A B A∩B A∪B U
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Chapter 1  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Sets

Master Every Set Operation — From Venn Diagrams to De Morgan's Laws

📋 50 MCQs ⭐ 34 PYQs ⏱ 75 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
24Easy
17Medium
9Hard
34PYQs
75 secAvg Time/Q
7Topics
Easy 48% Medium 34% Hard 18%

Why Practise These MCQs?

CBSE Class XIJEE MainJEE Advanced

This MCQ collection mixes CBSE Class XI basics with JEE Main and JEE Advanced style questions. You start with membership, subsets and simple Venn regions, then move to inclusion-exclusion counts, power sets, relations and equivalence classes. Many items are built in past-exam style so you can train both concept clarity and combinatorial speed in one place.

Topic-wise MCQ Breakdown

Representation & Types of Sets9 Q
Subsets, Power Sets & Complements11 Q
Set Operations & Standard Identities9 Q
Venn Diagrams & Counting (n(A∪B))7 Q
Relations & Power-Set Based Counts6 Q
Advanced Subset / Chain Logic (JEE)5 Q
Combinatorial Subset Problems3 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$n(A∪B) = n(A)+n(B)−n(A∩B)$
$(A∪B)' = A'∩B'$
$P(A) = 2^{n(A)}$
$n(A∪B∪C) = Σn(A)−Σn(A∩B)+n(A∩B∩C)$

MCQ Solving Strategy

Always draw a Venn diagram first — it converts abstract set problems into visible regions instantly. For De Morgan's Law MCQs, prove both sides rather than memorising directly. The single most common trap is confusing ∅ with {∅} — the first has zero elements, the second has one.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify types of sets, write roster/set-builder form, basic unions

② Medium

Two-set Venn diagrams, cardinal number problems, De Morgan's verification

③ Hard

Three-set inclusion-exclusion word problems, power set MCQs

★ PYQ

JEE Main — combined operations; CBSE — formal proof-based MCQs

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Relations & Functions MCQs
🎯 Knowledge Check

Maths — SETS

50 Questions Class 11 MCQs
1
Which of the following represents a well-defined set? (Exam: CBSE Class XI)
2
If \(A = \{1,2,3\}\), then the number of elements in \(A\) is: (Exam: CBSE Class XI)
3
Which of the following is an empty set? (Exam: CBSE Class XI)
4
If \(A = \{a,e,i,o,u\}\), then \(A\) is a subset of: (Exam: CBSE Class XI)
5
Which statement is always true? (Exam: CBSE Class XI)
6
If \(A = \{1,2\}\), how many subsets does \(A\) have? (Exam: CBSE Class XI)
7
If \(A = \{1,2,3\}\) and \(B = \{3,4\}\), then \(A \cap B\) is: (Exam: CBSE Class XI)
8
If \(A = \{1,2\}\) and \(B = \{3,4\}\), then \(A \cup B\) is: (Exam: CBSE Class XI)
9
Which of the following is true? (Exam: CBSE Class XI)
10
If \(U\) is the universal set and \(A \subset U\), then \(A \cup U =\): (Exam: CBSE Class XI)
11
The complement of the universal set \(U\) is: (Exam: CBSE Class XI)
12
If \(A' = \varnothing\), then \(A =\): (Exam: CBSE Class XI)
13
If \(A \subset B\), then \(A \cap B =\): (Exam: CBSE Class XI)
14
If \(A \subset B\), then \(A \cup B =\): (Exam: CBSE Class XI)
15
Which law is expressed by \(A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\)? (Exam: CBSE Class XI)
16
Which law is given by \((A \cup B)' = A' \cap B'\)? (Exam: CBSE Class XI)
17
If \(n(A)=10\), then the number of proper subsets of \(A\) is: (Exam: CBSE Class XI)
18
If \(A = \{x : x^2 = 1\}\), then \(A\) is: (Exam: CBSE Class XI)
19
Which of the following sets are equal? (Exam: CBSE Class XI)
20
If \(A = \{1,2,3,4\}\) and \(B = \{3,4,5,6\}\), then \(A - B\) is: (Exam: CBSE Class XI)
21
If \(A \cap B = \varnothing\), then sets \(A\) and \(B\) are called: (Exam: CBSE Class XI)
22
If \(n(A)=5\) and \(n(B)=7\) and \(A\cap B=\varnothing\), then \(n(A\cup B)\) is: (Exam: CBSE Class XI)
23
If \(A = \{x : x \in \mathbb{Z}, -2 \le x \le 2\}\), then \(n(A)\) is: (Exam: CBSE Class XI)
24
Which of the following is true? (Exam: CBSE Class XI)
25
The power set of a set with 3 elements has: (Exam: CBSE Class XI)
26
If \(A\subset B\) and \(B\subset A\), then: (Exam: CBSE Class XI)
27
If \(A = \{1,2,3\}\), then \(A' \cup A\) equals: (Exam: CBSE Class XI)
28
Which identity is \(A \cap (A \cup B) = A\)? (Exam: CBSE Class XI)
29
If \(n(A)=20\) and \(n(A')=15\), then \(n(U)\) is: (Exam: CBSE Class XI)
30
Which of the following represents De Morgan’s second law? (Exam: CBSE Class XI)
31
If \(A=\{x:x\in\mathbb{N}, x\le5\}\), then \(A'\) contains: (Exam: JEE Main)
32
If \(n(A\cup B)=15\), \(n(A)=8\), \(n(B)=9\), then \(n(A\cap B)\) is: (Exam: JEE Main)
33
If \(A\cap B=A\), then: (Exam: JEE Main)
34
If \(A\cup B=B\), then: (Exam: JEE Main)
35
Number of elements in the power set of the power set of a set with 2 elements is: (Exam: JEE Main)
36
If \(A=\{1,2,3\}\), number of relations from \(A\) to \(A\) is: (Exam: JEE Main)
37
If \(A\) has \(n\) elements, number of symmetric relations on \(A\) is: (Exam: JEE Advanced)
38
If \(A=\{1,2\}\), number of equivalence relations on \(A\) is: (Exam: JEE Advanced)
39
If \(A\subseteq B\subseteq C\), then: (Exam: JEE Main)
40
If \(A\cap B=\varnothing\) and \(A\cup B=U\), then: (Exam: JEE Main)
41
If \(A\) has 5 elements, number of subsets containing exactly 3 elements is: (Exam: JEE Main)
42
If \(A=\{1,2,3,4\}\), number of subsets containing 1 and 2 but not 3 is: (Exam: JEE Main)
43
If \(n(A)=n(B)=n(A\cup B)\), then: (Exam: JEE Main)
44
If \(A\subset U\), then \(A\cap A'=\): (Exam: JEE Main)
45
If \(A=\{x:x^2<9, x\in\mathbb{Z}\}\), then \(n(A)\) is: (Exam: JEE Main)
46
If \(A\cup B=A\), then \(B\) is: (Exam: JEE Main)
47
If \(A\cap B=B\), then: (Exam: JEE Main)
48
If \(A\) has 4 elements, number of proper subsets is: (Exam: JEE Main)
49
If \(A=\{1,2,3\}\), number of subsets having odd number of elements is: (Exam: JEE Advanced)
50
If \(A\) is finite and \(A\subseteq B\subseteq A\), then \(B\) equals: (Exam: JEE Advanced)
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Frequently Asked Questions

A set is a well-defined collection of distinct objects called elements.

So that it is possible to clearly decide whether a given object belongs to the set or not.

The individual objects or members contained in a set are called its elements.

Sets are generally denoted by capital letters such as \(A,\, B,\, C\).

Elements are represented by small letters such as \(a, \,b,\, x\).

It means “belongs to” or “is an element of”.

It means “does not belong to” a given set.

A method of listing all elements of a set within curly braces.

A representation describing a set by a common property satisfied by its elements.

(\A = {2,4,6,8}\).

\(A = {x : x \text{ is an even natural number}}\).

A set containing no elements, denoted by \(\varnothing\).

Yes, there is only one empty set.

A set containing exactly one element.

A set with a definite number of elements.

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