# Class 12 Maths Sample Question Paper | CBSE Exam 2021-22 Important Questions

Class 12th CBSE Maths Term 1 Board Exam Sample Question Paper and Important Questions 2021-22.

## CBSE 2021-22, Maths board exam sample question paper for Class 12. Check the important questions which need to be focused on while preparing for the class 12 Maths board exam.

• Subject Code – 041
• CLASS: XII
• Session: 2021-22
• Subject- Mathematics
• Term – 1
• Time Allowed: 90 minutes
• Maximum Marks: 40

General Instructions:
1. This question paper contains three sections β A, B and C. Each part is compulsory.
2. Section – A has 20 MCQs, attempt any 16 out of 20. 3. Section – B has 20 MCQs, attempt any 16 out of 20.
4. Section – C has 10 MCQs, attempt any 8 out of 10.
5. All questions carry equal marks.
6. There is no negative marking.

SECTION β A
In this section, attempt any 16 questions out of Questions 1 β 20.
Each Question is of 1 mark weightage.

1. sin [ )] is equal to:
a) b)
c) -1 d) 1

## 2. The value of k (k < 0) for which the function defined as is continuous at π₯ = 0 is:

a) Β±1 b) 1 c) d) 1 2

## 4. Value of k, for which A = is a singular matrix is:

a) 4 b) -4 c) Β±4 d) 0

## 5. Find the intervals in which the function f given by f (x) = x 2 β 4x + 6 is strictly increasing:

a) (β β, 2) (2, β) b) (2, β) c) (ββ, 2) d) (β β, 2] (2, β)

## 6. Given that A is a square matrix of order 3 and | A | = – 4, then | adj A | is equal to:

a) -4 b) 4 c) -16 d) 16

## 7. A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?

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

## 8. If , then value of a + b c + 2d is:

a) 8 b) 10 c) 4 d) 8

## 9. The point at which the normal to the curve y = π₯ + 1/x, x > 0 is perpendicular to the line 3x β 4y β 7 = 0 is:

a) (2, 5/2) b) (Β±2, 5/2)
c) (- 1/2, 5/2) d) (1/2, 5/2)

## 10. sin (tan-1x), where |x| < 1, is equal to:

11. Let the relation R in the set A =
b| is a multiple of 4}. Then [1], th
x Z e equi : 0 β€ x β€ 12}, given by R = valence class containing 1 {(a, b) : |a β , is:
a) {1, 5, 9} b) {0, 1, 2, 5}
c) d) A

## 12. If ex + ey = ex+y , then :

a) e y – x b) e x + y
c) β e y – x d) 2 e x – y

a) 3Γ5 b) 5Γ3
c) 3Γ3 d) 5Γ5

a) – y b) y
c) 25y d) 9y

## 15. For matrix A = is equal to:

a) b)

c) d)

16. The points on the curve axis are:
at which the tangents are parallel to y- 1

a) (0,Β±4) b) (Β±4,0)
c) (Β±3,0) d) (0, Β±3)

a) 7 b) -7
c) 0 d) 49

## 18. If y = log(cosππ₯), then ππ¦/ππ₯ is:

a) cosππ₯β1 b) πβπ₯ cosππ₯
c) ππ₯sin ππ₯ d) β ππ₯ tan ππ₯

## 19. Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum?

a) Point B b) Point C
c) Point D d) every point on the line segment CD

## 20. The least value of the function π(π₯) = 2πππ π₯ + π₯ in the closed interval [ is:

a) 2 b) π β
c) d) The least value does not exist.

SECTION β B
In this section, attempt any 16 questions out of the Questions 21 – 40.
Each question is of 1 mark weightage.

## 21. The function: R R defined as π(π₯) = π₯3 is:

a) One-on but not onto b) Not one-one but onto
c) Neither one-one nor onto d) One-one and onto

## 23. In the given graph, the feasible region for a LPP is shaded. The objective function Z = 2x β 3y, will be minimum at:

a) (4, 10) b) (6, 8)
c) (0, 8) d) (6, 5)

## 26. The real function f(x) = 2×3 β 3×2 β 36x + 7 is:

a) Strictly increasing in (ββ, β2) and strictly decreasing in ( β2, β)
b) Strictly decreasing in ( β2, 3)
c) Strictly decreasing in (ββ, 3) and strictly increasing in (3, β)
d) Strictly decreasing in (ββ, β2) βͺ (3, β)

a) b)
c) 64 d) 16

## 29. The value of for which the function π (π₯) = π₯ + πππ π₯ + π is strictly decreasing over R is:

a) π < 1 b) No value of b exists c) π β€ 1 d) π β₯ 1

## 30. Let R be the relation in the set N given by R = {(a, b) : a = b β 2, b > 6}, then:

a) (2,4) β R b) (3,8) β R
c) (6,8) β R d) (8,7) β R

## 31. The point(s), at which the function f gi ven by is continuous, is/are:

a) π₯πR b) π₯ = 0
c) π₯π R {0} d) = β1and

## 32. If A = , then the values of π, π and respectively are:

a) β6, β12, β18 b) β6, β4, β9
c) β6, 4, 9 d) β6, 12, 18

33. A linear programming problem is as follows:
πππππππ§π π = 30π₯ + 50π¦ subject to the constraints,
3π₯ + 5π¦ β₯ 15
2π₯ + 3π¦ β€ 18
π₯ β₯ 0, π¦ β₯ 0
In the feasible region, the minimum value of Z occurs at
a) a unique point b) no point

c) infinitely many points d) two points only

34. The area of a trapezium is defined by function π and given by π(π₯) = (10 +
, then the area when it is maximised is:
a) 75ππ2 b) 7β3ππ2
c) 75β3ππ2 d) 5ππ2

a) A b) I + A
c) I A d) I

## 36. If tan-1 x = y, then:

a) β1 < y < 1 b) c) d) y

## 37. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f= {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given infor mation, is best defined as:

a) Surjective function b) Injective function c) Bijective function d) function

a) b) c) d)

## 39. The point(s) on the curve y = x 3 β 11x + 5 at which the tangent is y = x β 11 is/are:

a) (-2,19) b) (2, – 9) c) (Β±2, 19) d) (-2, 19) and (2, -9)

## 40. Given that A = and A 2 = 3 , then:

a) 1 + πΌ2 + π½πΎ = 0 b) 1 β πΌ2 β π½πΎ = 0 c) 3 β πΌ2 β π½πΎ = 0 d) 3 + πΌ2 + π½πΎ = 0

SECTION β 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 π = ππ₯ + ππ¦, where π, π > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:

a) π β 3π = 0 b) π = 3π

c) π + 2π = 0 d) 2π β π = 0

a) b)

c) d)

## 44. In a linear programming problem, the constraints on the decision variables x and y are β 3π¦ β₯ 0, π¦ β₯ 0, 0 β€ π₯ β€ 3. The feasible region

a) is not in the first quadrant b) is bounded in the first quadrant
c) is unbounded in the first quadrant d) does not exist

## 45. Let A = , where 0 β€ Ξ± β€ 2Ο, then:

a) |A|=0 b) |A| π(2, β)
c) |A| π(2,4) d) |A| π[2,4]

CASE STUDY
The fuel cost per hour for running a train is proportional to the square of the speed it generates in km per hour. If the fuel costs βΉ 48 per hour at speed 16 km per hour and the fixed charges to run the train amount to βΉ 1200 per hour.
Assume the speed of the train as π£ km/h.

Based on the given information, answer the following questions.

a) 16/3 b) 1/3
c) 3 d) 3/16

## 48. The most economical speed to run the train is:

a) 18km/h b) 5km/h
c) 80km/h d) 40km/h

## 49. The fuel cost for the train to travel 500km at the most economical speed is:

a) βΉ 3750 b) βΉ 750
c) βΉ 7500 d) βΉ 75000

## 50. The total cost of the train to travel 500km at the most economical speed is:

a) βΉ 3750 b) βΉ 75000
c) βΉ 7500 d) βΉ 15000