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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 [ 𝜋3 −sin-1 (− 12)] is equal to
a) 12
b) 13
c) -1
d) 1

2. The value of k (k < 0) for which the function 𝑓 defined as𝑓(𝑥) = {1−𝑐𝑜𝑠𝑘𝑥𝑥𝑠𝑖𝑛𝑥 , 𝑥 ≠ 02 , 𝑥 = 0 is continuous at 𝑥 = 0 is
a) ±1
b) −1
c) ± 12
d) 12

3. If A = [aij] is a square matrix of order 2 such that aij = {1, 𝑤ℎ𝑒𝑛 𝑖 ≠ 𝑗0, 𝑤ℎ𝑒𝑛 𝑖 = 𝑗 , thenA2 is
a) [1 01 0]
b) |1 10 0|
c) |1 11 0|
d) [1 00 1]

4. Value of 𝑘, for which A = [𝑘 84 2𝑘] is a singular matrix is
a) 4
b) -4
c) ±4
d) 0

5. Find the intervals in which the function f given by f (x) = x 2 – 4x + 6 is strictly increasing
a) (– ∞, 2) ∪ (2, ∞)
b) (2, ∞)
c) (−∞, 2)
d) (– ∞, 2]∪ (2, ∞)

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 [2𝑎 + 𝑏 𝑎 − 2𝑏 5𝑐 − 𝑑 4𝑐 + 3𝑑] = [ 4 −3 11 24 ], 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 = 𝑥 + 1 𝑥, x > 0 is perpendicular to the line 3x – 4y – 7 = 0 is
a) (2, 5/2)
b) (±2, 5/2)
c) (- 1/2, 5/2)
d) (1/2, 5/2)

10. sin (tan-1x), where |x| < 1, is equal to
a) 𝑥√1−𝑥2
b) 1√1−𝑥2
c) 1√1+𝑥2
d) 𝑥√1+𝑥2

11. Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a –b| is a multiple of 4}. Then , the equivalence class containing 1, is:
a) {1, 5, 9}
b) {0, 1, 2, 5}
c) 𝜙
d) A

12. If ex + ey = ex+y , then 𝑑𝑦𝑑𝑥 is
a) e y – x
b) e x + y
c) – e y – x
d) 2 e x – y

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

14. If y = 5 cos x – 3 sin x, then 𝑑2𝑦𝑑𝑥2 is equal to
a) – y
b) y
c) 25y
d) 9y

15. For matrix A =[ 2 5−11 7], (𝑎𝑑𝑗𝐴)′ is equal to
a) [−2 −511 −7]
b) [ 7 5 11 2]
c) [ 7 11 −5 2 ]
d) [ 7 −5 11 2 ]

16. The points on the curve 𝑥2 9 + 𝑦2 16 = 1 at which the tangents are parallel to y- axis are
a) (0,±4)
b) (±4,0)
c) (±3,0)
d) (0, ±3)

17. Given that A = [𝑎𝑖𝑗 ] is a square matrix of order 3×3 and |A| = −7, then the value of ∑ 𝑎𝑖2𝐴𝑖2 3 𝑖=1 , where 𝐴𝑖𝑗 denotes the cofactor of element 𝑎𝑖𝑗 is:
a) 7
b) -7
c) 0
d)49

18. If y = log(cos 𝑒𝑥), then 𝑑𝑦𝑑𝑥 is
a) cos 𝑒𝑥−1
b) 𝑒−𝑥 cos 𝑒𝑥
c) 𝑒𝑥sin 𝑒𝑥
d) − 𝑒𝑥 tan 𝑒𝑥

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 𝑓(𝑥) = 2𝑐𝑜𝑠𝑥 + 𝑥 in the closed interval [0,𝜋2]is
a) 2
b) 𝜋6 + √3
c) 𝜋2
d) The least value does not exist 