JEE Main & Advanced Mathematics Sets Question Bank

done Self Evaluation Test - Sets Total Questions - 60

• question_answer1)
  If \[A=\{1,2,3,4,5\}\], then the number of proper subsets of A is
  A)
  31 done clear
  B)
                                 38 done clear
  C)
  48 done clear
  D)
  54 done clear
  View Solution play_arrow

• question_answer2)
  Which of the following is true?
  A)
  \[a\in \{\{a\},b\}\] done clear
  B)
  \[\{b,c\}\subset \{a,\{b,c\}\}\] done clear
  C)
  \[\{a,b\}\subset \{a,\{b,c\}\}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  Let S be a set of all distinct numbers of the form \[\frac{P}{Q}\], where \[p,q\in \{1,2,3,4,5,6\}.\] What is the cardinality of the set S?
  A)
  21 done clear
  B)
  23 done clear
  C)
  32 done clear
  D)
  36 done clear
  View Solution play_arrow

• question_answer4)
  Which of the following is a singleton set?
  A)
  \[\{x:\left| x \right|=5,x\in N\}\] done clear
  B)
  \[\{x:\left| x \right|=6,x\in Z\}\] done clear
  C)
   \[\{x:{{x}^{2}}+2x+1=0,x\in N\}\] done clear
  D)
  \[\{x:{{x}^{2}}=7,x\in N\}\] done clear
  View Solution play_arrow

• question_answer5)
  Let\[A=\{x|x\le 9,x\in N\}\]. Let \[B=\{a,b,c\}\] be the subset of A where \[\left( a+b+c \right)\] is a multiple of 3. What is the largest possible number of subsets like B?
  A)
  12 done clear
  B)
  21 done clear
  C)
  27 done clear
  D)
  30 done clear
  View Solution play_arrow

• question_answer6)
  Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then:
  A)
  \[m=3,n=6\]                  done clear
  B)
  \[m=6,n=3\] done clear
  C)
  \[m=5,n=6\]                  done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  If P denotes the power set of A and A is the void set, then what is number of elements in \[P\{P\{P\{P(A)\}\}\}\]?
  A)
  0                                  done clear
  B)
  1 done clear
  C)
  4                                  done clear
  D)
  16 done clear
  View Solution play_arrow

• question_answer8)
  Which of the following sets is a finite set?
  A)
  \[A=\{x:x\in Z\,\,and\,\,{{x}^{2}}-5x+6=0\}\] done clear
  B)
  \[B=\{x:x\in Z\,\,and\,\,{{x}^{2}}\,is\,even\}\] done clear
  C)
  \[D=\{x:x\in Z\,\,and\,\,x>-10\}\] done clear
  D)
  All of these done clear
  View Solution play_arrow

• question_answer9)
  Let S = the set of all triangles, P= the set of all isosceles triangles, Q= the set of all equilateral triangles, R= the set of all right - angled triangles. What do the sets \[P\cap Q\] and \[R-P\] represents respectively?
  A)
  The set of isosceles triangles; the set of non-isosceles right angled triangles done clear
  B)
  The set of isosceles triangles; the set of right angled triangles done clear
  C)
  The set of equilateral triangles; the set of right angled triangles done clear
  D)
  The set of isosceles triangles; the set of equilateral triangles done clear
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• question_answer10)
  If A, B, C are there sets, then what is \[A-(B-C)\]equal to?
  A)
  \[A-(B\cap C)\]               done clear
  B)
  \[(A-B)\cup C\] done clear
  C)
  \[(A-B)\cup (A\cap C)\] done clear
  D)
  \[(A-B)\cup (A-C)\] done clear
  View Solution play_arrow

• question_answer11)
  If A and B are two sets, then \[(A-B)\cup (B-A)\]\[\cup (A\cap B)\] is equal to
  A)
  Only A              done clear
  B)
  \[A\cup B\] done clear
  C)
  \[(A\cup B')\]                  done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and? Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is
  A)
  7                                  done clear
  B)
  5 done clear
  C)
  10                                 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer13)
  If A and B are subsets of a set X, then what is \[\{A\cap (X-B)\}\cup B\] equal to?
  A)
  \[A\cup B\] done clear
  B)
  \[A\cap B\] done clear
  C)
  A                                  done clear
  D)
  B done clear
  View Solution play_arrow

• question_answer14)
  A survey of 500 television viewers produced the following information, 285 watch football, 195 watch hockey, 115 watch basket-ball, 45 watch football and basketball, 70 watch football and hockey, 50 watch hockey and basketball, 50 do not watch any of the three games. The number of viewers, who watch exactly one of the three games are
  A)
  325 done clear
  B)
  310 done clear
  C)
  405                               done clear
  D)
  372 done clear
  View Solution play_arrow

• question_answer15)
  If \[A=\{4n+2|n\] is a natural number} and \[B=\{3n|n\] is a natural number,}, then what is \[(A\cap B)\] equal to?
  A)
  \[\{12{{n}^{2}}+6n|n\] is a natural number} done clear
  B)
  \[\{24n-12|n\] is a natural number} done clear
  C)
  \[\{60n+30|n\] is a natural number} done clear
  D)
  \[\{12n-6|n\] is a natural number} done clear
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• question_answer16)
  A dinner party is to be fixed for a group of 100 persons. In this party, 50 persons do not prefer fish, 60 prefer chicken and 10 do not prefer either chicken of fish. The number of persons who prefer both fish and chicken is.
  A)
  20 done clear
  B)
  22 done clear
  C)
  25                                 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  Which is the simplified representation of \[(A'\cap B'\cap C)\cup (B\cap C)\cup (A\cap C)\] where A, B, C are subsets of set X?
  A)
  A                                  done clear
  B)
  B done clear
  C)
  C done clear
  D)
  \[X\cap (A\cup B\cup C)\] done clear
  View Solution play_arrow

• question_answer18)
  Which one of the following is correct?
  A)
  \[A\cup (B-C)=A\cap (B\cap C')\] done clear
  B)
  \[A-(B\cup C)=(A\cap B')\cap C'\] done clear
  C)
  \[A-(B\cap C)=(A\cap B')\cap C\] done clear
  D)
  \[A\cap (B-C)=(A\cap B)\cap C\] done clear
  View Solution play_arrow

• question_answer19)
  If F (n) denotes the set of all divisors of n except 1. What is the least value of y satisfying \[[F(20)\cap F(16)]\subseteq F(y)?\]
  A)
  1                                  done clear
  B)
  2 done clear
  C)
  4                                  done clear
  D)
  8 done clear
  View Solution play_arrow

• question_answer20)
  If \[\mu \] is the universal set and P is a subset of \[\mu \], then what is \[P\cap (P-\mu )\cup (\mu -P)\}\] equal to?
  A)
  \[\phi \] done clear
  B)
  P? done clear
  C)
  m                                 done clear
  D)
  P done clear
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• question_answer21)
  Consider the following statements: For non-empty sets. A, B and C

  1. \[A-(B-C)=(A-B)\cup C\]

  2. \[A-(B\cup C)=(A-B)-C\]

  Which of the statements given above is/are correct?
  A)
  1 only               done clear
  B)
  2 only done clear
  C)
  Both 1 and 2                  done clear
  D)
  neither 1 nor 2 done clear
  View Solution play_arrow

• question_answer22)
  In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only?
  A)
  275                               done clear
  B)
  300 done clear
  C)
  325                               done clear
  D)
  350 done clear
  View Solution play_arrow

• question_answer23)
  Consider the following:

  1. \[A\cup (B\cap C)=(A\cap B)\cup (A\cap C)\]

  2. \[A\cap (B\cup C)=(A\cup B)\cap (A\cup C)\]

  Which of the above is/are correct?
  A)
  1 only               done clear
  B)
  2 only done clear
  C)
  Both 1 and 2                  done clear
  D)
  Neither 1 nor 2 done clear
  View Solution play_arrow

• question_answer24)
  In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then person travelling by car or bus is
  A)
  80 percent                      done clear
  B)
  40 percent done clear
  C)
  60 percent done clear
  D)
  70 percent done clear
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• question_answer25)
  In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Then, which of the following is/are true?

  I. 150 students were taking at least one juice.

  II. 225 students were taking neither apple juice nor orange juice.

  A)
  Only I is true done clear
  B)
  Only II is true done clear
  C)
  Both I and II are true done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  If A, B and C are three finite sets, then what is \[\left[ (A\cup B)\cap C \right]'\] equal to?
  A)
  \[A'\cup B'\cap C'\]                      done clear
  B)
  \[A'\cap B'\cap C'\] done clear
  C)
  \[A'\cap B'\cup C'\] done clear
  D)
  \[A\cap B\cap C\] done clear
  View Solution play_arrow

• question_answer27)
  A market research group conducted a survey of 2000 consumers and reported that 1720 consumers like product \[{{P}_{1}}\] and 1450 consumers like product \[{{P}_{2}}.\] What is the least number that must have liked both the products?
  A)
  1150                 done clear
  B)
  2000 done clear
  C)
  1170     done clear
  D)
  2500 done clear
  View Solution play_arrow

• question_answer28)
  If n  = 115, n  = 326, n(A - B) = 47, then what in \[n(A\cup B)\] equal to?
  A)
  373 done clear
  B)
  165 done clear
  C)
  370                               done clear
  D)
  394 done clear
  View Solution play_arrow

• question_answer29)
  If X and Y are two sets such that \[(X\cup Y)\] has 60 elements, X has 38 elements and Y has 42 elements, how many elements does \[(X\cap Y)\]have?
  A)
  11                                 done clear
  B)
  20 done clear
  C)
  13                                 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  Let A, B, C be finite sets. Suppose that \[n(A)=10,\]\[n(B)=15,\] \[n(C)=20,\] \[n(A\cap B)=8\] and \[n(B\cap C)=9.\] Then the possible value of \[n(A\cup B\cup C)\] is
  A)
  26 done clear
  B)
  27 done clear
  C)
  28 done clear
  D)
  Any of the three values 26, 27, 28 is possible done clear
  View Solution play_arrow

• question_answer31)
  A survey shows that 61%, 46% and 29% of the people watched ?3 idiots??, ?Raajneeti? and ?Avatar? respectively. 25% people watched exactly two of the three movies and 3% watches none. What percentage of people watched all the three movies?
  A)
  39%                  done clear
  B)
  11% done clear
  C)
  14%      done clear
  D)
  7% done clear
  View Solution play_arrow

• question_answer32)
  In a class of 80 students numbered a to 80, all odd numbered students opt if Cricket, students whose numbers are divisible by 5 opt for football and those whose numbers are divisible by 7 opt for Hockey. The number of students who do not opt any of the three games, is
  A)
  13 done clear
  B)
                                 24 done clear
  C)
  28 done clear
  D)
                                 52 done clear
  View Solution play_arrow

• question_answer33)
  20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is
  A)
  12 done clear
  B)
                                 8 done clear
  C)
  16 done clear
  D)
                                 None of these done clear
  View Solution play_arrow

• question_answer34)
  In a B School there are 15 teachers who teach marketing or finance. Of these, 8 teach finance. How many teach marketing but not finance?
  A)
  15 done clear
  B)
                                 20 done clear
  C)
  11 done clear
  D)
                                 None of these done clear
  View Solution play_arrow

• question_answer35)
  The cardinality of the set \[P\left\{ P\left[ P(\phi ) \right] \right\}\] is
  A)
  0 done clear
  B)
                                 1 done clear
  C)
  2 done clear
  D)
                                 4 done clear
  View Solution play_arrow

• question_answer36)
  The number of elements in the set \[\{(a,b):2{{a}^{2}}+3{{b}^{2}}=35,a,b\in Z\}\], where Z is the set of all integers, is
  A)
  2 done clear
  B)
                                 4 done clear
  C)
  8 done clear
  D)
                                 12 done clear
  View Solution play_arrow

• question_answer37)
  Which of the following is/are true?

  I. If A is a subset of the universal set U then its complement A? is also a subset of U.

  II. If \[U=\{1,2,3,....,10\}\] and \[A=\{1,3,5,7,9\}\]then \[{{(A')}^{'}}=A.\]

  A)
  Only I is true done clear
  B)
  Only II is true done clear
  C)
  Both I and II are true done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer38)
  For a set A, consider the following statements:

  1. \[A\cup P(A)=P(A)\]

  2. \[\{A\}\cap P(A)=A\]

  3. \[P(A)-\{A\}=P(A)\]

  where P denotes power set. Which of the statements given above is/are correct?
  A)
  1 only done clear
  B)
                    2 only done clear
  C)
  3 only done clear
  D)
                     1, 2 and 3 done clear
  View Solution play_arrow

• question_answer39)
  If A and B are two disjoint sets, then which one of the following is correct?
  A)
  \[A-B=A-(A\cap B)\] done clear
  B)
  \[B-A'=A\cap B\] done clear
  C)
  \[A\cap B=(A-B)\cap B\] done clear
  D)
  All of these done clear
  View Solution play_arrow

• question_answer40)
  Let n denote the set of natural numbers and \[A=\{{{n}^{2}}:n\in N\}\] and \[B=\{{{n}^{3}}:n\in N\},\] which one of the following is incorrect?
  A)
  \[A\cup B=N\] done clear
  B)
  The complement of \[(A\cup B)\] is an infinite set done clear
  C)
  \[A\cap B\] Must be a finite set done clear
  D)
  \[A\cap B\] Must be proper subset of \[\{{{m}^{6}}:m\in N\}\] done clear
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• question_answer41)
  If the cardinality of a set A is 4 and that of a set B in 3, then what is the cardinality of the set A \[\Delta \] B?
  A)
  1 done clear
  B)
  5 done clear
  C)
  7 done clear
  D)
  Cannot be determined as the sets A and B are not given done clear
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• question_answer42)
  Let N be the set of non-negative integers, I the set of integers, \[{{N}_{P}}\] the set of non-positive integers, E the set of even integers and P the set of prime numbers. Then
  A)
  \[I-N={{N}_{p}}\] done clear
  B)
                     \[N\cap {{N}_{p}}=\phi \] done clear
  C)
  \[E\cap P=\phi \] done clear
  D)
         \[N\Delta {{N}_{p}}=I-\{0\}\] done clear
  View Solution play_arrow

• question_answer43)
  Let A and B be two sets then \[(A\cup B)'\cup (A'\cap B)\] is equal to
  A)
  A? done clear
  B)
                                 A done clear
  C)
  B? done clear
  D)
         None of these done clear
  View Solution play_arrow

• question_answer44)
  What does the shaded portion of the Venn diagram given below represent?
  A)
  \[(P\cap Q)\cap (P\cap R)\] done clear
  B)
  \[((P\cap Q)-R)\cup ((P\cap R)-Q)\] done clear
  C)
  \[((P\cup Q)-R)\cap ((P\cap R)-Q)\] done clear
  D)
  \[((P\cap Q)\cup R)\cap ((P\cup Q)-R)\] done clear
  View Solution play_arrow

• question_answer45)
  A, B, C and D are four sets such that \[A\cap B=C\cap D=\phi .\] Consider the following:

  1. \[A\cup B\] and \[B\cup D\] are always disjoint.

  2. \[A\cap C\] and \[B\cap D\] are always disjoint.

  Which of the above statements is/are correct?

  A)
  1 Only done clear
  B)
                    2 only done clear
  C)
  Both 1 and 2 done clear
  D)
         neither 1 nor 2s done clear
  View Solution play_arrow

• question_answer46)
  Let A, B, C are three non-empty sets. If \[A\subset B\]and \[B\subset C,\]then which of the following is true?
  A)
  \[B-A=C-B\] done clear
  B)
         \[A\cap B\cap C=B\] done clear
  C)
  \[A\cup B=B\cap C\] done clear
  D)
         \[A\cup B\cup C=A\] done clear
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• question_answer47)
  Let X and Y be two non-empty sets such that \[X\cap A=Y\cap A=\phi \] and \[X\cup A=Y\cup A\]for some non-empty set A. Then
  A)
  X is a proper subset of Y done clear
  B)
  Y is a proper subset of X done clear
  C)
  X = Y done clear
  D)
  X and Y are disjoint sets done clear
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• question_answer48)
  Which one of the following is correct?
  A)
  \[A\cup P(A)=P(A)(b)\] done clear
  B)
         \[A\cap P(A)=A\] done clear
  C)
  \[A-P(A)=A\] done clear
  D)
         \[P(A)-\{A\}=P(A)\] Here P  denotes the power set of a set A. done clear
  View Solution play_arrow

• question_answer49)
  If \[(A-B)\cup (B-A)=A\] for subsets A and B of the universal set U, then which one of the following is correct?
  A)
  B is proper non-empty subset of A done clear
  B)
  A and B are non-empty disjoint sets done clear
  C)
  \[B=\phi \] done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer50)
  What does the shaded region in the Venn diagram given below represent?
  A)
  \[C\cap (A'\cap B')\] done clear
  B)
  \[C\cup (C'\cap A\cap B)\] done clear
  C)
  \[C\cup (C\cap A)\cup (C\cap B)\] done clear
  D)
  \[C\cup (A/B)\] done clear
  View Solution play_arrow

• question_answer51)
  Let\[n(U)=700,n(A)=200,n(B)=300,n(A\cap B)=100\]then \[n(A'\cap B')\] is equal to
  A)
  400 done clear
  B)
                     600 done clear
  C)
  300 done clear
  D)
                                 None of these done clear
  View Solution play_arrow

• question_answer52)
  There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:
  A)
  100 done clear
  B)
                                 200 done clear
  C)
  300 done clear
  D)
                                 400 done clear
  View Solution play_arrow

• question_answer53)
  In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people were diagnosed with high blood pressure. What is the minimum number of people who were having diabetes and high blood pressure?
  A)
  0 done clear
  B)
                                 10 done clear
  C)
  20 done clear
  D)
                                 30 done clear
  View Solution play_arrow

• question_answer54)
  Out of 32 persons, 30 invest in national savings certificates and 17 invest in shares. What is the number of persons who invest in both?
  A)
  13 done clear
  B)
                                 15 done clear
  C)
  17 done clear
  D)
                                 19 done clear
  View Solution play_arrow

• question_answer55)
  Which of the following is correct?

  I. \[n(S\cup T)\] is maximum when n \[n(S\cap T)\] is least,

  II. If \[n(U)=1000,n(S)=720,n(T)=450,\] then least value of \[n(S\cap T)=170.\]

  A)
  Only I is true done clear
  B)
  Only II is true done clear
  C)
  Both I and II are true done clear
  D)
  Both I and II are false done clear
  View Solution play_arrow

• question_answer56)
  In a school, there are 20 teachers who teach mathematics of physics of these, 12 teach mathematics and 4 teach both math?s and physics then the number of teachers teaching only physics are
  A)
  4 done clear
  B)
                                 8 done clear
  C)
  12 done clear
  D)
                                 16 done clear
  View Solution play_arrow

• question_answer57)
  Given \[n(U)=20,n(A)=12,n(B)=9,n(A\cap B)=4,\]where U is the universal set, A and B are subsets of U, then \[n({{(A\cup B)}^{c}})=\]
  A)
  17 done clear
  B)
                                 9 done clear
  C)
  11 done clear
  D)
                                 3 done clear
  View Solution play_arrow

• question_answer58)
  In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% buy A and B, 3% buy B and C and 4% buy A and C. if 2% families buy all of three newspapers, then the number of families which buy A only, is
  A)
  4400 done clear
  B)
                     3300 done clear
  C)
  2000     done clear
  D)
                     500 done clear
  View Solution play_arrow

• question_answer59)
  In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is
  A)
  16 done clear
  B)
                                 6 done clear
  C)
  8 done clear
  D)
                                 20 done clear
  View Solution play_arrow

• question_answer60)
  Consider the following statements.

  I. If \[{{A}_{n}}\]is the set of first n prime numbers, then \[\underset{n=2}{\overset{10}{\mathop{U}}}\,{{A}_{n}}\]is equal to {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

  II. If A and B are two sets such that \[n(A\cup B)=50,\]\[n(A)=28,\,\,n(B)=32,\] then \[n(A\cap B)=10.\] Which of these is correct?

  A)
  Only I is true done clear
  B)
                     Only II is true done clear
  C)
  Both are true done clear
  D)
                     Both are false done clear
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