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# CBSE Academic Class XII Mathematics Sample Question Paper 2021-22

Name of the Board : Central Board of Secondary Education (CBSE)
Class : XII STD
Document Type : Sample Question Paper
Subject : Mathematics
Term : 1 and 2
Year : 2021-22

Contents :

## CBSE XII Mathematics Question Paper

CBSE Students can download the Mathematics Sample Question Paper Term 1 and 2 for the year 2021-22 from the website of CBSE Academic.

Related / Similar Question Paper : CBSE Academic Class XII Applied Mathematics Sample Question Paper 2021-22

## Sample Question Paper For CBSE XII Mathematics

Section-A :
1. sin [ π3 βsin-1 (β 12)] is equal to
a) 12
b) 13
c) -1
d) 1

2. The value of k (k < 0) for which the function π defined asπ(π₯) = {1βπππ ππ₯π₯π πππ₯ , π₯ β  02 , π₯ = 0 is continuous at π₯ = 0 is
a) Β±1
b) β1
c) Β± 12
d) 12

3. If A = [aij] is a square matrix of order 2 such that aij = {1, π€βππ π β  π0, π€βππ π = π , thenA2 is
a) [1 01 0]
b) |1 10 0|
c) |1 11 0|
d) [1 00 1]

4. Value of π, for which A = [π 84 2π] 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) βͺ (2, β)
b) (2, β)
c) (ββ, 2)
d) (β β, 2]βͺ (2, β)

6. Given that A is a square matrix of order 3 and | A | = β 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 [2π + π π β 2π 5π β π 4π + 3π] = [ 4 β3 11 24 ], then value of a + b β c + 2d is
a) 8
b) 10
c) 4
d) β8

9. The point at which the normal to the curve y = π₯ + 1 π₯, 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
a) π₯β1βπ₯2
b) 1β1βπ₯2
c) 1β1+π₯2
d) π₯β1+π₯2

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

12. If ex + ey = ex+y , then ππ¦ππ₯ is
a) e y β x
b) e x + y
c) β e y β x
d) 2 e x β y

13. Given that matrices A and B are of order 3Γn and mΓ5 respectively, then the order of matrix C = 5A +3B is
a) 3Γ5
b) 5Γ3
c) 3Γ3
d) 5Γ5

14. If y = 5 cos x β 3 sin x, then π2π¦ππ₯2 is equal to
a) β y
b) y
c) 25y
d) 9y

15. For matrix A =[ 2 5β11 7], (ππππ΄)β² is equal to
a) [β2 β511 β7]
b) [ 7 5 11 2]
c) [ 7 11 β5 2 ]
d) [ 7 β5 11 2 ]

16. The points on the curve π₯2 9 + π¦2 16 = 1 at which the tangents are parallel to y- axis are
a) (0,Β±4)
b) (Β±4,0)
c) (Β±3,0)
d) (0, Β±3)

17. Given that A = [πππ ] is a square matrix of order 3Γ3 and |A| = β7, then the value of β ππ2π΄π2 3 π=1 , where π΄ππ denotes the cofactor of element πππ is:
a) 7
b) -7
c) 0
d)49

18. If y = log(cos ππ₯), then ππ¦ππ₯ is
a) cos ππ₯β1
b) πβπ₯ cos π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 [0,π2]is
a) 2
b) π6 + β3
c) π2
d) The least value does not exist