# Relations and Functions MCQ Class 11 Mathematics

Please refer to Chapter 2 Relations and Functions MCQ Class 11 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 11 Mathematics. Students should refer to MCQ Questions for Class 11 Mathematics with Answers to score more marks in Grade 11 Mathematics exams. Students should read the chapter Relations and Functions and then attempt the following objective questions.

## MCQ Questions Class 11 Mathematics Chapter 2 Relations and Functions

The Relations and Functions MCQ Class 11 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. Let R be the relation on Z defined by R = {(a, b) : a, b ∈ z, a – b is an interger}. Find the domain and Range of R.
(a) z, z
(b) z+ , z
(c) z, z
(d) None of these

A

Question. If A and B are two sets, then A ´ B = B ´ A . If and only if
(a) A ⊂ B
(b) B ⊂ A
(c) A = B
(d) None of the above

C

Question. Let Rbe a relation from a set A to a set B, then
(a) R = A ∪ B
(b) R = A ∩ B
(c) R ⊆ A x B
(d) R ⊆ B x A

C

Question. If the relation R: A → B, where A = {1, 2, 3, 4} and B = {1, 3, 5} is defined by R = {(x, y) : x < y, x ∈ A, y ∈ B}, then R-1OR is
(a) {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
(b) {(3, 1), (5, 1), (5, 2), (5, 3), (5, 4)}
(c) {(3, 3), (3, 5), (5, 3), (5, 5)
(d) None of the above

C

Question. Let a relation R be defined by R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}, then RORis equal to
(a) {(1, 5), (1, 6), (3, 6)}
(b) {(1, 4), (1, 5), (3, 6)}
(c) {(1, 5), (1, 6), (3, 7)}
(d) {(1, 4), (1, 5), (3, 7)}

A

Question. The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(x, y) : | x – y | < } 2 2 16 is given by
(a) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}
(b) {(2, 2), (3, 2), (4, 2), (2, 4)}
(c) {(3, 3), (4, 3), (5, 4), (3, 4)}
(d) None of the above

D

Question. Domain of √a2 – x2(a>0) is
(a) (-a, a)
(b) [-a, a]
(c) [0, a]
(d) (-a, 0]

B

Question. If f (x) = ax + b, where a and b are integers, f (-1) = – 5 and f (3) = 3, then a and b are equal to
(a) a = – 3, b = -1
(b) a = 2, b = – 3
(c) a = 0 , b = 2
(d) a = 2, b = 3

B

Question. Find the range of the function f(x) = x2 + 2.
(a) (– 2, 2)
(b) [2, ∞)
(c) [3, ∞)
(d) None of these

B

Question. The domain of the function f(x) = (2 – 2x – x ) 2 is
(a) – √3 ≤ x ≤ √3
(b) -1- √3 ≤ x ≤ -1+ √3
(c) -2 ≤ x ≤ 2
(d) -2 – √3 ≤ x ≤ – 2 + √3

B

Question. Which of the following function is invertible?
(a) f (x) = 2x
(b) f(x) = x3 – x
(c) f(x) = x2
(d) None of these

A

Question. If f(x) = sin2 x and the composite function g{f(x)} = | sin x |, then the function g(x) is equal to
(a) (√x – 1)
(b) √x
(c) √(x + 1)
(d) – √x

B

Question. If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A ´ B and B ´ A are
(a) 299
(b) 992
(c) 100
(d) 18

B

Question. If n (A) = 3, n (B) = 4, then n (A ´ A ´ B) is equal to
(a) 36
(b) 12
(c) 108
(d) None of these

A

Question. Let a relation R be defined by
R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}. The relation R-1oR is given by
(a) {(1, 1), (4, 4), (7, 4), (4, 7), (7, 7)}
(b) {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}
(c) {(1, 5), (1, 6), (3, 6)}
(d) None of the above

B

Question. If the set A has 3 elements and the set B = {1, 3, 4, 5}, then the number of elements in (A x B) is
(a) 11
(b) 12
(c) 13
(d) 15

B

Question. Let A = {1, 2}B = {1, 2, 3, 4}, C = {5, 6}and D = {5, 6, 7, 8} Following statements are given below :
I A x (B ∩ C) = (A x B) ∩ (A x C)
II A x C is a subset of B x D.
Which of the following statment is correct ?
(a) Only I
(b) Only II
(c) Both I and II
(d) None of these

C

Question. Let f (x) = √1 + x , 2 then
(a) f(xy) = f(x) × f(y)
(b) f(xy) ³ f(x) × f(y)
(c) f(xy) £ f(x) × f(y)
(d) None of these

C

Question. If A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, then (A x B) ∩ (B x C) is equal to
(a) {(1, 4)}
(b) {(3, 4)}
(c) {(1, 4), (3, 4)}
(d) None of these

B

Question. If A = {1, 2, 3}, B = {3, 8}, then (A ∪ B) x (A ∩ B) is equal to
(a) {(8, 3), (8, 2), (8, 1), (8, 8)}
(b) {(1, 2), (2, 2), (3, 3), (8, 8)}
(c) {(3, 1), (3, 2), (3, 3), (3, 8)}
(d) {(1, 3), (2, 3), (3, 3), (8, 3)}

D

Question. Consider the following statements
I. If A ∩ B = Φ, then either A = Φ or B = Φ.
II. For a ¹ b, {a, b} = {b, a} and (a, b) ¹ (b, a).
III. If A ⊆ B, then A x A ⊆ (A x B) ∩ (B x A).
IV. If A ⊆ B and C ⊆ D, then A x C ⊆ B ´ D.
Which of these is/are correct?
(a) Only (II)
(b) Only (I)
(c) Only (IV)
(d) (II), (III) and (IV)

D

Question. If A = {x : x – x + = } 2 5 6 0 , B = {2, 4}, C = {4, 5}, then
A x (B ∩C) is
(a) {(2, 4), (3, 4)}
(b) {(4, 2), (4, 3)}
(c) {(2, 4), (3, 4), (4, 4)}
(d) {(2, 2), (3, 3), (4, 4), (5, 5)}

A

Question. If[x] 2 – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, then
(a) x ∈ [3, 4]
(b) x ∈ (2, 3]
(c) x ∈ [2, 3]
(d) x ∈ [2, 4)

D

Question. Let f (x) = x2 – x + 1, x ≥ 1/2 , then the solution of the equation f (x) = f -1(x) is
(a) x = 1
(b) x = 2
(c) x = 1/2
(d) None of these

A

Question. Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is
(a) 29
(b) 6
(c) 8
(d) None of these

A

Question. Let n(A) = m and n(B) = n.Then, the total number of non-empty relations that can be defined from A to B is
(a) mn
(b) nm – 1
(c) mn – 1
(d) 2 1 mn –

D

Question. The relation Rdefined on set A = {x : x < 3, x ∈I }by R = {(x, y) : y = x } is
(a) {(- 2, 2), (- 1, 1), (0, 0), (1, 1), (2, 2)}
(b) {(- 2, – 2), (- 2, 2), (- 1, 1), (0, 0), (1, – 2), (1, 2), (2, -1), (2, – 2)}
(c) {(0, 0), (1, 1), (2, 2)}
(d) None of the above

A

Question. The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}, is given by
(a) {(1, 4), (2, 5), (3, 6), . . . . }
(b) {(4, 1), (5, 2), (6, 3), . . . . }
(c) {(1, 3), (2, 6), (3, 9), . . . . }
(d) None of the above

B

Question. If the function f (x) = ax + a-x (a >2) =, then f(x + y) + f(x – y) is equal to
(a) 2f(x) f(y)
(b) f(x) f(y)
(c) f (x)/f (y)
(d) None of these

A

Question. Domain and range of f(x) |x-3 /x-3| = are respectively
(a) R, [-1, 1]
(b) R – {3}, {1, -1}
(c) R R T ,
(d) None of these

B

Question. Let R be the relation from A = {2, 3, 4, 5} to B = {3, 6, 7, 10} defined by ‘x divides y’, then R-1 is equal to
(a) {(6, 2), (3, 3)}
(b) {(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}
(c) {(6, 2), (10, 2), (3, 3), (6, 3)}
(d) None of the above

B

Question. R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R-1 is
(a) {(11, 8), (13, 10)}
(b) {(8, 11), (10, 13)}
(c) {(8, 11), (9, 12), (10, 13)}
(d) None of these

B

Question. If R is a relation from a set A to the set B and S is a relation from B to C, then the relation SoR
(a) is from C to A
(b) is from A to C
(c) does not exist
(d) None of these

B

Question. The domain and range of the real function f defined by f (x)=4-x/x-4 is given by
(a) Domain = R, Range = {-1, 1}
(b) Domain = R – {1}, Range = R
(c) Domain R=- { }4 , Range ={-}1
(d) Domain = R – {-4}, Range = {-1, 1}

C

Question. The domain of the function f given by f (x) = x2 +2x+1 /x2 – x- 6
(a) R – {3, – 2}
(b) R – {-3, 2}
(c) R – [3, – 2]
(d) R – (3, – 2)

A

Question. The domain and range of the function f given by f (x) = 2 -|x – 5|is
(a) Domain = R+ , Range = (-∞, 1]
(b) Domain = R, Range = (-∞, 2]
(c) Domain = R , Range = (-∞, 2)
(d) Domain = R+ , Range = (-∞, 2]

B

Question. If f : R → R, g : R → R and h : R → R are such that f (x) = x2, g(x) = tan x and h(x) = log x, then the value of (ho( gof ))(x), if x = √π/4 will be
(a) 0
(b) 1
(c) –1
(d) π

A

Question. If R = {(x, y) : x, y ∈ I, x2 + y≤ 4 } is a relation in I, then domain of R is
(a) {0, 1, 2}
(b) {- 2, – 1, 0}
(c) {- 2, – 1, 0, 1, 2}
(d) None of these

C

Question. Let R be a relation on N defined by x + 2y = 8. The domain of R is
(a) {2, 4, 8}
(b) {2, 4, 6, 8}
(c) {2, 4, 6}
(d) {1, 2, 3, 4}

C

Question. A real valued function f (x) satisfies the functional equation
f (x – y) = f (x) f ( y) – f (a – x) f (a + y)
where a is a given constant and f (0) = 1, f (2a – x) is equal to
(a) f(-x)
(b) f(a) + f(a – x)
(c) f(x)
(d) -f(x)