JEE Main & Advanced Mathematics Sets Question Bank

done Set theory Total Questions - 81

• question_answer1)
  The set of intelligent students in a class is [AMU 1998]
  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
  View Solution play_arrow

• question_answer2)
  Which of the following is the empty set [Karnataka CET 1990]
  A)
  \[\{x:x\] is a real number and \[{{x}^{2}}-1=0\}\] done clear
  B)
  {x : x  is a real number and \[{{x}^{2}}+1=0\}\] done clear
  C)
  {x : x is a real number and \[{{x}^{2}}-9=0\}\] done clear
  D)
  {x : x is a real number and \[{{x}^{2}}=x+2\}\] done clear
  View Solution play_arrow

• question_answer3)
  The set \[A=\{x:x\in R,\,{{x}^{2}}=16\] and \[2x=6\}\] equals [Karnataka CET 1995]
  A)
  \[\varphi \] done clear
  B)
  {14, 3, 4} done clear
  C)
  {3} done clear
  D)
  {4} done clear
  View Solution play_arrow

• question_answer4)
  If a set A has n  elements, then the total number of subsets of A  is [Roorkee 1991; Karnataka CET 1992,  2000]
  A)
  n done clear
  B)
  \[{{n}^{2}}\] done clear
  C)
  \[{{2}^{n}}\] done clear
  D)
  \[2n\] done clear
  View Solution play_arrow

• question_answer5)
  The number of proper subsets of the set {1, 2, 3} is  [JMIEE 2000]
  A)
  8 done clear
  B)
  7 done clear
  C)
  6 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer6)
  Given the sets \[A=\{1,\,2,\,3\},\,B=\{3,4\}\], C = {4, 5, 6}, then \[A\cup (B\cap C)\] is   [MNR 1988; Kurukshetra CEE 1996]
  A)
  {3} done clear
  B)
  {1, 2, 3, 4} done clear
  C)
  {1, 2, 4, 5} done clear
  D)
  {1, 2, 3, 4, 5, 6} done clear
  View Solution play_arrow

• question_answer7)
  If A  and B are any two sets, then \[A\cup (A\cap B)\]is equal to [Karnataka CET 1996]
  A)
  A done clear
  B)
  B done clear
  C)
  \[{{A}^{c}}\] done clear
  D)
  \[{{B}^{c}}\] done clear
  View Solution play_arrow

• question_answer8)
  If A and B  are two given sets, then \[A\cap {{(A\cap B)}^{c}}\] is equal to                       [AMU 1998; Kurukshetra CEE 1999]
  A)
  A done clear
  B)
  B done clear
  C)
  \[\varphi \] done clear
  D)
  \[A\cap {{B}^{c}}\] done clear
  View Solution play_arrow

• question_answer9)
  If the sets A and B are defined as\[A=\{(x,\,y):y=\frac{1}{x},\,0\ne x\in R\}\]\[\bigcup\limits_{i=1}^{30}{{{A}_{i}}}=\bigcup\limits_{j=1}^{n}{{{B}_{j}}}\], then
  A)
  \[A\cap B=A\] done clear
  B)
  \[A\cap B=B\] done clear
  C)
  \[A\cap B=\varphi \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer10)
  Let \[A=[x:x\in R,\,|x|\,<1]\,;\] \[B=[x:x\in R,\,|x-1|\ge 1]\] and \[A\cup B=R-D,\] then the set D is
  A)
  \[[x:1<x\le 2]\] done clear
  B)
  \[[x:1\le x<2]\] done clear
  C)
  \[[x:1\le x\le 2]\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer11)
  If the sets A and B are defined as \[A=\{(x,\,y):y={{e}^{x}},\,x\in R\}\]; \[B=\{(x,\,y):y=x,\,x\in R\},\] then [UPSEAT 1994, 99, 2002]
  A)
  \[B\subseteq A\] done clear
  B)
  \[A\subseteq B\] done clear
  C)
  \[A\cap B=\varphi \] done clear
  D)
  \[A\cup B=A\] done clear
  View Solution play_arrow

• question_answer12)
  If \[X=\{{{4}^{n}}-3n-1:n\in N\}\] and \[Y=\{9(n-1):n\in N\},\] then \[X\cup Y\] is equal to [Karnataka CET 1997]
  A)
  X done clear
  B)
  Y done clear
  C)
  N done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  Let \[n(U)=700,\,n(A)=200,\,n(B)=300\] and \[n(A\cap B)=100,\] then \[n({{A}^{c}}\cap {{B}^{c}})=\] [Kurukshetra CEE 1999]
  A)
  400 done clear
  B)
  600 done clear
  C)
  300 done clear
  D)
  200 done clear
  View Solution play_arrow

• question_answer14)
  In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 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 newspapers, then number of families which buy A only is  [Roorkee 1997]
  A)
  3100 done clear
  B)
  3300 done clear
  C)
  2900 done clear
  D)
  1400 done clear
  View Solution play_arrow

• question_answer15)
  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 persons travelling by car or bus is  [Kerala (Engg.) 2002]
  A)
  80 percent done clear
  B)
  40 percent done clear
  C)
  60 percent done clear
  D)
  70 percent done clear
  View Solution play_arrow

• question_answer16)
  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 [UPSEAT 1990]
  A)
  6 done clear
  B)
  9 done clear
  C)
  7 done clear
  D)
  All of these done clear
  View Solution play_arrow

• question_answer17)
  If A, B and C are any three sets, then \[A\text{ }\times \text{ }\left( B\text{ }\cup \text{ }C \right)\] is equal to [Pb. CET 2001]
  A)
  \[\left( A\text{ }\times \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\times \text{ }C \right)\] done clear
  B)
  \[\left( A\text{ }\cup \text{ }B \right)\text{ }\times \text{ }\left( A\text{ }\cup \text{ }C \right)\] done clear
  C)
  \[\left( A\text{ }\times \text{ }B \right)\text{ }\cap \text{ }\left( A\text{ }\times \text{ }C \right)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  If A, B and C are any three sets, then A - (B U C) is equal to
  A)
  (A - B) U (A - C) done clear
  B)
  (A - B) U (A - C) done clear
  C)
  (A - B) U C done clear
  D)
  (A - B) U C done clear
  View Solution play_arrow

• question_answer19)
  If A, B and C are non-empty sets, then (A - B) U (B - A) equals                      [AMU 1992, 1998; DCE 1998]
  A)
  (A U B) - B done clear
  B)
  \[A\text{ }-\text{ }\left( A\text{ }\cap \text{ }B \right)\] done clear
  C)
  \[\left( A\text{ }\cup \text{ }B \right)\text{ }-\text{ }\left( A\text{ }\cap \text{ }B \right)\] done clear
  D)
  \[\left( A\text{ }\cap \text{ }B \right)\text{ }\cup \text{ }\left( A\cup \text{ }B \right)\] done clear
  View Solution play_arrow

• question_answer20)
  If \[A=\{2,\,4,\,5\},\,\,B=\{7,\,\,8,\,9\},\] then \[n(A\times B)\] is equal to
  A)
  6 done clear
  B)
  9 done clear
  C)
  3 done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer21)
  If the set A has p elements, B has q elements, then the number of elements in A × B is [Karnataka CET 1999]
  A)
  \[p+q\] done clear
  B)
  \[p+q+1\] done clear
  C)
  \[pq\] done clear
  D)
  \[{{p}^{2}}\] done clear
  View Solution play_arrow

• question_answer22)
  If \[A=\{a,\,b\},\,B=\{c,\,d\},\,C=\{d,\,e\},\,\] then\[\{(a,\,c),\,(a,\,d),\,(a,\,e),\,(b,\,c),\,(b,\,d),\,(b,\,e)\}\] is equal to [AMU 1999; Him. CET 2002]
  A)
  \[A\text{ }\cap \text{ }\left( B~\text{ }\cup \text{ }C \right)\] done clear
  B)
  \[A\text{ }\cup \text{ }\left( B\text{ }\cap \text{ }C \right)\] done clear
  C)
  \[A\text{ }\times \text{ }\left( B\text{ }\cup \text{ }C \right)\] done clear
  D)
  \[A\text{ }\times \text{ }\left( B\text{ }\cap \text{ }C \right)\] done clear
  View Solution play_arrow

• question_answer23)
  If P, Q and R are subsets of a set A, then \[R\times {{\left( {{P}^{c}}\text{ }\cup \text{ }{{Q}^{c}} \right)}^{c}}=\] [Karnataka CET 1993]
  A)
  \[\left( R\text{ }\times \text{ }P \right)\text{ }\cap \text{ }\left( R\text{ }\times \text{ }Q \right)\] done clear
  B)
  \[(R\times Q)\cap (R\times P)\] done clear
  C)
  \[(R\times P)\cup (R\times Q)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  In rule method the null set is represented by [Karnataka CET 1998]
  A)
  {} done clear
  B)
  \[\varphi \] done clear
  C)
  \[\{x:x=x\}\] done clear
  D)
  \[\{x:x\ne x\}\] done clear
  View Solution play_arrow

• question_answer25)
  \[A=\{x:x\ne x\}\] represents [Kurukshetra CEE 1998]
  A)
  {0} done clear
  B)
  {} done clear
  C)
  {1} done clear
  D)
  {x} done clear
  View Solution play_arrow

• question_answer26)
  If \[Q=\left\{ x:x=\frac{1}{y},\,\text{where }y\in N \right\}\], then
  A)
  \[0\in Q\] done clear
  B)
  \[1\in Q\] done clear
  C)
  \[2\in Q\] done clear
  D)
  \[\frac{2}{3}\in Q\] done clear
  View Solution play_arrow

• question_answer27)
  Which set is the subset of all given sets
  A)
  {1, 2, 3, 4,......} done clear
  B)
  {1} done clear
  C)
  {0} done clear
  D)
  {} done clear
  View Solution play_arrow

• question_answer28)
  Let \[S=\{0,\,1,\,5,\,4,\,7\}\]. Then the total number of subsets of S is
  A)
  64 done clear
  B)
  32 done clear
  C)
  40 done clear
  D)
  20 done clear
  View Solution play_arrow

• question_answer29)
  The number of non-empty subsets of the set {1, 2, 3, 4} is [Karnataka CET 1997; AMU 1998]
  A)
  15 done clear
  B)
  14 done clear
  C)
  16 done clear
  D)
  17 done clear
  View Solution play_arrow

• question_answer30)
  The smallest set A such that A U {1, 2} = {1, 2, 3, 5, 9} is
  A)
  {2, 3, 5} done clear
  B)
  {3, 5, 9} done clear
  C)
  {1, 2, 5, 9} done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer31)
  If \[A\text{ }\cap \text{ }B\text{ }=\text{ }B,\] then [JMIEE 2000]
  A)
  \[A\subset B\] done clear
  B)
  \[B\subset A\] done clear
  C)
  \[A=\varphi \] done clear
  D)
  \[B=\varphi \] done clear
  View Solution play_arrow

• question_answer32)
  If A and B are two sets, then \[A\cup B=A\cap B\] iff
  A)
  \[A\subseteq B\] done clear
  B)
  \[B\subseteq A\] done clear
  C)
  \[A=B\] done clear
  D)
  None of these\[\] done clear
  View Solution play_arrow

• question_answer33)
  Let A and B be two sets. Then
  A)
  \[A\text{ }\cup \text{ }B\] \[\subseteq \] \[A\text{ }\cap \text{ }B\] done clear
  B)
  \[A\text{ }\cap B\text{ }\subseteq \text{ }A\text{ }\cup B\]   done clear
  C)
  \[A\text{ }\cap \text{ }B\text{ }=\text{ }A\text{ }\cup \text{ }B\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  Let\[A=\{(x,\,y):y={{e}^{x}},\,x\in R\}\], \[B=\{(x,\,y):y={{e}^{-x}},\,x\in R\}.\] Then
  A)
  \[A\cap B=\varphi \] done clear
  B)
  \[A\cap B\ne \varphi \] done clear
  C)
  \[A\cup B={{R}^{2}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  If   A = {2, 3, 4, 8, 10}, B = {3, 4, 5, 10, 12}, C = {4, 5, 6, 12, 14} then \[\left( A\text{ }\cap \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\cap \text{ }C \right)\] is equal to 
  A)
  {3, 4, 10} done clear
  B)
  {2, 8, 10} done clear
  C)
  {4, 5, 6} done clear
  D)
  {3, 5, 14} done clear
  View Solution play_arrow

• question_answer36)
  If A and B are any two sets, then \[A\text{ }\cap \text{ }\left( A\text{ }\cup \text{ }B \right)\] is equal to
  A)
  A done clear
  B)
  B done clear
  C)
  \[{{A}^{c}}\] done clear
  D)
  \[{{B}^{c}}\] done clear
  View Solution play_arrow

• question_answer37)
  If A, B, C be three sets such that \[A\text{ }\cup \text{ }B\text{ }=\text{ }A\text{ }\cup \text{ }C\] and \[A\text{ }\cap \text{ }B\text{ }=\text{ }A\text{ }\cap \text{ }C,\] then [Roorkee 1991]
  A)
  A = B done clear
  B)
  B = C done clear
  C)
  A = C done clear
  D)
  A = B = C done clear
  View Solution play_arrow

• question_answer38)
  Let A = {a, b, c}, B  = {b, c, d}, C = {a, b, d, e}, then  is  \[A\text{ }\cap \text{ }\left( B\text{ }\cup \text{ }C \right)\]   [Kurukshetra CEE 1997]
  A)
  {a, b, c} done clear
  B)
  {b, c, d} done clear
  C)
  {a, b, d, e} done clear
  D)
  {e} done clear
  View Solution play_arrow

• question_answer39)
  If A and B are sets, then \[A\text{ }\cap \text{ }\left( B\text{ }-\text{ }A \right)\] is
  A)
  \[\varphi \] done clear
  B)
  A done clear
  C)
  B done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer40)
  If A and B are two sets, then \[A\cap (A\cup B{)}'\] is equal to
  A)
  A done clear
  B)
  B done clear
  C)
  \[\varphi \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer41)
  Let \[U=\{1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9,\,10\}\], \[A=\{1,\,2,\,5\},\,B=\{6,\,7\}\], then \[A\cap {B}'\] is
  A)
  \[{B}'\] done clear
  B)
  A done clear
  C)
  \[{A}'\] done clear
  D)
  B done clear
  View Solution play_arrow

• question_answer42)
  If A is any set, then
  A)
  \[A\cup {A}'=\varphi \] done clear
  B)
  \[A\cup {A}'=U\] done clear
  C)
  \[A\cap {A}'=U\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer43)
  If \[{{N}_{a}}=[an:n\in N\},\] then \[{{N}_{5}}\cap {{N}_{7}}=\] [Kerala (Engg.) 2005]
  A)
  \[{{N}_{7}}\] done clear
  B)
  N done clear
  C)
  \[{{N}_{35}}\] done clear
  D)
  \[{{N}_{5}}\] \[{{N}_{12}}\] done clear
  View Solution play_arrow

• question_answer44)
  If \[aN=\{ax:x\in N\},\] then the set \[3N\cap 7N\] is
  A)
  21 N done clear
  B)
  10 N done clear
  C)
  4 N done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer45)
  The shaded region in the given figure is [NDA 2000]
  A)
  \[A\text{ }\cap \text{ }\left( B\text{ }\cup \text{ }C \right)\] done clear
  B)
  \[A\text{ }\cup \text{ }\left( B\text{ }\cap \text{ }C \right)\] done clear
  C)
  \[A\text{ }\cap \text{ }\left( B\text{ }-\text{ }C \right)\] done clear
  D)
  \[A\text{ }-\text{ }\left( B\text{ }\cup \text{ }C \right)\] done clear
  View Solution play_arrow

• question_answer46)
  If A and B are two sets then \[\left( A\text{ }-\text{ }B \right)\text{ }\cup \text{ }\left( B\text{ }-\text{ }A \right)\text{ }\cup \text{ }\left( A\text{ }\cap \text{ }B \right)\] is equal to
  A)
  \[A\text{ }\cup \text{ }B\] done clear
  B)
  \[A\text{ }\cap \text{ }B\] done clear
  C)
  A done clear
  D)
  \[{B}'\] done clear
  View Solution play_arrow

• question_answer47)
  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_answer48)
  Let \[U\] be the universal set and\[A\cup B\cup C=U\]. Then \[\{(A-B)\cup (B-C)\cup (C-A){\}}'\] is equal to
  A)
  \[A\cup B\cup C\] done clear
  B)
  \[A\cup (B\cap C)\] done clear
  C)
  \[A\cap B\cap C\] done clear
  D)
  \[A\cap (B\cup C)\] done clear
  View Solution play_arrow

• question_answer49)
  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
  View Solution play_arrow

• question_answer50)
  Let A and B be 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 [JMIEE 2001]
  A)
  0.3 done clear
  B)
  0.5 done clear
  C)
  0.05 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer51)
  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)
  \[n(A)+n(B)\] done clear
  D)
  \[n(A)\,.\,n(B)\] done clear
  View Solution play_arrow

• question_answer52)
  If A and B are not disjoint sets, then \[n(A\cup B)\] is equal to [Kerala (Engg.)  2001]
  A)
  \[n(A)+n(B)\] done clear
  B)
  \[n(A)+n(B)-n(A\cap B)\] done clear
  C)
  \[n(A)+n(B)+n(A\cap B)\] done clear
  D)
  \[n(A)\,n(B)\]   \[n(A)-n(B)\] done clear
  View Solution play_arrow

• question_answer53)
  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
  A)
  10 done clear
  B)
  12 done clear
  C)
  15 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer54)
  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                                      [DCE 1995; MP PET 1996]
  A)
  128 done clear
  B)
  216 done clear
  C)
  240 done clear
  D)
  160 done clear
  View Solution play_arrow

• question_answer55)
  A survey shows that 63% of the 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)
  None of these done clear
  View Solution play_arrow

• question_answer56)
  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_answer57)
  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, and 12 play football and cricket. Eight 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
  View Solution play_arrow

• question_answer58)
  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 [DCE 1993; ISM Dhanbad 1994]
  A)
  22 done clear
  B)
  33 done clear
  C)
  10 done clear
  D)
  45 done clear
  View Solution play_arrow

• question_answer59)
  If A and B are two sets, then A × B = B × A iff
  A)
  \[A\subseteq B\] done clear
  B)
  \[B\subseteq A\] done clear
  C)
  \[A=B\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer60)
  If A and B be any two sets, then \[(A\cap B)'\] is equal to
  A)
  \[A'\cap B'\] done clear
  B)
  \[{A}'\cup {B}'\] done clear
  C)
  \[A\cap B\] done clear
  D)
  \[A\cup B\] done clear
  View Solution play_arrow

• question_answer61)
  Let A and B be subsets of a set X. Then
  A)
  \[A-B=A\cup B\] done clear
  B)
  \[A-B=A\cap B\] done clear
  C)
  \[A-B={{A}^{c}}\cap B\] done clear
  D)
  \[A-B=A\cap {{B}^{c}}\] done clear
  View Solution play_arrow

• question_answer62)
  Let A and B be two sets in the universal set. Then \[A-B\] equals
  A)
  \[A\cap {{B}^{c}}\] done clear
  B)
  \[{{A}^{c}}\cap B\] done clear
  C)
  \[A\cap B\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer63)
  If A, B and C are any three sets, then \[A-(B\cap C)\] is equal to
  A)
  x done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer64)
  If A, B, C are three sets, then \[A\text{ }\cap \text{ }\left( B~\text{ }\cup \text{ }C \right)\] is equal to
  A)
  \[\left( A\text{ }\cup \text{ }B \right)\text{ }\cap \text{ }\left( A\text{ }\cup \text{ }C \right)\] done clear
  B)
  \[\left( A\text{ }\cap \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\cap \text{ }C \right)\] done clear
  C)
  \[\left( A\text{ }\cup \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\cup \text{ }C \right)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer65)
  If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A - B) × (B - C) is
  A)
  {(1, 2), (1, 5), (2, 5)} done clear
  B)
  {(1, 4)} done clear
  C)
  (1, 4) done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer66)
  If (1, 3), (2, 5) and (3, 3) are three elements of A × B and the total number of elements in \[A\times B\] is 6, then the remaining elements of \[A\times B\] are
  A)
  (1, 5); (2, 3); (3, 5) done clear
  B)
  (5, 1); (3, 2); (5, 3) done clear
  C)
  (1, 5); (2, 3); (5, 3) done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer67)
  A = {1, 2, 3} and B = {3, 8}, then  \[\left( A\text{ }\cup \text{ }B \right)\text{ }\times \text{ }\left( A\text{ }\cap \text{ }B \right)\] is
  A)
  {(3, 1), (3, 2), (3, 3), (3, 8)} done clear
  B)
  {(1, 3), (2, 3), (3, 3), (8, 3)} done clear
  C)
  {(1, 2), (2, 2), (3, 3), (8, 8)} done clear
  D)
  {(8, 3), (8, 2), (8, 1), (8, 8)} done clear
  View Solution play_arrow

• question_answer68)
  If A = {2, 3, 5}, B = {2, 5, 6}, then \[\left( A\text{ }-\text{ }B \right)\text{ }\times \text{ }\left( A\text{ }\cap \text{ }B \right)\] is
  A)
  {(3, 2), (3, 3), (3, 5)} done clear
  B)
  {(3, 2), (3, 5), (3, 6)} done clear
  C)
  {(3, 2), (3, 5)} done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer69)
  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 [J & K 2005]
  A)
  16 done clear
  B)
  6 done clear
  C)
  8 done clear
  D)
  20 done clear
  View Solution play_arrow

• question_answer70)
  If \[n(A)=4\], \[n(B)=3\], \[n(A\times B\times C)=24\], then \[n(C)=\]  [Kerala (Engg.) 2005]
  A)
  288 done clear
  B)
  1 done clear
  C)
  12 done clear
  D)
  17 done clear
  E)
  2 done clear
  View Solution play_arrow

• question_answer71)
  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 [Kerala (Engg.) 2005]
  A)
  2 done clear
  B)
  4 done clear
  C)
  8 done clear
  D)
  12 done clear
  E)
  16 done clear
  View Solution play_arrow

• question_answer72)
  If \[A=\{1,\,2,\,3,\,4\}\]; \[B=\{a,\,b\}\] and f is a mapping such that \[f:A\to B\], then \[A\times B\] is [DCE 2005]
  A)
  {(a, 1), (3, b)} done clear
  B)
  {(a, 2), (4, b)} done clear
  C)
  {(1, a), (1, b), (2, a), (2, b), (3, a), (3, b), (4, a), (4, b)} done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer73)
  If A = {1, 2, 3, 4, 5}, B = {2, 4, 6}, C = {3, 4, 6}, then \[(A\cup B)\cap C\] is [Orissa JEE 2004]
  A)
  {3, 4, 6} done clear
  B)
  {1, 2, 3} done clear
  C)
  {1, 4, 3} done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer74)
  If A = {x, y} then the power set of A is [Pb. CET 2004, UPSEAT 2000]
  A)
  \[\{{{x}^{x}},\,{{y}^{y}}\}\] done clear
  B)
  {f, x, y} done clear
  C)
  {f, {x}, {2y}} done clear
  D)
  {f, {x}, {y}, {x, y}} done clear
  View Solution play_arrow

• question_answer75)
  A set contains \[2n+1\] elements. The number of subsets of this set containing more than n elements is equal to [UPSEAT 2001, 04]
  A)
  \[{{2}^{n-1}}\] done clear
  B)
  \[{{2}^{n}}\] done clear
  C)
  \[{{2}^{n+1}}\] done clear
  D)
  \[{{2}^{2n}}\] done clear
  View Solution play_arrow

• question_answer76)
  Which of the following is a true statement [UPSEAT 2005]
  A)
  \[\left\{ a \right\}\text{ {I} }\left\{ a,\text{ }b,\text{ }c \right\}\] done clear
  B)
  \[\left\{ a \right\}\text{ }\overset{,}{\mathop{\text{I}}}\,\text{ }\left\{ a,\text{ }b,\text{ }c \right\}\] done clear
  C)
  \[f\text{ {I} }\left\{ a,\text{ }b,\text{ }c \right\}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer77)
  If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6} then A I B consists of all multiples of [UPSEAT 2000]
  A)
  16 done clear
  B)
  12 done clear
  C)
  8 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer78)
  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 [Kerala (Engg.) 2003]
  A)
  35 done clear
  B)
  48 done clear
  C)
  60 done clear
  D)
  22 30 done clear
  View Solution play_arrow

• question_answer79)
  Consider the following relations :(1) \[A-B=A-(A\cap B)\](2) \[A=(A\cap B)\cup (A-B)\](3) \[A-(B\cup C)=(A-B)\cup (A-C)\]which of these is/are correct [NDA 2003]
  A)
  1 and 3 done clear
  B)
  2 only done clear
  C)
  2 and 3 done clear
  D)
  1 and 2 done clear
  View Solution play_arrow

• question_answer80)
  If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets \[A\times B\] and \[B\times A\] are [Kerala (Engg.) 2004]
  A)
  \[{{2}^{99}}\] done clear
  B)
  \[{{99}^{2}}\] done clear
  C)
  100 done clear
  D)
  18 done clear
  E)
  9 done clear
  View Solution play_arrow

• question_answer81)
  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 \[n({{(A\cup B)}^{C}})=\] [Kerala (Engg.) 2004]
  A)
  17 done clear
  B)
  9 done clear
  C)
  11 done clear
  D)
  3 done clear
  E)
  16 done clear
  View Solution play_arrow