Class 12 Mathematics Sample Paper Term 1 With Solutions Set A

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

SECTION-A

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

1. Let f : R Þ R be defined as f(x) = x⁴ Then the correct option is:
(A) f is one – one but not onto
(B) f is many – one onto
(C) f is one – one onto
(D) f is neither one – one nor onto

2. The domain of the tan–1 x is:
(A) [– ∞, ∞]
(B) (– ∞, ∞)
(C) (-1, 1)
(D) [-1, 1]

3. A set is given as A = {1, 2, 3} and a relation on it is defined as R = {(1, 2), (2, 3)}. The minimum number of ordered pairs we need to add more to make the relation symmetric, transitive and reflexive are:
(A) 6
(B) 5
(C) 7
(D) 10

4. The principal value branch of cos–1 x is:
(A) (-1, 1)
(B) [0, π]
(C) (– ∞, ∞)
(D) [-π/2 , π/2]

5. If A =

6. A matrix with the determinant equal to 0 is known as
(A) Non-singular matrix
(B) Adjoint matrix
(C) Singular matrix
(D) Cofactor matrix

7. If the matrix A is both symmetric and skew symmetric, then
(A) A is a diagonal matrix
(B) A is a zero matrix
(C) A is a identity matrix
(D) None of these

8. Is the value of the determinant

dependent on the value of q.
(A) Yes
(B) No
(C) None of the above
(D) All of the above

9. If x^ey = 1 then dy/dx is:
(A) y1 = -y/y log x
(B) y 1= -1/y log x
(C) y1 = -y/x log y
(D) y1 = -1/x log x

10. Which of the following statements are true for the function f (x)= x² −4x+4 ?
(A) function is decreasing in x < 2.
(B) function is increasing in x < 2.
(C) function is constant in x < 2.
(D) None of the above

11. Equation of tangent to the curve y = 4x² at x = 1 is:
(A) 8x – y – 6 = 0
(B) 8x – y – 5 = 0
(C) 8x – 3y – 5 = 0
(D) 4x – y – 6 = 0

12. If y = log sec x, then dy/dx is:
(A) tan x
(B) cosec x
(C) cot x
(D) sin x

13. If A is non-singular and (A – 2I)(A – 4I) = 0 then the value of 1/6 A + 4/3 A-1 is equal
(A) 0
(B) I
(C) 2I
(D) 6I

14. The function f(x) = e|x| is
(A) continuous everywhere but not differentiable at x = 0
(B) continuous and differentiable everywhere
(C) not continuous at x = 0
(D) none of these

15. The points on the curve x² + y² – 2x – 3 = 0 at which the tangents are parallel to the y-axis are:
(A) (1, 2) and (2, 1)
(B) (0, 0)(1, 2)
(C) (1, 2) and (1, –2)
(D) (2, 1) and (–2, 1)

16. The contentment obtained after eating x units of a new dish at a trial function is given by the function f(x) = x³ + 6x² + 5x + 3. The marginal contentment when 3 units of dish are consumed is ____________.
(A) 60
(B) 68
(C) 24
(D) 48

17. The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 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 the information supplied.

18. If the function f(x) =

is continuous then the value of a is:
(A) –1
(B) 3
(C) –2
(D) 2

19.

(A) scalar matrix
(B) Null matrix
(C) unit matrix
(D) none of these

20. If

(A) 20
(B) 17
(C) 18
(D) 19

SECTION-B

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

21. Number of relations that can be defined on the set A = {1, 2, 3} is:
(A) 2⁹
(B) 4⁴
(C) 16
(D) 216

22. If f(x) =

is continuous at x = π/2 then
(A) m = 1, n = 0
(B) m = nπ/2 + 1
(C) n = mπ/2
(D) m = n = π/2

23. Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is
(A) p = 2q
(B) p = q/2
(C) p = 3q
(D) p = q

24. If y = ex/log x then dy/dx is:
(A) x log x- ex/(logx)²
(B) xex log x – ex/log x
(C) xex log x – ex/x(logx)²
(D) none of these

25. The area of a triangle with points (0, 0), (6, 0) and (x, 3) is:
(A) 9 sq. units
(B) 8 sq. units
(C) 19 sq. units
(D) 18 sq. units

26. For the curve y = 5x – 2x³, If x increases at the rate of 2 units/sec, then at x = 3, the slope of curve is:
(A) increasing by 36 unit/sec
(B) decreasing by 36 unit/sec
(C) decreasing by 72 unit/sec
(D) increasing by 72 unit/sec

27. The principal value branch of sin–1 x is:
(A) (-1, 1)
(B) [-1, 1]
(C) (– ∞, ∞)
(D) [-π/2 , π/2]

28. Let A be a 2 × 2 matrix, then adj(adj A) is:
(A) adj A
(B) A^–1
(C) A(adj A)
(D) A

29. The total revenue received from the sale of x units of a product is given by R(x) = 3×2 + 36x + 5 in rupees. The marginal revenue when x = 5 is:
(A) 65
(B) 66
(C) 68
(D) 70

30. Let T be the set of all triangles in the Euclidean plane, and let a relation R on T 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

31. f(x) = [x]ex is:
(A) continuous
(B) not continuous
(C) continuous at x = –1
(D) none of these

32. Let Two matrices be A =

33. A linear programming problem is as follows:
Z = 45x + 80y subject to constraints, 5x + 20y ≤ 400, 10x + 15y ≤ 450, x ≥ 0, y ≥ 0.
In the feasible region, the maximum value of Z at:
(A) (0, 20)
(B) (24, 14)
(C) (0, 30)
(D) (80, 0)

34. The slope of the normal to the curve y = 2sin²3x at x = π/x is:
(A) not defined
(B) –1
(C) 2
(D) –2

35. If

(A) –2, 14
(B) –1, 12
(C) 1, 7
(D) 3, 7

36. The principal value of cot^–1(–1) is:
(A) π/2
(B) 3π/4
(C) π/4
(D) 3π/2

37. The domain of the function f(x) = – √-5-6x – x² is:
(A) [–4, –9)
(B) [–3, –1]
(C) [–5, –1]
(D) [–2, –1]

38. The value of

(A) 1
(B) 0
(C) –1
(D) 1/2

39. If x² + xy + y² = 10, then dy/dx is:
(A) -2x + y/x + 2y
(B) 2x + y/x + 2y
(C) 2x – y/x – 2y
(D) x – 2y/2x – y

40. Given that A =

(A) 3/4
(B) 4/3
(C) 1/4
(D) -1/3

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. For an objective function Z = 3x₁ + 2x₂, where x₁, x₂ > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 0), (0, 4), (3, 1) and (2, 0). The condition on x₁ and x₂ such that the maximum and minimum Z occur at the points (3, 1) and (0, 0) respectively, then the maximum and minimum values are:
(A) Max. = 8, Mini. = 6
(B) Max. = 6, Mini. = 0
(C) Max. = 8, Mini. = 0
(D) Max. = 11, Mini. = 0

42. The slope of the tangent to the curve x = 1 – cos q and y = q – sin q at q = π/4 is:
(A) 1
(B) √2
(C) √2 -1
(D) 1- √2

43. The absolute maximum value of (x – 1)2 + 3 in [–3, 1] is:
(A) 3
(B) 18
(C) 20
(D) 19

44. For an objective function Z = 200x + 500y, subject to the constraints, x + 2y ≥ 10, 3x + 4y ≤ 24, x ≥ 0 and y ≥ 0. Then the minimum value of Z is:
(A) 2500
(B) 3000
(C) 2300
(D) 2800

45. Let A =

(A) 0
(B) 1
(C) 4
(D) –4

CASE-STUDY

The shape of a toy is given as f(x) = 6(2x⁴ – x²). To make the toy beautiful 2 sticks which are perpendicular to each other were placed at a point (2, 3) above the toy.

Based on the given information, answer the following questions.

46. Which value from the following may be abscissa of critical point?
(A) ±1/4
(B) ± 1/2
(C) ±1
(D) None of these

47. Find the slope of the normal based on the position of the stick.
(A) 360
(B) –360
(C) 1/360
(D) -1/360

48. What will be the equation of the tangent at the critical point if it passes through (2, 3)?
(A) x + 360y = 1082
(B) y = 360x – 717
(C) x = 717y + 360
(D) None of these

49. Find the second order derivative of the function at x = 5.
(A) 598
(B) 1,176
(C) 3,588
(D) 3,312

50. At which of the following intervals will f(x) be increasing?
(A) (- ∞ , -1/2) ∪ (1/2 , ∞)
(B) (-1/2 , 0) ∪ (1/2 , ∞)
(C) (0 , 1/2) ∪ (1/2 , ∞)
(D) (∞ , -1/2) ∪ (0 , 1/2)