Relations and Functions

What you'll learn

A from-scratch, NCERT-aligned guide to ordered pairs, Cartesian products, relations, domain, range and codomain, and the different types of functions, built up with everyday Indian analogies and fully worked examples so you truly understand the ideas that power JEE, NEET and CUET maths.

This chapter has

Relations and Functions — solved practice questions

8 Class 11 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   If A = {1, 2} and B = {3, 4}, then the number of elements in A x B is:

   • A2
   • B4
   • C6
   • D8
   Show answer & solution

   Correct answer: (B) 4

   n(A x B) = n(A) x n(B) = 2 x 2 = 4 ordered pairs.

2. Q2easy

   If A = {1, 2} and B = {3, 4}, then A x B is:

   • A{(1, 3), (1, 4), (2, 3), (2, 4)}
   • B{(3, 1), (4, 1), (3, 2), (4, 2)}
   • C{(1, 3), (2, 4)}
   • D{(1, 2), (3, 4)}
   Show answer & solution

   Correct answer: (A) {(1, 3), (1, 4), (2, 3), (2, 4)}

   A x B is the set of all ordered pairs (a, b) with a in A and b in B: {(1, 3), (1, 4), (2, 3), (2, 4)}.

3. Q3easy

   If (x + 1, y - 2) = (3, 1), then the values of x and y are:

   • A(3, 2)
   • B(2, 3)
   • C(2, 1)
   • D(4, 3)
   Show answer & solution

   Correct answer: (B) (2, 3)

   Two ordered pairs are equal when corresponding entries match: x + 1 = 3 gives x = 2, and y - 2 = 1 gives y = 3.

4. Q4easy

   A relation R from a set A to a set B is defined as a subset of:

   • AA x B
   • BB x A
   • CA union B
   • DA intersection B
   Show answer & solution

   Correct answer: (A) A x B

   A relation from A to B is any subset of the Cartesian product A x B.

5. Q5medium

   The domain of the real function f(x) = 1/(x - 3) is:

   • AR
   • BR - {3}
   • CR - {-3}
   • D(3, infinity)
   Show answer & solution

   Correct answer: (B) R - {3}

   The function is undefined when the denominator is zero, at x = 3, so the domain is all real numbers except 3: R - {3}.

6. Q6medium

   The range of the function f(x) = x squared, where x is in R, is:

   • AR
   • B(0, infinity)
   • C[0, infinity)
   • D(-infinity, 0]
   Show answer & solution

   Correct answer: (C) [0, infinity)

   A square is never negative and takes every value from 0 upward, with f(0) = 0, so the range is [0, infinity).

7. Q7easy

   If f(x) = x squared + 1, then f(-2) equals:

   • A3
   • B4
   • C-3
   • D5
   Show answer & solution

   Correct answer: (D) 5

   f(-2) = (-2) squared + 1 = 4 + 1 = 5.

8. Q8medium

   The domain of the function f(x) = square root of (x - 2) is:

   • A[2, infinity)
   • B(2, infinity)
   • C(-infinity, 2]
   • DR - {2}
   Show answer & solution

   Correct answer: (A) [2, infinity)

   The expression under a square root must be non-negative: x - 2 >= 0, that is x >= 2, so the domain is [2, infinity).

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