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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) \(\phi\)
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
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) \(\phi\)
Q4
If \(A\subset B\), then \(A\cup B\) equals
(Exam: BITSAT Year: 2005)
(A) \(A\)
(B) \(B\)
(C) \(\phi\)
(D) \(A\cap B\)
Q5
If \(A=\phi\), then \(A\cup B\) equals
(Exam: KVPY Year: 2008)
(A) \(\phi\)
(B) \(A\)
(C) \(B\)
(D) \(U\)
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
Q7
Number of subsets of a set containing 5 elements is
(Exam: IIT-JEE Year: 1992)
(A) 10
(B) 25
(C) 32
(D) 120
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) \(\{2,6\}\)
Q9
If \(A=\{1,2\}\), number of relations on \(A\) is
(Exam: Olympiad Year: 2010)
(A) 4
(B) 8
(C) 16
(D) 32
Q10
If \(A\cup B=A\), then
(Exam: IIT-JEE Year: 2000)
(A) \(A\subset B\)
(B) \(B\subset A\)
(C) \(A=B\)
(D) \(A\cap B=\phi\)
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) \(\{2,3,4\}\)
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) \(A\cap C=\phi\)
Q13
If \(A=\{1,2,3\}\), then power set \(P(A)\) has how many elements?
(Exam: IIT-JEE Year: 1995)
(A) 3
(B) 6
(C) 8
(D) 9
Q14
If \(A\cap B=B\), then
(Exam: BITSAT Year: 2009)
(A) \(A\subset B\)
(B) \(B\subset A\)
(C) \(A=B\)
(D) \(A\cup B=B\)
Q15
If \(A=\{1,2,3\}\), then \(\phi\) is
(Exam: State Engg Year: 2011)
(A) \(\{0\}\)
(B) \(\{\phi\}\)
(C) \(\emptyset\)
(D) \(\{1\}\)
Q16
If \(A=\{1,2,3\}\), then number of proper subsets is
(Exam: IIT-JEE Year: 1999)
(A) 6
(B) 7
(C) 8
(D) 9
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) \(A\cap B=\phi\)
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) \(U\)
Q19
If \(A=\{1,2\}\) and \(B=\{2,3\}\), then \(A-B\) is
(Exam: Olympiad Year: 2012)
(A) \(\{2\}\)
(B) \(\{1\}\)
(C) \(\{3\}\)
(D) \(\phi\)
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) \(\phi\)
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) \(U\)
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
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) \(\phi\)
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) \(A\subset B\)
Q25
If \(A=\{1,2\}\) and \(B=\{x,y,z\}\), then number of elements in \(A\times B\) is
(Exam: NEET Year: 2016)
(A) 2
(B) 3
(C) 5
(D) 6
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) \(3^3\)
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) \(A\cap B=\phi\)
Q28
If \(A\subset U\), then \(A\cup A'\) equals
(Exam: JEE Main Year: 2018)
(A) \(A\)
(B) \(A'\)
(C) \(\phi\)
(D) \(U\)
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
Q30
If \(A-B=\phi\), then
(Exam: BITSAT Year: 2012)
(A) \(A=B\)
(B) \(A\subset B\)
(C) \(B\subset A\)
(D) \(A\cap B=\phi\)
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) \(10!\)
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) \((2,\infty)\)
Q33
If \(A\cap B=A\), then
(Exam: IIT-JEE Year: 2001)
(A) \(A\subset B\)
(B) \(B\subset A\)
(C) \(A=B\)
(D) \(A=\phi\)
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
Q35
If \(A\cup B=B\), then
(Exam: JEE Main Year: 2020)
(A) \(A=B\)
(B) \(A\subset B\)
(C) \(B\subset A\)
(D) \(A\cap B=\phi\)
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) \(\{1,2,3\}\)
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) \(U\)
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)
Q39
Number of equivalence relations on a set with one element is
(Exam: KVPY Year: 2010)
(A) 0
(B) 1
(C) 2
(D) 3
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) \(A\cup B=\phi\)
Q41
If \(A=\{1,2,3\}\), then number of ordered pairs in \(A\times A\) is
(Exam: NEET Year: 2019)
(A) 3
(B) 6
(C) 9
(D) 27
Q42
If \(A\subset B\), then \(A\cap B\) equals
(Exam: BITSAT Year: 2007)
(A) \(A\)
(B) \(B\)
(C) \(\phi\)
(D) \(U\)
Q43
If \(A=\{1,2,3\}\), number of subsets containing element 1 is
(Exam: IIT-JEE Year: 1997)
(A) 3
(B) 4
(C) 5
(D) 8
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
Q45
If \(A=\phi\), then \(P(A)\) equals
(Exam: NEET Year: 2017)
(A) \(\phi\)
(B) \(\{\phi\}\)
(C) \(\{0\}\)
(D) \(U\)
Q46
If \(A=\{x:x\in\mathbb{Z}, -2\le x\le2\}\), then \(n(A)\) is
(Exam: State Engg Year: 2012)
(A) 3
(B) 4
(C) 5
(D) 6
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) \(\phi\)
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
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) \(A\times B\)
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) \(A'\cup B'=U\)

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