Sets

What you'll learn

A friendly, first-principles walk through Class 11 Sets — what a set really is, its types, subsets and power sets, union/intersection/complement, and the n(A∪B) counting formula, with a fully solved survey problem. Your foundation for JEE, NEET and CUET.

This chapter has

Sets — solved practice questions

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

1. Q1easy

   Which of the following is the roster (tabular) form of the set A = {x : x is a positive integer and x squared < 40}?

   • A{1, 2, 3, 4, 5}
   • B{2, 3, 4, 5, 6}
   • C{1, 2, 3, 4, 5, 6, 7}
   • D{1, 2, 3, 4, 5, 6}
   Show answer & solution

   Correct answer: (D) {1, 2, 3, 4, 5, 6}

   The positive integers whose squares are below 40 are 1 to 6, since 6 squared = 36 < 40 but 7 squared = 49 > 40. So A = {1, 2, 3, 4, 5, 6}.

2. Q2easy

   How many subsets does a set with 5 elements have?

   • A10
   • B25
   • C32
   • D31
   Show answer & solution

   Correct answer: (C) 32

   A set with n elements has 2^n subsets. Here 2^5 = 32, a count that includes the empty set and the set itself.

3. Q3easy

   The number of proper subsets of the set {a, b, c} is:

   • A7
   • B8
   • C6
   • D5
   Show answer & solution

   Correct answer: (A) 7

   A set with n elements has 2^n subsets; proper subsets exclude the set itself, giving 2^n - 1. For n = 3 that is 8 - 1 = 7.

4. Q4easy

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

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

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

   The union collects every element that is in A or in B, listing common elements only once: A union B = {1, 2, 3, 4}.

5. Q5easy

   If A is the set of factors of 12 and B is the set of factors of 18, then A intersection B is:

   • A{1, 2, 3}
   • B{6}
   • C{1, 2, 3, 6, 9}
   • D{1, 2, 3, 6}
   Show answer & solution

   Correct answer: (D) {1, 2, 3, 6}

   Factors of 12 = {1, 2, 3, 4, 6, 12} and factors of 18 = {1, 2, 3, 6, 9, 18}. Their common factors are {1, 2, 3, 6}.

6. Q6medium

   If n(A) = 20, n(B) = 28 and n(A union B) = 36, then n(A intersection B) equals:

   • A8
   • B12
   • C16
   • D4
   Show answer & solution

   Correct answer: (B) 12

   Using n(A union B) = n(A) + n(B) - n(A intersection B): 36 = 20 + 28 - n(A intersection B), so n(A intersection B) = 48 - 36 = 12.

7. Q7medium

   In a class of 35 students, 24 like cricket and 16 like football, and every student likes at least one of the two. How many like both?

   • A5
   • B6
   • C9
   • D11
   Show answer & solution

   Correct answer: (A) 5

   Since every student likes at least one, n(both) = n(cricket) + n(football) - total = 24 + 16 - 35 = 5.

8. Q8medium

   By De Morgan's law, (A union B)' equals:

   • AA' union B'
   • BA' intersection B'
   • CA intersection B
   • DA' union B
   Show answer & solution

   Correct answer: (B) A' intersection B'

   De Morgan's law states (A union B)' = A' intersection B' — the complement of a union is the intersection of the complements.

Want the full set? Practise all 15 Sets questions →