JEE Main & Advanced Mathematics Sets Question Bank

done Mock Test - Sets Total Questions - 25

• question_answer1)
  If A=\[\{x|x\in \,N\,\]and \[({{x}^{2}}-4)\]\[({{x}^{2}}-5)\]=0} and B=\[\{x|x\in {{l}^{+}}\]and \[x(x-1)\]\[(x-2)\]=0} then \[(A\cup B)\]-\[(A\cap B)\]is
  A)
  {1, 2} done clear
  B)
  {1} done clear
  C)
  {2}                   done clear
  D)
  \[\phi \] done clear
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• question_answer2)
  If A=\[\{x|{{x}^{3}}-3{{x}^{2}}+2x=0\}\],B=\[\{x|{{x}^{2}}-2x=0\}\], then B-A is
  A)
  {2}                   done clear
  B)
  {0} done clear
  C)
  \[\phi \]  done clear
  D)
  {1} done clear
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• question_answer3)
  The number of non-trivial subsets of a set with 5 elements is
  A)
  32                     done clear
  B)
  34 done clear
  C)
  30         done clear
  D)
  35 done clear
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• question_answer4)
  If A= {2, 3, 5}, B = {2, 6, 9}, C = {6, 7, 8} and U= {x|x \[\in \] N and x < 10} then\[A\cup (B\cap C)\] is
  A)
  {2, 3, 5, 6}        done clear
  B)
  {3, 5, 6, 9} done clear
  C)
  {2, 3, 4, 5, 7, 8, 9}        done clear
  D)
  {2, 3, 5, 6, 7, 8, 9} done clear
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• question_answer5)
  If. A={x|\[{{x}^{2}}\]-5x+6=0},B={0,3,4}, C= {x\[\in \] N and x\[\le \]3} then\[(A-B)\times (C-B)\]is
  A)
  {(2, 1), (2, 4)} done clear
  B)
  {(2, 1), (2, 2)} done clear
  C)
  {(2, 1), (2, 2), (3, 2)} done clear
  D)
  {(2, 2), (3, 2)} done clear
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• question_answer6)
  If A={0},B={l, 2}, and C={3}, then\[A\times B\times C\]is
  A)
  {(0, 1, 3), (0, 2, 3)} done clear
  B)
  {(0, 1, 2), (0, 2, 3)} done clear
  C)
  \[\phi \] done clear
  D)
  {(0, 2, 3), (1, 2, 3)} done clear
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• question_answer7)
  If A = {1, 2, 3, 4, 5} and B = {2, 3, 6, 7} then the number of elements in \[(A\times B)\cap (B\times A)\] is
  A)
  20                     done clear
  B)
  18 done clear
  C)
  6                      done clear
  D)
  4 done clear
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• question_answer8)
  If y =\[\left| x \right|+\left| x-1 \right|\]. then for x \[\le \] 0, y is equal to
  A)
  2x-l                   done clear
  B)
  1 done clear
  C)
  1 - 2x done clear
  D)
  x + 1 done clear
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• question_answer9)
  If A = {2, 3, 7, 9}, B = {3, 7, 8}, then \[A\,\Delta \,B\]is
  A)
  {3, 7}   done clear
  B)
  {2, 8, 9} done clear
  C)
  {2, 3, 7, 8, 9} done clear
  D)
  {3, 8, 9} done clear
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• question_answer10)
  If A and B have n elements in common, then the number of elements common to A x B and B x  is
  A)
  \[n\]                  done clear
  B)
  \[2n\] done clear
  C)
  \[{{n}^{2}}\]               done clear
  D)
  0 done clear
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• question_answer11)
  If A contains m elements and B contains n elements, then total number of distinct relations from a set A to a set B is
  A)
  \[mn\]                done clear
  B)
  \[{{2}^{n}}\] done clear
  C)
  \[{{2}^{m}}\]              done clear
  D)
  \[{{2}^{mn}}\] done clear
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• question_answer12)
  If A = {x|x \[\in \] N and x \[\le \] 5}, B = {2, 3, 6, 7} then \[(A-B)\cap (B-A)\]
  A)
  {1, 4, 5, 6, 7}    done clear
  B)
  {1, 4, 5} done clear
  C)
  {6, 7}   done clear
  D)
  \[\phi \] done clear
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• question_answer13)
  If A x B = {(1, 0), (1, 2), (2, 3), (1, 3), (0, 2)}, then A and B are respectively
  A)
  {1, 2} and {0, 2, 3} done clear
  B)
  {1, 2, 0} and {0, 2} done clear
  C)
  {1, 2, 0} and {0, 2, 3} done clear
  D)
  {1, 2} and {2, 3} done clear
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• question_answer14)
  Number of integers satisfying the inequality, \[{{x}^{4}}-29{{x}^{2}}+100\le 0\]is
  A)
  2                      done clear
  B)
  4 done clear
  C)
  6                      done clear
  D)
  8 done clear
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• question_answer15)
  Let \[{{F}_{1}}\]be the set of parallelograms, \[{{F}_{2}}\] the set of rectangles, \[{{F}_{3}}\] be the set of rhombuses, \[{{F}_{4}}\] be the set of squares and \[{{F}_{5}}\] be the set of trapeziums in a plane. Then \[{{F}_{1}}\] may be equal to
  A)
  \[{{F}_{2}}\cap {{F}_{3}}\]      done clear
  B)
  \[{{F}_{3}}\cap {{F}_{4}}\] done clear
  C)
  \[{{F}_{2}}\cup {{F}_{5}}\] done clear
  D)
  \[{{F}_{2}}\cup {{F}_{3}}\cup {{F}_{4}}\cup {{F}_{1}}\] done clear
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• question_answer16)
  The set \[(A\cap B')'\cup (B\cap C)\]is equal to
  A)
  \[A'\cup B\cup C\]           done clear
  B)
  \[A'\cup B\] done clear
  C)
  \[A'\cup C'\]        done clear
  D)
  \[A'\cap B\] done clear
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• question_answer17)
  Let A and 5 be two non-empty subsets of a set X such that A is not a subset of B. Then
  A)
  A is a subset of complement of B done clear
  B)
  B is a subset of .4 done clear
  C)
  A and -5 are disjoint sets done clear
  D)
  A and complement of B are non-disjoint sets done clear
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• question_answer18)
  if the sets A and B are defined as A=\[\{(x,y)|y=1/x,x\ne 0,x\in R\}\]  B=\[\{(x,y)|y=-x,x\in R\}\] Then
  A)
  \[A\cap B=A\]                done clear
  B)
  \[A\cap B=B\] done clear
  C)
  \[A\cap B=\phi \] done clear
  D)
  \[A\cup B=A\] done clear
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• question_answer19)
  Let U be the universal set and \[A\cup B\cup C=U\]. Then \[[(A-B)\cup (B-C)\cup (C-A)]'\]equals
  A)
  \[A\cup B\cup C\]                       done clear
  B)
  \[A\cap B\cap C\] done clear
  C)
  \[A\cup (B\cap C)\]                     done clear
  D)
  \[A\cap (B\cup C)\] done clear
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• question_answer20)
  If \[\left| {{x}^{2}}-2x+2 \right|-\left| 2{{x}^{2}}-5x+2 \right|\]=\[\left| {{x}^{2}}-3x \right|\], then the set of values of x is
  A)
  \[\left( -\infty ,0 \right]\cup \left[ 3,\infty  \right)\] done clear
  B)
  \[\left[ 0,\frac{1}{2} \right]\cup \left[ 2,3 \right]\] done clear
  C)
  \[\left( -\infty ,0 \right]\cup \left[ \frac{1}{2},2 \right]\cup \left[ 3,\infty  \right)\] done clear
  D)
  \[\left[ 0,2 \right]\cup \left[ 3,\infty  \right)\] done clear
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• question_answer21)
  In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% buy newspaper B and 10% buy newspaper C. Also, 5% families buy newspapers A and B 3% buy newspapers B and C and 4% buy newspapers A and C. if 2% families buy all the three newspapers, then number of families which buy newspaper A only is _________.
  A)
  3300 done clear
  B)
  3200 done clear
  C)
  3000 done clear
  D)
  3400 done clear
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• question_answer22)
  in statistical survey of 1003 families of Kolkata, it was found that 63 families has neither a radio nor a TV. 794 families has a radio and 187 has TV. The number of families in that group having both a radio and a TV is ________.
  A)
  40 done clear
  B)
  41 done clear
  C)
  42 done clear
  D)
  43 done clear
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• question_answer23)
  Number of solutions of the equation \[\left| 2-\left| x \right| \right|=x+4\] is _________.
  A)
  2 done clear
  B)
  4 done clear
  C)
  1 done clear
  D)
  5 done clear
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• question_answer24)
  Sum of solutions of the equation \[{{\left| x \right|}^{3}}-4{{\left| x \right|}^{2}}+3\left| x=0 \right|\] is _________.
  A)
  5 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  0 done clear
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• question_answer25)
  The number of integral values of x if 5x-1<\[{{(x+1)}^{2}}\]<7x-3, is _________.
  A)
  4 done clear
  B)
  6 done clear
  C)
  2 done clear
  D)
  1 done clear
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