8th Class Mathematics Related to Competitive Exam Question Bank

done Applied Mathematics: Operation on Sets and Venn Diagrams Total Questions - 40

• question_answer1)
  If \[U=\left\{ 1,\text{ }7,\text{ }11,\text{ }13,\text{ }15,\text{ }18,\text{ }21,\text{ }32,\text{ }35,\text{ }39 \right\},\]then which of the following is not a subset of U.
  A)
   \[A=\left\{ 1,\text{ }18,\text{ }7,\text{ }35 \right\}\] done clear
  B)
   \[B=\left\{ 21,\text{ }11,\text{ }35,\text{ }7,\text{ }13 \right\}\] done clear
  C)
   \[C=\left\{ 7,\text{ }18,\text{ }32,\text{ }11 \right\}\]              done clear
  D)
   \[D=\left\{ 1,\text{ }7,\text{ }18,\text{ }15,\text{ }13,\text{ }2 \right\}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer2)
  Let  \[M=\left\{ 3,\text{ }5,\text{ }7,\text{ }8,\text{ }10,\text{ }12 \right\},\text{ }N=\left\{ 2,\text{ }4,\text{ }7,\text{ }8 \right\}\]and \[P=\left\{ 5,\text{ }10 \right\},\]then which among the following statements is incorrect?
  A)
   \[P~\subseteq M\]   done clear
  B)
                      \[M\not\subset ~P\] done clear
  C)
   \[\phi \subset P\] done clear
  D)
          \[N\subset M\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer3)
  Which among the following is a universal set for the other three sets?
  A)
   The set of natural numbers. done clear
  B)
   The set of whole numbers. done clear
  C)
   The set of integers. done clear
  D)
   The set of negative of natural numbers. done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer4)
  Which among the following is not a proper subset of\[\left\{ a,\text{ }b,\text{ }c \right\}\]?
  A)
   \[\left\{ a,\text{ }b \right\}\]         done clear
  B)
                     \[\left\{ a,\text{ }b,\text{ }c \right\}\]       done clear
  C)
   {b, c}              done clear
  D)
          \[\left\{ a \right\}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer5)
  If M is a proper subset of N, then M \[\bigcap \] N =
  A)
   \[\phi \]                         done clear
  B)
         M          done clear
  C)
   N                     done clear
  D)
          M\[\bigcup \]N done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer6)
  If M is a subset of N, then M \[\bigcup \] N =
  A)
   M                    done clear
  B)
          N            done clear
  C)
   M\[\bigcap \]N               done clear
  D)
          \[\phi \] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer7)

  Which among the following is an example of disjoint sets?

  P = {The set of odd numbers}

  Q = {The set of even numbers}

  R = {The set of prime numbers}

  A)
   P and R              done clear
  B)
          P and Q done clear
  C)
   Q and R           done clear
  D)
          All the above done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer8)
  If \[P=\left\{ 1,\text{ }2,\text{ }3 \right\}\]and \[Q=\left\{ 3,\text{ }4,\text{ }5 \right\},\]then \[(P\bigcup ~Q)\text{ }=\text{ }\_\_\_\_\]
  A)
   \[\left\{ 1,\text{ }2,\text{ }3 \right\}\] done clear
  B)
          \[\left\{ 1,\text{ }2,\text{ }4,\text{ }5 \right\}\] done clear
  C)
   \[\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5 \right\}\]      done clear
  D)
          \[\left\{ 3 \right\}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer9)
  If \[U=\left\{ 1,\text{ }3,\text{ }5,\text{ }7,\text{ }9,\text{ }a,\text{ }b,\text{ }c,\text{ }d \right\}\]and \[A=\left\{ 1,\text{ }3,\text{ }5 \right\}\]and \[B=\left\{ a,\text{ }b,\text{ }c \right\}\]then \[\left( A\bigcup B \right)'\]
  A)
   \[\left\{ 3,\text{ }3,\text{ }5,\text{ }a,\text{ }b,\text{ }c \right\}\] done clear
  B)
          1, 3, 5 done clear
  C)
   \[\left\{ a,\text{ }b,\text{ }c \right\}\] done clear
  D)
     \[\left\{ 7,\text{ }9,\text{ }d \right\}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer10)
  lf \[P=\{x:x\in ,x\le 2\}\]and \[Q\text{ }=\left\{ x:x\in N,x<20 \right\}\]then \[n\text{ }(P\bigcup Q)=\_\_\_\_\]
  A)
   13                    done clear
  B)
          12     done clear
  C)
   11                    done clear
  D)
          8 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer11)
    Which among the following venn diagram represents '?
  A)
    done clear
  B)
      done clear
  C)
    done clear
  D)
    done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer12)
  If \[P\bigcap Q=Q\]and \[P\bigcap Q=P\] then which among the following cannot be true?
  A)
   \[P=\left\{ \text{1, }2,\text{ }3 \right\}\]and\[Q=\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5 \right\}\] done clear
  B)
   \[P=\left\{ a,\text{ }b \right\}\]and \[Q=\left\{ a,\text{ }b,\text{ }c \right\}\] done clear
  C)
   \[P=\left\{ s \right\}\]and \[Q=\left\{ m,\text{ }n,\text{ }s \right\}\] done clear
  D)
   \[P=\left\{ I,\text{ }m,\text{ }n \right\}\]and \[Q=\left\{ I,\text{ }m,\text{ }1,\text{ }2,\text{ }3 \right\}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer13)
  If M' = N, then \[(M\bigcap ~N)'\]is ____
  A)
   M                    done clear
  B)
          N            done clear
  C)
   \[\phi \]             done clear
  D)
          \[\bigcup \] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer14)
  If \[P=Q',\]then \[(P\bigcup ~Q)'\]is ____
  A)
   P                         done clear
  B)
          Q done clear
  C)
   \[\bigcup \]                        done clear
  D)
        \[\phi \] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer15)
  If \[A=\left\{ a,\text{ }b,\text{ }e,\text{ }g,\text{ }k,\text{ }I,\text{ }m,\text{ }n \right\},\]\[B=\left\{ c,\text{ }d,\text{ }s,\text{ }t,\text{ v}, \right\}\] and \[\bigcup \] is the set of all the letters of English alphabet, the\[A'~\bigcup ((A~\bigcap B)~\bigcup B')\]is equal to ____
  A)
   \[A~\bigcup B\] done clear
  B)
          \[A'~\bigcap B'\] done clear
  C)
   \[\bigcup \]                   done clear
  D)
          B done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer16)
  Which one among the following is incorrect?
  A)
   \[P-(Q~\bigcup R)=\left( P-Q \right)~\bigcap \left( P-R \right)\] done clear
  B)
   \[(P\Delta Q)\Delta R=P\Delta (Q\Delta ~R)\] done clear
  C)
   \[(P~\bigcup Q\bigcup ~R)'=P'\bigcap Q'\bigcap ~R'\] done clear
  D)
   P - (Q - R) = (P - Q) ? R done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer17)
  For any two non empty sets P and Q, if \[P-Q=P\]and \[Q-P=Q,\]then ______
  A)
   \[(P\bigcup Q)'=\phi \]                done clear
  B)
          \[P\bigcap Q=\phi \]  done clear
  C)
   \[P\subset Q\]                done clear
  D)
          \[Q\subset P\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer18)
  If n(P) = 18 - x, n (Q) = 24 + x and n (P\[\bigcup \]Q) = 34, then n(P\[\Delta \]Q) = _____
  A)
   x+20               done clear
  B)
          26        done clear
  C)
   34-x                 done clear
  D)
          30 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer19)
  If \[P=\left\{ a,\text{ }b,\text{ }c,\text{ }d \right\}\]and \[Q=\left\{ a,\text{ }c,\text{ }e \right\}\]then \[P\Delta Q=?\]
  A)
   \[\left\{ a,\text{ }b,\text{ }c,\text{ }d,\text{ }e \right\}\] done clear
  B)
          \[\left\{ b,\text{ }d,\text{ }e \right\}\] done clear
  C)
   \[\left\{ b,\text{ }d \right\}\] done clear
  D)
         \[\left\{ a,\text{ }c \right\}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer20)
  If P and Q are two non-empty sets and P - Q is a null set, then ____
  A)
   P\[\subset \]Q                 done clear
  B)
      Q\[\subset \]P done clear
  C)
   P=Q                    done clear
  D)
          P\[\in \]Q done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer21)
  If n(P - Q) = 28, n(P\[\bigcup \]Q) = 80 and n(P\[\bigcap \]Q) = 35, then the value of n (Q) is
  A)
   17                    done clear
  B)
          52          done clear
  C)
   42                    done clear
  D)
          38 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer22)
  Which of the following number can represent the subset of a non empty set?
  A)
   343                     done clear
  B)
          2048 done clear
  C)
   68                        done clear
  D)
          743 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer23)
  In a class 40% of the student enrolled for maths and 60% enrolled for English. If 25% of the student enrolled for both maths and English, what % of the student of the class did not enroll for either of the two subject?
  A)
   5                     done clear
  B)
          10           done clear
  C)
   15                    done clear
  D)
          25 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer24)
  In a laboratory, there are 48 students, in which 22 are enrolled in physics and chemistry, 26 are enrolled in chemistry. If the students in the laboratory are of atleast one of the two subjects, then how many students are enrolled in only physics and not of chemistry?
  A)
   18                    done clear
  B)
          26           done clear
  C)
   22           done clear
  D)
          30 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer25)
  If n\[\left( A\text{ }\times \text{ }B \right)\text{ }=\text{ }48\], n \[(B\,\,\times \,\,C)=\,\,64\] and n (B) =4, then n \[\left( A\text{ }\times \text{ }C \right)\] =?
  A)
  180                  done clear
  B)
  192      done clear
  C)
  178                  done clear
  D)
  208 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  If (P \[\bigcup \] Q) \[\bigcap \] (P \[\bigcap \] Q) = P, then which one among the following is true?
  A)
   Q\[\subset \]P                done clear
  B)
   \[\phi \] done clear
  C)
   P\[\subset \]Q        done clear
  D)
       both A and B done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer27)
  If n (a) = 28, then which one among the following value of n (b) may result in n (A\[\bigcap \]B) being maximum?
  A)
   24                    done clear
  B)
          29      done clear
  C)
   26                    done clear
  D)
          25 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer28)
  If P and Q are two non-empty equivalent sets, then which one among the following is a possible value of n\[\left( P\text{ }\times \text{ }Q \right)\]?
  A)
   8                     done clear
  B)
          2            done clear
  C)
   1            done clear
  D)
          6 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer29)
  Which one among the following statements is true for two given sets P and Q where n(P) = 26 and n(Q) = 5
  A)
   The minimum possible value of n \[(P\Delta Q)\]is 31. done clear
  B)
   The maximum possible value of n \[(P\Delta Q)\]is 31. done clear
  C)
   The minimum possible value of n \[(P\Delta Q)\]is 26. done clear
  D)
   The maximum possible value of n \[(P\Delta Q)\]is 26. done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer30)
  The set of intelligent students in a class is ______
  A)
   A null set done clear
  B)
   A singleton set done clear
  C)
   A finite set done clear
  D)
   not a well-defined collection done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer31)
  Which of the following is the empty set
  A)
   {x: x is a natural number and \[{{x}^{2}}-1=0\]} done clear
  B)
   {x: x is a natural number and \[{{x}^{2}}+1=0\]} done clear
  C)
   {x: x is a an integer number and \[{{x}^{2}}-9=0\]} done clear
  D)
   {x: x is a an integer number and \[{{x}^{2}}=x+2\]} done clear
  E)
   None of these done clear
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• question_answer32)
  Let n (\[\bigcup \]) =700, n A = 200, n B = 300 and n (A \[\bigcap \] B) = 100, then n(A' \[\bigcap \] B')
  A)
   400                    done clear
  B)
          600 done clear
  C)
   300               done clear
  D)
          200 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer33)
  If A and B are any two sets, then A \[\cup \] (A \[\cup \] B) is equal to ______
  A)
   A      done clear
  B)
                      B            done clear
  C)
   A'                    done clear
  D)
          B' done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer34)
  If A = {2, 4, 5}, B = {7, 8, 9}, then n \[\left( A\text{ }\times \text{ }B \right)\] is equal to  
  A)
   6                     done clear
  B)
          9      done clear
  C)
   3                     done clear
  D)
          0 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer35)
  Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 5}, B = {6, 7}, then A n B' is
  A)
   B?                    done clear
  B)
          A            done clear
  C)
   A'                    done clear
  D)
          B done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer36)
  If A and B are disjoint, then n(A \[\cup \] B) is equal to
  A)
   \[n(A)\]            done clear
  B)
          \[n(B)\] done clear
  C)
   \[n\left( A \right)+n\left( B \right)\] done clear
  D)
          \[n\left( A \right).n\left( B \right)\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer37)
  30 teachers of a school either teach mathematics or physics. 22 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)
          15 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer38)
  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
  E)
   None of these done clear
  View Solution play_arrow

• question_answer39)
  If \[A=\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5 \right\},\text{ }B=\left\{ 2,\text{ }4,\text{ }6 \right\},\text{ }C=\left\{ 3,\text{ }4,\text{ }6 \right\},\]then (A\[\cup \]B) \[\cap \] C is ?___
  A)
   \[\left\{ 3,\text{ }4,\text{ }6 \right\}\] done clear
  B)
          \[\left\{ 1,\text{ }2,\text{ }3 \right\}\] done clear
  C)
   \[\left\{ 1,\text{ }4,\text{ }3 \right\}\] done clear
  D)
          \[\left\{ 1,~2 \right\}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer40)
  If W is the set of all whole numbers and P is the set of all prime numbers and C is the set of all composite numbers, then W - (CUP) is equal to?.........
  A)
   \[\left\{ 0 \right\}\] done clear
  B)
          \[\left\{ 1 \right\}\] done clear
  C)
   \[\left\{ 0,\text{ }1 \right\}\]     done clear
  D)
         \[\{\phi \}\] done clear
  E)
   None of these done clear
  View Solution play_arrow