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question_answer1) 25 people for programme A, 50 people for programme B, 10 people for both programmes are employed. So, number of employee employed for only A is
question_answer2) 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
question_answer3) 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 \[n({{(A\cup B)}^{c}})=\]
question_answer4) In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V is
question_answer5) Let \[S=\{1,2,3,...,100\}\]. If the number of non-empty subsets A of S such that the product of elements in A is even is \[{{2}^{x}}({{2}^{y}}-1),\] then \[x+y=\]
question_answer6) 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 or fish. The number of persons who prefer both fish and chicken is
question_answer7) Let Z be the set of integers. If \[A=\{x\in Z:{{2}^{(x+2)\,\,({{x}^{2}}-5x+6)}}=1\}\] and \[B=\{x\in Z:-3<2x-1<9\},\] then the number of subsets of the set \[A\times B,\] is
question_answer8) Let \[n(U)=700,\] \[n(A)=200,\] \[n(B)=300,\]\[n(A\,C\,B)=100,\] then \[n(A'C\,B')\] is equal to
question_answer9) Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey, 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is
question_answer10) 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
question_answer11) 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 total number of students who have taken exactly one subject is
question_answer12) 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.
question_answer13) There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.
question_answer14) 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
question_answer15) In a battle 70% of the combatants lost one eye, 80% an ear, 75% an arm, 85% a leg, x % lost all the four limbs. The minimum value of x is
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