SETS--Objective Questions for Entrance Exams The concept of Sets forms the logical foundation of modern mathematics and plays a decisive role in competitive examinations such as JEE (Main & Advanced), NEET, BITSAT, KVPY, Olympiads, and state engineering entrance tests. Questions from this chapter test not only factual knowledge but also analytical precision, logical reasoning, and the ability to interpret symbolic relationships accurately. The following carefully curated set of 50 multiple-choice questions reflects authentic examination patterns and repeatedly tested models across national-level entrance exams. These MCQs progressively advance from fundamental ideas like subsets and operations on sets to higher-order applications involving De Morgan’s laws, Cartesian products, relations, equivalence of sets, symmetric difference, and logical traps commonly used to challenge aspirants. Each question is accompanied by a concise explanation to reinforce conceptual clarity and exam temperament. Practicing these problems enables students to strengthen their mathematical reasoning, avoid common pitfalls, and develop the confidence required to tackle high-stakes competitive examinations with accuracy and speed.
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📚 PYQ Question Bank
Actual questions from IIT-JEE, NEET, AIIMS, BITSAT & KVPY —
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Q1
If \(A=\{1,2,3\}\) and \(B=\{2,3,4\}\), then \(A\cap B\) is (Exam: IIT-JEE Year: 1998)
(A) \(\{1,4\}\)
(B) \(\{2,3\}\)
(C) \(\{1,2,3,4\}\)
(D) \(\phi\)
Reveal Answer
✅ Correct: (B)
Q2
If \(n(A)=20\), \(n(B)=15\) and \(n(A\cap B)=5\), then \(n(A\cup B)\) is (Exam: AIPMT Year: 2001)
(A) 30
(B) 35
(C) 25
(D) 40
Reveal Answer
✅ Correct: (C)
Q3
If \(U=\{1,2,3,4,5\}\) and \(A=\{1,3\}\), then \(A'\) is (Exam: NEET Year: 2013)
(A) \(\{2,4,5\}\)
(B) \(\{1,3\}\)
(C) \(\{1,2,3\}\)
(D) \(\phi\)
Reveal Answer
✅ Correct: (A)
Q4
If \(A\subset B\), then \(A\cup B\) equals (Exam: BITSAT Year: 2005)
(A) \(A\)
(B) \(B\)
(C) \(\phi\)
(D) \(A\cap B\)
Reveal Answer
✅ Correct: (B)
Q5
If \(A=\phi\), then \(A\cup B\) equals (Exam: KVPY Year: 2008)
(A) \(\phi\)
(B) \(A\)
(C) \(B\)
(D) \(U\)
Reveal Answer
✅ Correct: (C)
Q6
If \(A\cap B=\phi\), then sets \(A\) and \(B\) are (Exam: JEE Main Year: 2014)
(A) Equal
(B) Finite
(C) Disjoint
(D) Universal
Reveal Answer
✅ Correct: (C)
Q7
Number of subsets of a set containing 5 elements is (Exam: IIT-JEE Year: 1992)
(A) 10
(B) 25
(C) 32
(D) 120
Reveal Answer
✅ Correct: (C)
Q8
If \(A=\{x:x^2-5x+6=0\}\), then \(A\) is (Exam: JEE Advanced Year: 2016)
(A) \(\{1,6\}\)
(B) \(\{2,3\}\)
(C) \(\{3,5\}\)
(D) \(\{2,6\}\)
Reveal Answer
✅ Correct: (B)
Q9
If \(A=\{1,2\}\), number of relations on \(A\) is (Exam: Olympiad Year: 2010)
(A) 4
(B) 8
(C) 16
(D) 32
Reveal Answer
✅ Correct: (C)
Q10
If \(A\cup B=A\), then (Exam: IIT-JEE Year: 2000)
(A) \(A\subset B\)
(B) \(B\subset A\)
(C) \(A=B\)
(D) \(A\cap B=\phi\)
Reveal Answer
✅ Correct: (B)
Q11
If \(A=\{x:x\in \mathbb{N}, x<5\}\), then \(A\) equals (Exam: NEET Year: 2018)
(A) \(\{1,2,3,4\}\)
(B) \(\{0,1,2,3,4\}\)
(C) \(\{1,2,3\}\)
(D) \(\{2,3,4\}\)
Reveal Answer
✅ Correct: (A)
Q12
If \(A\subset B\) and \(B\subset C\), then (Exam: JEE Main Year: 2017)
(A) \(A=C\)
(B) \(A\subset C\)
(C) \(C\subset A\)
(D) \(A\cap C=\phi\)
Reveal Answer
✅ Correct: (B)
Q13
If \(A=\{1,2,3\}\), then power set \(P(A)\) has how many elements? (Exam: IIT-JEE Year: 1995)
Reveal Answer
✅ Correct: (C)
Q14
If \(A\cap B=B\), then (Exam: BITSAT Year: 2009)
(A) \(A\subset B\)
(B) \(B\subset A\)
(C) \(A=B\)
(D) \(A\cup B=B\)
Reveal Answer
✅ Correct: (B)
Q15
If \(A=\{1,2,3\}\), then \(\phi\) is (Exam: State Engg Year: 2011)
(A) \(\{0\}\)
(B) \(\{\phi\}\)
(C) \(\emptyset\)
(D) \(\{1\}\)
Reveal Answer
✅ Correct: (C)
Q16
If \(A=\{1,2,3\}\), then number of proper subsets is (Exam: IIT-JEE Year: 1999)
Reveal Answer
✅ Correct: (B)
Q17
If \(A\subseteq B\) and \(B\subseteq A\), then (Exam: JEE Main Year: 2015)
(A) \(A=\phi\)
(B) \(B=\phi\)
(C) \(A=B\)
(D) \(A\cap B=\phi\)
Reveal Answer
✅ Correct: (C)
Q18
If \(U=\{1,2,3,4\}\) and \(A=\{2,4\}\), then \(A'\cap A\) is (Exam: NEET Year: 2020)
(A) \(\{2,4\}\)
(B) \(\{1,3\}\)
(C) \(\phi\)
(D) \(U\)
Reveal Answer
✅ Correct: (C)
Q19
If \(A=\{1,2\}\) and \(B=\{2,3\}\), then \(A-B\) is (Exam: Olympiad Year: 2012)
(A) \(\{2\}\)
(B) \(\{1\}\)
(C) \(\{3\}\)
(D) \(\phi\)
Reveal Answer
✅ Correct: (B)
Q20
If \(A\cup B=U\) and \(A\cap B=\phi\), then \(B\) equals (Exam: IIT-JEE Year: 1997)
(A) \(A\)
(B) \(A'\)
(C) \(U\)
(D) \(\phi\)
Reveal Answer
✅ Correct: (B)
Q21
If \(A\) and \(B\) are subsets of universal set \(U\), then \((A\cup B)'\) equals (Exam: IIT-JEE Year: 1996)
(A) \(A'\cup B'\)
(B) \(A'\cap B'\)
(C) \(A\cap B\)
(D) \(U\)
Reveal Answer
✅ Correct: (B)
Q22
If \((A\cap B)'=A'\cup B'\), then the law used is (Exam: JEE Main Year: 2019)
(A) Commutative law
(B) Associative law
(C) De Morgan’s law
(D) Distributive law
Reveal Answer
✅ Correct: (C)
Q23
If \(A=\{1,2,3\}\) and \(B=\{3,4,5\}\), then \(A\triangle B\) is (Exam: BITSAT Year: 2010)
(A) \(\{3\}\)
(B) \(\{1,2,4,5\}\)
(C) \(\{1,2,3,4,5\}\)
(D) \(\phi\)
Reveal Answer
✅ Correct: (B)
Q24
If \(A\triangle B=\phi\), then (Exam: IIT-JEE Year: 2002)
(A) \(A\cap B=\phi\)
(B) \(A\cup B=\phi\)
(C) \(A=B\)
(D) \(A\subset B\)
Reveal Answer
✅ Correct: (C)
Q25
If \(A=\{1,2\}\) and \(B=\{x,y,z\}\), then number of elements in \(A\times B\) is (Exam: NEET Year: 2016)
Reveal Answer
✅ Correct: (D)
Q26
If \(A=\{1,2,3\}\), number of relations on \(A\) is (Exam: IIT-JEE Year: 1994)
(A) \(2^3\)
(B) \(2^6\)
(C) \(3^2\)
(D) \(3^3\)
Reveal Answer
✅ Correct: (B)
Q27
Two sets \(A\) and \(B\) are equivalent if (Exam: Olympiad Year: 2011)
(A) \(A=B\)
(B) \(A\subset B\)
(C) \(n(A)=n(B)\)
(D) \(A\cap B=\phi\)
Reveal Answer
✅ Correct: (C)
Q28
If \(A\subset U\), then \(A\cup A'\) equals (Exam: JEE Main Year: 2018)
(A) \(A\)
(B) \(A'\)
(C) \(\phi\)
(D) \(U\)
Reveal Answer
✅ Correct: (D)
Q29
If \(A\cap (B\cup C)=(A\cap B)\cup(A\cap C)\), the law illustrated is (Exam: IIT-JEE Year: 1993)
(A) Commutative
(B) Associative
(C) Distributive
(D) Identity
Reveal Answer
✅ Correct: (C)
Q30
If \(A-B=\phi\), then (Exam: BITSAT Year: 2012)
(A) \(A=B\)
(B) \(A\subset B\)
(C) \(B\subset A\)
(D) \(A\cap B=\phi\)
Reveal Answer
✅ Correct: (B)
Q31
If \(n(A)=10\) and number of proper subsets of \(A\) is (Exam: IIT-JEE Year: 1991)
(A) \(2^{10}\)
(B) \(2^{10}-1\)
(C) \(10\)
(D) \(10!\)
Reveal Answer
✅ Correct: (B)
Q32
If \(A=\{x:x\in\mathbb{R}, x^2<4\}\), then \(A\) equals (Exam: NEET Year: 2021)
(A) \((-2,2)\)
(B) \([-2,2]\)
(C) \((-\infty,2)\)
(D) \((2,\infty)\)
Reveal Answer
✅ Correct: (A)
Q33
If \(A\cap B=A\), then (Exam: IIT-JEE Year: 2001)
(A) \(A\subset B\)
(B) \(B\subset A\)
(C) \(A=B\)
(D) \(A=\phi\)
Reveal Answer
✅ Correct: (A)
Q34
If \(A=\{1,2\}\), then \(P(A)\) contains (Exam: State Engg Year: 2014)
(A) 2 elements
(B) 3 elements
(C) 4 elements
(D) 5 elements
Reveal Answer
✅ Correct: (C)
Q35
If \(A\cup B=B\), then (Exam: JEE Main Year: 2020)
(A) \(A=B\)
(B) \(A\subset B\)
(C) \(B\subset A\)
(D) \(A\cap B=\phi\)
Reveal Answer
✅ Correct: (B)
Q36
If \(A=\{1,2,3\}\) and \(B=\{2,3\}\), then \(B-A\) is (Exam: NEET Year: 2015)
(A) \(\{2,3\}\)
(B) \(\{1\}\)
(C) \(\phi\)
(D) \(\{1,2,3\}\)
Reveal Answer
✅ Correct: (C)
Q37
If \(U=\{1,2,3,4\}\) and \(A=\{1,2\}\), then \(A'-A\) equals (Exam: Olympiad Year: 2013)
(A) \(\{3,4\}\)
(B) \(\{1,2\}\)
(C) \(\phi\)
(D) \(U\)
Reveal Answer
✅ Correct: (A)
Q38
If \(A\times B=B\times A\) and both are non-empty finite sets, then (Exam: IIT-JEE Year: 1998)
(A) \(A=B\)
(B) \(n(A)=n(B)\)
(C) \(A\subset B\)
(D) Either a) or b)
Reveal Answer
✅ Correct: (A)
Q39
Number of equivalence relations on a set with one element is (Exam: KVPY Year: 2010)
Reveal Answer
✅ Correct: (B)
Q40
If \(A\cap B=\phi\) and both are non-empty, then (Exam: IIT-JEE Year: 1990)
(A) \(A=B\)
(B) \(A\subset B\)
(C) \(A\cup B\) has more elements than each
(D) \(A\cup B=\phi\)
Reveal Answer
✅ Correct: (C)
Q41
If \(A=\{1,2,3\}\), then number of ordered pairs in \(A\times A\) is (Exam: NEET Year: 2019)
Reveal Answer
✅ Correct: (C)
Q42
If \(A\subset B\), then \(A\cap B\) equals (Exam: BITSAT Year: 2007)
(A) \(A\)
(B) \(B\)
(C) \(\phi\)
(D) \(U\)
Reveal Answer
✅ Correct: (A)
Q43
If \(A=\{1,2,3\}\), number of subsets containing element 1 is (Exam: IIT-JEE Year: 1997)
Reveal Answer
✅ Correct: (B)
Q44
If \(A\triangle B=(A\cup B)-(A\cap B)\), the statement is (Exam: JEE Main Year: 2016)
(A) False
(B) Conditionally true
(C) Always true
(D) Never true
Reveal Answer
✅ Correct: (C)
Q45
If \(A=\phi\), then \(P(A)\) equals (Exam: NEET Year: 2017)
(A) \(\phi\)
(B) \(\{\phi\}\)
(C) \(\{0\}\)
(D) \(U\)
Reveal Answer
✅ Correct: (B)
Q46
If \(A=\{x:x\in\mathbb{Z}, -2\le x\le2\}\), then \(n(A)\) is (Exam: State Engg Year: 2012)
Reveal Answer
✅ Correct: (C)
Q47
If \(A\subset B\) and \(B\subset C\), then \(A\cap C\) equals (Exam: IIT-JEE Year: 1995)
(A) \(A\)
(B) \(B\)
(C) \(C\)
(D) \(\phi\)
Reveal Answer
✅ Correct: (A)
Q48
If \(n(A)=n(B)=n(A\cap B)=5\), then (Exam: Olympiad Year: 2014)
(A) \(A\ne B\)
(B) \(A=B\)
(C) \(A\cap B=\phi\)
(D) \(A\subset B\) only
Reveal Answer
✅ Correct: (B)
Q49
If \(A=\{1,2\}\) and \(B=\{3,4\}\), then \(A\times B\cap B\times A\) is (Exam: IIT-JEE Year: 2003)
(A) \(\phi\)
(B) \(\{(1,3)\}\)
(C) \(\{(3,1)\}\)
(D) \(A\times B\)
Reveal Answer
✅ Correct: (A)
Q50
If \(A\cup B=U\) and \(A\cap B\ne\phi\), then (Exam: JEE Advanced Year: 2021)
(A) \(A=B\)
(B) \(A\) and \(B\) are complements
(C) \(A'\cap B'=\phi\)
(D) \(A'\cup B'=U\)
Reveal Answer
✅ Correct: (C)
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.
\(A = {x : x \text{ is an even natural number}}\).
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.
