SSC Quantitative Aptitude Number System and its Operations Question Bank

done Set Theory (II) Total Questions - 29

• question_answer1)
  X,,mmvv If the number of items of a set A n [A] = 40, \[n\,(B)=26\]and \[n\,(A\cap B)=16,\]then \[n\,(A\cup B)\]is equal to [SSC CGL Tier II, 2017]
  A)
  30 done clear
  B)
  40 done clear
  C)
  50                                                               done clear
  D)
  60 done clear
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• question_answer2)
  In an exam, 60% of the candidates passed in Maths and 70% candidates passed in English and 10% candidates failed in both the subjects. If 300 candidates passed in both the subjects, then find he total number of candidates appeared in the exam, if they took test in only two subjects viz Maths and English.
  A)
  730 done clear
  B)
  750 done clear
  C)
  550 done clear
  D)
  780 done clear
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• question_answer3)
  If \[n\,(A)=115,\]\[n\,(B)=326\]and \[n\,(A-B)=47,\]then what is \[n\,(A\cup B)\]?
  A)
  373 done clear
  B)
  375 done clear
  C)
  300 done clear
  D)
  None of these done clear
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• question_answer4)
  In a town of 10000 families, it was found that 40% family buy newspaper A, 20% buy newspaper B, 10% families buy newspaper C, 5%  families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspaper, then find the number of families which buy A only.
  A)
  3200 done clear
  B)
  3000 done clear
  C)
  4200 done clear
  D)
  3300 done clear
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• question_answer5)
  In a group of 1000 people, 700 can speak English and 500 can speak Hindi. If all the people speak atleast one of the two languages, then find how many can speak both the languages?
  A)
  200 done clear
  B)
  300 done clear
  C)
  400 done clear
  D)
  500 done clear
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• question_answer6)
  A survey shows that 63% of Americans like cheese, whereas 76% like apples. If x% of the Americans like both cheese and apples, then
  A)
  \[x=39\] done clear
  B)
  \[x=63\] done clear
  C)
  \[39\le x\le 63\] done clear
  D)
  Nona of the above done clear
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• question_answer7)
  In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is
  A)
  6 done clear
  B)
  5 done clear
  C)
  8 done clear
  D)
  None of the above done clear
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• question_answer8)
  If A and B are two sets satisfying \[A-B=B-A,\]then which one of the following is correct?
  A)
  \[A=\phi \] done clear
  B)
  \[A\cap B=\phi \] done clear
  C)
  \[A=B\] done clear
  D)
  None of the above done clear
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• question_answer9)
  In a city, 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus is
  A)
  80% done clear
  B)
  40% done clear
  C)
  60% done clear
  D)
  70% done clear
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• question_answer10)
  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 a proper non-empty subset of A done clear
  B)
  A and 8 are non-empty disjoint sets done clear
  C)
  \[B=\phi \] done clear
  D)
  None of the above done clear
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• question_answer11)
  Which one of the following is correct?
  A)
  \[A\cup P(A)=P(A)\] done clear
  B)
  \[A\cup P(A)=A\] done clear
  C)
  \[A-P\,(A)=A\] done clear
  D)
  \[P\,(A)-\{A\}=P(A)\] done clear
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• question_answer12)
  The order of a set A is 3 and that of a set B is 2. What is the number of relations from A of B?
  A)
  4 done clear
  B)
  6 done clear
  C)
  32 done clear
  D)
  64 done clear
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• question_answer13)
  If A, B and C are three sets and U is the universal set such that \[n\,(U)=700,\]\[n\,(A)=200,\]\[n\,(B)=300\]and \[n\,(A\cap B)=100,\] then what is the value of\[(A\cap B)\]?
  A)
  100 done clear
  B)
  200 done clear
  C)
  300 done clear
  D)
  400 done clear
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• question_answer14)
  If A and B are two sets such that \[n\,(A)=0.16,\]\[n\,(B)=0.14,\]\[n\,(A\cup B)=0.25.\]Then,\[n\,(A\cap B)\]is equal to
  A)
  0.3 done clear
  B)
  0.5 done clear
  C)
  0.05 done clear
  D)
  None of these done clear
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• question_answer15)
  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 is
  A)
  12 done clear
  B)
  8 done clear
  C)
  16 done clear
  D)
  None of these done clear
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• question_answer16)
  For non-empty subsets A, B and C of a set X such that \[A\cup B=B\cup C,\]which one of the following is the strongest inference that can be derived?
  A)
  \[A=B=C\] done clear
  B)
  \[A\subseteq B=C\] done clear
  C)
  \[A=B\subseteq C\] done clear
  D)
  \[A\subseteq B\subseteq C\] done clear
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• question_answer17)
  If A and B are two subsets of a set X, then what is \[A\cap (A\cup B)'\]equal to?
  A)
  A done clear
  B)
  B done clear
  C)
  \[\phi \] done clear
  D)
  A' done clear
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• question_answer18)
  In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then, the number of students who have passed in Physics only is
  A)
  22 done clear
  B)
  33 done clear
  C)
  10 done clear
  D)
  45 done clear
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• question_answer19)
  What is the number of proper subsets of a given finite set with n elements?
  A)
  \[2n-1\] done clear
  B)
  \[2n-2\] done clear
  C)
  \[{{2}^{n}}-1\] done clear
  D)
  \[{{2}^{n}}-2\] done clear
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• question_answer20)
  Of the members of three athletic teams in a school, 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, 12 play football and cricket. 8 play all the three games. The total number of members in the three athletic teams is
  A)
  43 done clear
  B)
  76 done clear
  C)
  49 done clear
  D)
  None of these done clear
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• question_answer21)
  In a class of 30 pupils, 12 take Chemistry, 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
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• question_answer22)
    The union of a finite or countable collection of countable sets is
  A)
  countable done clear
  B)
  uncountable done clear
  C)
  infinite done clear
  D)
  None of the above done clear
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• question_answer23)
  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 integer; is
  A)
  2 done clear
  B)
  4 done clear
  C)
  8 done clear
  D)
  12                                                                                    done clear
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• question_answer24)
  If \[A=P\{1,2\},\] where P denotes the power set, then which one of the following is correct?
  A)
  \[\{1,\,2\}\subset A\] done clear
  B)
  \[1\in A\] done clear
  C)
  \[\phi \notin A\] done clear
  D)
  \[\{1,\,2\}\in A\] done clear
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• question_answer25)
  If \[n\,(A)=3,\]\[n\,(B)=6\]and \[A\subseteq B.\] Then, the number of elements in \[A\cup B\]is equal to
  A)
  3 done clear
  B)
  9 done clear
  C)
  6 done clear
  D)
  None of these done clear
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• question_answer26)
  If A, B and C are three finite sets, then what is \[[(A\cup B)\cap C]'\]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
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• question_answer27)

  What does the shaded region in the following diagram represent?

  A)
  \[(A\cap B)\cap C\] done clear
  B)
  \[(A\cup B)\cap C\] done clear
  C)
  \[(A\cup B)\cap C\] done clear
  D)
  None of these done clear
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• question_answer28)
  A class has 175 students. The following data shows the number of students obtaining one or more subjects Mathematics 100, Physics 70, Chemistry 40, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?
  A)
  35 done clear
  B)
  48 done clear
  C)
  60 done clear
  D)
  22 done clear
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• question_answer29)
  If A, B, C are three sets, then what is \[A-\left( ~B~-C \right)\]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
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