Class 11 Maths Chapter 2 Relations and Functions MCQs with answers (CBSE Class 11 and JEE Main; based on NCERT)

10 multiple-choice questions on Relations and Functions, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1

If n(A × B) = 15 and n(A) = 5, then n(B) is

(a) 10(b) 3(c) 20(d) 75

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Answer: (b) 3

n(A × B) = n(A) × n(B), so 15 = 5 × n(B) and n(B) = 3. 10 subtracts, 20 adds and 75 multiplies the two given numbers.

Question 2

If A = {2, 4, 6} and B = φ, the number of elements in A × B is

(a) 0(b) 3(c) 1(d) 6

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Answer: (a) 0

A × B is the set of pairs (a, b) with b ∈ B; B has no element, so no pair can be formed and A × B = φ, with 0 elements.

Question 3

The rule f(x) = x + k for −4 ≤ x ≤ 1 and f(x) = 3x − 1 for 1 ≤ x ≤ 6 defines a function on [−4, 6] only when k equals

(a) 2(b) 0(c) 1(d) −1

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Answer: (c) 1

x = 1 lies in both pieces, so its two values must agree: 1 + k = 3 × 1 − 1 = 2, giving k = 1. For any other k the element 1 has two images and the rule is not a function.

Question 4

If A = {1, 2} and B = {2, 3}, then (A × B) ∩ (B × A) is

(a) φ(b) {(1, 2), (2, 1)}(c) {(2, 3), (3, 2)}(d) {(2, 2)}

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Answer: (d) {(2, 2)}

A × B = {(1, 2), (1, 3), (2, 2), (2, 3)} and B × A = {(2, 1), (2, 2), (3, 1), (3, 2)}. Order matters, so (1, 2) and (2, 1) are different pairs; the only pair in both is (2, 2).

Question 5

The real number x for which the ordered pairs (x², 4) and (9, x + 7) are equal is

(a) 3(b) ±3(c) −3(d) no such x

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Answer: (c) −3

Equal ordered pairs need x² = 9 and 4 = x + 7. The second gives x = −3, which also satisfies the first. x = 3 satisfies only the first.

Question 6

The number of relations on a set A having 3 elements is

(a) 9(b) 512(c) 64(d) 8

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Answer: (b) 512

A relation on A is a subset of A × A, which has 3 × 3 = 9 elements, so there are 2⁹ = 512 relations. 9 counts the pairs, not the subsets; 8 = 2³ counts the subsets of A.

Question 7

The number of relations from A to B is 4096. If n(A) = 4, then n(B) is

(a) 3(b) 8(c) 4(d) 1024

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Answer: (a) 3

The number of relations is 2^{n(A) n(B)} = 2^{4 n(B)} = 4096 = 2¹², so 4 n(B) = 12 and n(B) = 3. 1024 divides 4096 by 4 without taking the logarithm.

Question 8

The range of the relation R = {(x, y) : y = x², x ∈ {−2, −1, 0, 1, 2}} is

(a) {−2, −1, 0, 1, 2}(b) {1, 4}(c) {0, 1, 2, 4}(d) {0, 1, 4}

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Answer: (d) {0, 1, 4}

R = {(−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4)}. The range is the set of second elements, {0, 1, 4}; {−2, −1, 0, 1, 2} is the domain.

Question 9

A relation R from A = {1, 2, 3, 4} to B = {1, 3, 5, 7} is R = {(x, y) : x + y is a multiple of 4}. The domain of R is

(a) {1, 2, 3, 4}(b) {1, 3, 5, 7}(c) {2, 4}(d) {1, 3}

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Answer: (d) {1, 3}

R = {(1, 3), (1, 7), (3, 1), (3, 5)}; for x = 2 or 4, x + y is odd. The domain, the set of first elements, is {1, 3}. A is the set the first elements come from, not the domain.

Question 10

If f(x) = x² and g(x) = 3x − 1, then (f − 2g)(2) equals

(a) −6(b) −1(c) 6(d) 14

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Answer: (a) −6

(f − 2g)(2) = f(2) − 2g(2) = 4 − 2 × 5 = −6. Forgetting the scalar 2 gives 4 − 5 = −1; adding gives 14.

Class 11 Maths Chapter 2: Relations and Functions MCQs with answers