JEE Main & Advanced Mathematics Sets Question Bank

done Critical Thinking Total Questions - 15

• question_answer1)
  If \[X=\{{{8}^{n}}-7n-1:n\in N\}\] and \[Y=\{49(n-1):n\in N\},\] then
  A)
  \[X\subseteq Y\] done clear
  B)
  \[Y\subseteq X\] done clear
  C)
  \[X=Y\] done clear
  D)
  None of these done clear
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• question_answer2)
  If \[{{N}_{a}}=\{an:n\in N\},\] then \[{{N}_{3}}\cap {{N}_{4}}=\]
  A)
  \[{{N}_{7}}\] done clear
  B)
  \[{{N}_{12}}\] done clear
  C)
  \[{{N}_{3}}\] done clear
  D)
  \[{{N}_{4}}\] done clear
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• question_answer3)
  Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A U B [MNR 1987; Karnataka CET 1996]
  A)
  3 done clear
  B)
  6 done clear
  C)
  9 done clear
  D)
  18 done clear
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• question_answer4)
  If \[A=[(x,\,y):{{x}^{2}}+{{y}^{2}}=25]\] and B = \[[(x,\,y):{{x}^{2}}+9{{y}^{2}}=144]\], then \[A\cap B\] contains [AMU 1996; Pb. CET 2002]
  A)
  One point done clear
  B)
  Three points done clear
  C)
  Two points done clear
  D)
  Four points done clear
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• question_answer5)
  If \[A=[x:x\] is a multiple of 3] and \[B=[x:x\] is a multiple of 5], then A - B is (\[\bar{A}\] means complement of A) [AMU 1998]
  A)
  \[\bar{A}\cap B\] done clear
  B)
  \[A\cap \bar{B}\] done clear
  C)
  \[\bar{A}\cap \bar{B}\] done clear
  D)
  \[\overline{A\cap B}\] done clear
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• question_answer6)
  If \[A=\{x:{{x}^{2}}-5x+6=0\},\,B=\{2,\,4\},\,C=\{4,\,5\},\] then \[A\times (B\cap C)\] is [Kerala (Engg.) 2002]
  A)
  {(2, 4), (3, 4)} done clear
  B)
  {(4, 2), (4, 3)} done clear
  C)
  {(2, 4), (3, 4), (4, 4)} done clear
  D)
  {(2,2), (3,3), (4,4), (5,5)} done clear
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• question_answer7)
  In a college of 300 students, every student reads 5 newspaper and every newspaper is read by 60 students. The no. of newspaper is [IIT 1998]
  A)
  At least 30 done clear
  B)
  At most 20 done clear
  C)
  Exactly 25 done clear
  D)
  None of these done clear
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• question_answer8)
  Let A = {1, 2, 3, 4, 5}; B = {2, 3, 6, 7}. Then the number of elements in \[\left( A\text{ }~\times \text{ }B \right)\text{ }\cap \text{ }\left( B\text{ }\times \text{ }A \right)\] is
  A)
  18 done clear
  B)
  6 done clear
  C)
  4 done clear
  D)
  0 done clear
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• question_answer9)
  Let A = {1, 2, 3}, B = {1, 3, 5}. A relation \[R:A\to B\] is defined by R = {(1, 3), (1, 5), (2, 1)}. Then \[{{R}^{-1}}\] is defined by
  A)
  {(1,2), (3,1), (1,3), (1,5)} done clear
  B)
  {(1, 2), (3, 1), (2, 1)} done clear
  C)
  {(1, 2), (5, 1), (3, 1)} done clear
  D)
  None of these done clear
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• question_answer10)
  Let R be the relation on the set R of all real numbers defined by a R b iff \[|a-b|\le 1\]. Then R is [Roorkee 1998]
  A)
  Reflexive and Symmetric done clear
  B)
  Symmetric only done clear
  C)
  Transitive only done clear
  D)
  Anti-symmetric only done clear
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• question_answer11)
  With reference to a universal set, the inclusion of a subset in another, is relation, which is [Karnataka CET 1995]
  A)
  Symmetric only done clear
  B)
  Equivalence relation done clear
  C)
  Reflexive only done clear
  D)
  None of these done clear
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• question_answer12)
  Let R be a relation on the set N of natural numbers defined by nRm \[\Leftrightarrow \] n is a factor of m (i.e., n|m). Then R is
  A)
  Reflexive and symmetric done clear
  B)
  Transitive and symmetric done clear
  C)
  Equivalence done clear
  D)
  Reflexive, transitive but not symmetric done clear
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• question_answer13)
  Let R and S be two non-void relations on a set A. Which of the following statements is false
  A)
  R and S are transitive \[\Rightarrow \text{ }R\text{ }\cup \text{ }S\] is transitive done clear
  B)
  R and S are transitive \[\Rightarrow \text{ }R\text{ }\cap \text{ }S\] is transitive done clear
  C)
  R and S are symmetric \[\Rightarrow \text{ }R\text{ }\cup \text{ }S\] is symmetric done clear
  D)
  R and S are reflexive \[\Rightarrow \text{ }R\text{ }\cap \text{ }S\] is reflexive done clear
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• question_answer14)
  Let a relation R be defined by R = {(4, 5); (1, 4); (4, 6);     (7, 6); (3, 7)} then \[{{R}^{-1}}oR\] is
  A)
  {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)} done clear
  B)
  {(1, 1), (4, 4), (7, 7), (3, 3)} done clear
  C)
  {(1, 5), (1, 6), (3, 6)} done clear
  D)
  None of these done clear
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• question_answer15)
  Let R be a relation on the set N be defined by {(x, y)| x, y  \[\overset{\hat{\ }}{\mathop{i}}\,\] N, 2x + y = 41}. Then R is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
  Transitive done clear
  D)
  None of these done clear
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