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CBSE · Class 11 · Mathematics

Relations and Functions

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
If n(A) = 2 and n(B) = 3, the number of relations from A to B is:
  1. 25
  2. 6
  3. 23
  4. 26
2.
If (x + 6, y − 3) = (8, 6), then (x, y) is:
  1. (14, 3)
  2. (9, 2)
  3. (2, 9)
  4. (2, 3)
3.
The domain of the relation R = {(2, 2), (5, 2), (8, 1), (8, 6), (4, 7)} is:
  1. {2, 4, 5}
  2. {2, 4, 5, 8}
  3. {1, 2, 6, 7}
  4. {1, 2, 4, 5, 6, 7, 8}
4.
If f(x) = −3x2 + 2x, then f(0) is:
  1. 1
  2. −6
  3. 0
  4. 2
5.
The Cartesian product A × B is the set of all:
  1. unordered pairs
  2. elements in A or B
  3. elements in both A and B
  4. ordered pairs (a, b) with a ∈ A and b ∈ B
6.
Which of these relations is a function?
  1. {(3, 7), (4, 9), (2, 8), (1, 2)}
  2. {(2, 7), (1, 8), (3, 3), (2, 2)}
  3. {(4, 7), (5, 8), (2, 9), (4, 4)}
  4. {(4, 9), (5, 7), (3, 5), (3, 9)}
7.
If f(x) = 2x + 1 and g(x) = 3x − 8, then (f + g)(−3) is:
  1. −22
  2. 85
  3. −21
  4. 22
8.
Assertion (A): If A has 4 elements and B has 3, then A × B has 12 elements.
Reason (R): n(A × B) = n(A) + n(B).
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find x and y if (x + 5, y − 2) = (23/4, −3/2).
10.
If A = {4, 5} and B = {3, 5}, write A × B. How many elements does it have?
11.
For A = {6, 7, 8}, define R = {(x, y) : y = x + 4, x ∈ A}. Write R in roster form and find its domain and range.
12.
For f(x) = −2x − 1, find f(4) and the value of x for which f(x) = 4.
13.
If f(x) = x2 − 4 and g(x) = x + 1, find (f + g)(x), (f − g)(x) and (fg)(x).
14.
Find the domain of the real function f(x) = (x2 + 2) / (x2 − 6x + 5).
15.
Find the range of the real function f(x) = −x2 − 1, x ∈ R.
16.
A has 3 elements and B has 1. How many elements does A × B have, and how many relations are there from A to B?
Section C — Word problems4 × 4 = 16 marks
17.
A relation R on A = {1, 2, 3, 4, 5, 6} is defined by R = {(x, y) : x divides y and x ≠ y; x, y ∈ A}. Write R in roster form and find its domain, codomain and range.
18.
A linear function f(x) = mx + c has f(−5) = 20 and f(−4) = 17. Find m and c, write f(x), and find f(−6).
19.
Let A = {1, 4}, B = {1, 2, 4, 5} and C = {5, 6}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C).
20.
f(x) = x2 for x < 0; f(x) = 3x for 0 ≤ x < 3; f(x) = 9 for x ≥ 3. Find f(−3), f(2), f(4). What is the range of f?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Mathematics

Answer key

Relations and Functions · AW-11M-RNF-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 26subsets of A × B, which has 6 elements
2(c) (2, 9)equal ordered pairs: first = first, second = second
3(b) {2, 4, 5, 8}—
4(c) 0—
5(d) ordered pairs (a, b) with a ∈ A and b ∈ B—
6(a) {(3, 7), (4, 9), (2, 8), (1, 2)}no first element may appear twice
7(a) −22f(−3) = −5, g(−3) = −17
8(c) A is true, but R is false.A is true: 4 × 3 = 12. R is false.
9x = 3/4, y = 1/2equate first and second elements
10{(4, 3), (4, 5), (5, 3), (5, 5)}; 4 elements—
11R = {(6, 10), (7, 11), (8, 12)}; domain {6, 7, 8}; range {10, 11, 12}—
12f(4) = −9; x = −5/2−2x − 1 = 4
13(f + g)(x) = x2 + x − 3; (f − g)(x) = x2 − x − 5; (fg)(x) = x3 + x2 − 4x − 4add, subtract or multiply the expressions
14R − {1, 5}the denominator is (x − 1)(x − 5), zero at x = 1, 5
15(−∞, −1]x2 ≥ 0, so f(x) ≤ −1
163; 23 = 8every subset of A × B is a relation
17R = {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 4), (2, 6), (3, 6)}; domain {1, 2, 3}; codomain {1, 2, 3, 4, 5, 6}; range {2, 3, 4, 5, 6}—
18m = −3, c = 5; f(x) = −3x + 5; f(−6) = 23m = (17 − 20) ÷ (−4 − (−5))
19B ∩ C = {5}, so A × (B ∩ C) = {(1, 5), (4, 5)}. (A × B) ∩ (A × C) keeps the pairs whose second element is in both B and C, which is the same set.—
20f(−3) = 9, f(2) = 6, f(4) = 9; range [0, ∞)use the rule for the interval each x lies in; x2 covers all positive values