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CBSE · Class 11 · Mathematics

Sets

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.
A set has 4 elements. How many subsets does it have?
  1. 8
  2. 15
  3. 17
  4. 16
2.
If A = {1, 4, 5, 7, 8, 10} and B = {2, 5, 8}, then A ∩ B is:
  1. {5, 8}
  2. {1, 2, 4, 5, 7, 8, 10}
  3. {1, 4, 7, 10}
  4. {2}
3.
If n(A) = 17, n(B) = 13 and n(A ∩ B) = 4, then n(A ∪ B) is:
  1. 26
  2. 22
  3. 30
  4. 34
4.
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 6, 7, 9, 10}, then A′ is:
  1. {1, 4}
  2. {2, 3, 5, 6, 7, 9, 10}
  3. {1, 4, 8}
  4. {4, 8}
5.
The empty set is written as:
  1. 0
  2. {0}
  3. {φ}
  4. φ or { }
6.
In roster form, {x : x ∈ N and x2 < 69} is:
  1. {2, 3, 4, 5, 6, 7, 8}
  2. {1, 2, 3, 4, 5, 6, 7}
  3. {1, 2, 3, 4, 5, 6, 7, 8}
  4. {1, 2, 3, 4, 5, 6, 7, 8, 9}
7.
How many integers are there in the interval (1, 11)?
  1. 11
  2. 8
  3. 10
  4. 9
8.
Assertion (A): If n(A) = 26, n(B) = 18 and n(A ∩ B) = 8, then n(A ∪ B) = 44.
Reason (R): n(A ∪ B) = n(A) + n(B) − n(A ∩ B), so that the common elements are not counted twice.
  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.
If A = {1, 2, 5, 6, 9, 10} and B = {2, 7, 9}, find A ∪ B, A ∩ B and A − B.
10.
In a group of 98 people, 49 like tea, 70 like coffee and 35 like both. How many like neither? How many like tea only?
11.
Write down all the subsets of {2, 6, 8}. How many elements does its power set have?
12.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {3, 5, 6, 7, 9, 10} and B = {1, 3, 4, 7, 9, 10}. Find (A ∪ B)′ and A′ ∩ B′. What do you notice?
13.
(a) Write {x : x ∈ R, −9 < x ≤ −5} as an interval. (b) Write [1, 10) in set-builder form.
14.
Write {x : x is a positive multiple of 6 and x ≤ 31} in roster form. How many elements does it have?
15.
n(A) = 29, n(B) = 35, n(C) = 32, n(A ∩ B) = 15, n(A ∩ C) = 16, n(B ∩ C) = 15 and n(A ∩ B ∩ C) = 7. Find n(A ∪ B ∪ C).
16.
If n(A) = 41, n(B) = 49 and n(A ∩ B) = 19, find n(A − B), n(B − A) and n(A ∪ B).
Section C — Word problems4 × 4 = 16 marks
17.
In a survey of 118 students, 36 read Hindi newspapers, 72 read English, 59 read Punjabi; 17 read Hindi and English, 21 read Hindi and Punjabi, 32 read English and Punjabi, and 5 read all three. How many read (a) none of them, (b) exactly one, (c) Hindi only?
18.
In a class of 93, 60 play cricket, 44 play football and 14 play neither. Find how many play (a) both, (b) cricket only, (c) football only. Draw a Venn diagram.
19.
Let A = {2, 6, 7, 8}, B = {2, 6, 8, 9, 10} and C = {1, 3, 4, 7, 8, 9}. Verify that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
20.
Set A has 2 more elements than set B, and A has 96 more subsets than B. How many elements does each set have?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Mathematics

Answer key

Sets · AW-11M-SET-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 1624
2(a) {5, 8}—
3(a) 26n(A) + n(B) − n(A ∩ B)
4(c) {1, 4, 8}the elements of U not in A
5(d) φ or { }{0} has one element, 0
6(c) {1, 2, 3, 4, 5, 6, 7, 8}—
7(d) 9excludes 1; excludes 11
8(d) A is false, but R is true.A is false: 26 + 18 − 8 = 36. R is true.
9A ∪ B = {1, 2, 5, 6, 7, 9, 10}; A ∩ B = {2, 9}; A − B = {1, 5, 6, 10}—
10Neither: 14; tea only: 14n(T ∪ C) = 49 + 70 − 35 = 84
11φ, {2}, {6}, {8}, {2, 6}, {2, 8}, {6, 8}, {2, 6, 8}; 8 elements23 = 8
12Both are {2, 8}: (A ∪ B)′ = A′ ∩ B′ (De Morgan's law)A ∪ B = {1, 3, 4, 5, 6, 7, 9, 10}
13(a) (−9, −5]; (b) {x : x ∈ R, 1 ≤ x < 10}—
14{6, 12, 18, 24, 30}; 5 elements—
155729 + 35 + 32 − 15 − 16 − 15 + 7
16n(A − B) = 22; n(B − A) = 30; n(A ∪ B) = 71n(A − B) = n(A) − n(A ∩ B)
17(a) 16; (b) 42; (c) 3fill the Venn diagram from the centre outwards
18(a) 25; (b) 35; (c) 19n(C ∪ F) = 93 − 14 = 79; both = 60 + 44 − 79
19B ∩ C = {8, 9}, so A ∪ (B ∩ C) = {2, 6, 7, 8, 9}. A ∪ B = {2, 6, 7, 8, 9, 10}, A ∪ C = {1, 2, 3, 4, 6, 7, 8, 9}, and their intersection is {2, 6, 7, 8, 9}. Both sides are equal.—
20A has 7, B has 52ᵐ − 2ᵏ = 96 = 2ᵏ(22 − 1) = 25 × 3