3 and y = t2 + 1, then dy/dx at t = 2/3 is equal to
(a) 1/a
(b) a
(c) – a
(d) -1/a

A

49. If x = et + e-t and y = et – e-t , then dy/dx is equal to
(a) e2t – 1/e2t + 1
(b) e2t + 1/e2t – 1
(c) et + 1/et – 1
(d) et – 1/et + 1