DELHI PUBLIC SCHOOL, HYDERABAD
MCQ FROM ALL CHAPTERS
Chapter 1 - Relations & Functions
Select the correct option (s) in the followings.
Q01. The relation R = {(1, 2)} on A = {1, 2,3} is
(a) Reflexive only
(b) Symmetric only
(c) Transitive only
(d) Equivalence i.e., reflexive, symmetric and transitive
Q02. Let f : A → B be a one-one function s.t. range of f is {b}. Then the value of n(A) is
(a) 1 (b) 2 (c) 0 (d) 4
Q03. For real numbers x and y, define x R y if and only if x − y + 2 is an irrational
number. Then the relation R is
(a) only reflexive (b) only symmetric (c) only transitive (d) equivalence
Q04. Let R be the relation in the set N given by R = (a, b) : a = b − 2, b 6 .
Which of the following is true?
(a) (2,4) R (b) (3,8) R (c) (6,8) R (d) (8,7) R
3
Q05. If f (x) = cos x , then f is
4
1 1
(a) 1 (b) −1 (c) − (d)
2 2
Chapter 2 - Inverse Trigonometric Functions
Select the correct option (s) in the followings.
Q06. The value of cos−1 (−1) − sin −1 (1) is
3 3
(a) (b) (c) (d) −
2 2 2
π
Q07. If tan −1x = , for some x R , then the value of cot −1x is
10
π 2π 3π 4π
(a) (b) (c) (d)
5 5 5 5
−1
Q08. The domain of the function defined by f (x) = sin x + cos x is
(a) [–1, 1] (b) [−1, π +1] (c) (−, ) (d)
1
Q09. The range of f (x) = sin −1 2x is
2
(a) − , (b) −1, 1 (c) (d) − ,
2 2 2 4 4
Q10. If y = sin x is invertible i.e., inverse of y = sin x exists, then which of the following is
correct?
, 3
(a) x − , , y [−1, 1] (b) x , , y [−1, 1]
2 2 2 2
3
(c) x [−1, 1], y − , (d) x R, y ,
2 2 2 2
2 2
+n
Q11. Let m = cos −1 − and n = sin −1 − . Then (m + n) 4 =
2 2
(a) 0 (b) 1 (c) (d) −
2 2
1 + tan x
Q12. If x , then tan −1 =
4 2 1 − tan x
3 3
(a) + x (b) − x (c) −x (d) x −
4 4 4 4
Chapters 3 & 4 - Matrices & Determinants
Select the correct option (s) in the followings.
Q13. If A and B are two matrices such that A + B and AB are both defined then
(a) A and B can be any matrices
(b) A and B are square matrices not necessarily of same order
(c) Number of columns in A = Number of rows in B
(d) A and B are square matrices of same order.
2 −1
Q14. If A = then, AAT is equal to
3 1
5 5 1 1 1 1
(a) (b) 5 (c) 5 I 2 (d)
10 5 1 2 1 2
a b c
Q15. Let A = d e f = 4 . Then adj.A =
g h i
(a) 16 (b) 2 only (c) –2 only (d) –16
x 2
Q16. If is a singular matrix, then the product of all possible values of x is
3 x − 1
(a) 6 (b) −6 (c) 0 (d) −7
−1
A 1
Q17. If = , where A is a 3 3 matrix, then the value of k is
2 kA
1 1
(a) (b) 8 (c) 2 (d)
8 2
0 1
Q18. If A = , then A2023 is equal to
0 0
0 1 0 2023 0 0 2023 0
(a) (b)
0
(c) (d)
0 0 0 0 0 0 2023
2 0
Q19. If = P + Q, where P is a symmetric and Q is a skew symmetric matrix, then
5 4
Q=
