JEE Main & Advanced Mathematics Sets Question Bank

done Relations Total Questions - 56

• question_answer1)
  Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is
  A)
  \[{{2}^{9}}\] done clear
  B)
  6 done clear
  C)
  8 done clear
  D)
  None of these done clear
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• question_answer2)
  Let \[X=\{1,\,2,\,3,\,4,\,5\}\] and \[Y=\{1,\,3,\,5,\,7,\,9\}\]. Which of the following is/are relations from X to Y
  A)
  \[{{R}_{1}}=\{(x,\,y)|y=2+x,\,x\in X,\,y\in Y\}\] done clear
  B)
  \[{{R}_{2}}=\{(1,\,1),\,(2,\,1),\,(3,\,3),\,(4,\,3),\,(5,\,5)\}\] done clear
  C)
  \[{{R}_{3}}=\{(1,\,1),\,(1,\,3)(3,\,5),\,(3,\,7),\,(5,\,7)\}\] done clear
  D)
  \[{{R}_{4}}=\{(1,\,3),\,(2,\,5),\,(2,\,4),\,(7,\,9)\}\] done clear
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• question_answer3)
  Given two finite sets A  and B  such that n = 2, n = 3. Then total number of relations from A to B is
  A)
  4 done clear
  B)
  8 done clear
  C)
  64 done clear
  D)
  None of these done clear
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• question_answer4)
  The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}, is given by
  A)
  {(1, 4, (2, 5), (3, 6),.....} done clear
  B)
  {(4, 1), (5, 2), (6, 3),.....} done clear
  C)
  {(1, 3), (2, 6), (3, 9),..} done clear
  D)
  None of these done clear
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• question_answer5)
  The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then \[{{R}^{-1}}\] is given by
  A)
  {(2, 1), (4, 2), (6, 3).....} done clear
  B)
  {(1, 2), (2, 4), (3, 6)....} done clear
  C)
  \[{{R}^{-1}}\] is not defined done clear
  D)
  None of these done clear
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• question_answer6)
  The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
  A)
  Reflexive but not symmetric done clear
  B)
  Reflexive but not transitive done clear
  C)
  Symmetric and Transitive done clear
  D)
  Neither symmetric nor transitive done clear
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• question_answer7)
  The relation ?less than? in the set of natural numbers is                                    [UPSEAT 1994, 98, 99; AMU 1999]
  A)
  Only symmetric done clear
  B)
  Only transitive done clear
  C)
  Only reflexive done clear
  D)
  Equivalence relation done clear
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• question_answer8)
  Let \[P=\{(x,\,y)|{{x}^{2}}+{{y}^{2}}=1,\,x,\,y\in R\}\]. Then P is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
  Transitive done clear
  D)
  Anti-symmetric done clear
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• question_answer9)
  Let R be an equivalence relation on a finite set A having n elements. Then the number of ordered pairs in R is
  A)
  Less than n done clear
  B)
  Greater than or equal to n done clear
  C)
  Less than or equal to n done clear
  D)
  None of these done clear
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• question_answer10)
  For real numbers x and y, we write \[x\,R\,y\Leftrightarrow \] \[x-y+\sqrt{2}\] is an irrational number. Then the relation R  is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
  Transitive done clear
  D)
  None of these done clear
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• question_answer11)
  Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then R is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
   Anti-symmetric done clear
  D)
  Transitive done clear
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• question_answer12)
  If R  is a relation from a set A  to a set B and S is a relation from B to a set C, then the relation SoR
  A)
  Is from A to C done clear
  B)
  Is from C to A done clear
  C)
  Does not exist done clear
  D)
  None of these done clear
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• question_answer13)
  If \[R\subset A\times B\] and \[S\subset B\times C\,\] be two relations, then \[{{(SoR)}^{-1}}=\]
  A)
  \[{{S}^{-1}}o{{R}^{-1}}\] done clear
  B)
  \[{{R}^{-1}}o{{S}^{-1}}\] done clear
  C)
  \[SoR\] done clear
  D)
  \[RoS\] done clear
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• question_answer14)
  If R be a relation < from A = {1,2, 3, 4} to B = {1, 3, 5} i.e., \[(a,\,b)\in R\Leftrightarrow a<b,\] then \[Ro{{R}^{-1}}\] is
  A)
  {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)} done clear
  B)
  {(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)} done clear
  C)
  {(3, 3), (3, 5), (5, 3), (5, 5)} done clear
  D)
  {(3, 3) (3, 4), (4, 5)} done clear
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• question_answer15)
  A relation from P to Q  is
  A)
  A universal set of P × Q done clear
  B)
  P × Q done clear
  C)
  An equivalent set of P × Q done clear
  D)
  A subset of P × Q done clear
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• question_answer16)
  Let A = {a, b, c} and B = {1, 2}. Consider a relation R  defined from set A to set B. Then R  is equal to set [Kurukshetra CEE 1995]
  A)
  A done clear
  B)
  B done clear
  C)
  A × B done clear
  D)
  B × A done clear
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• question_answer17)
  Let n = n. Then the number of all relations on A is
  A)
  \[{{2}^{n}}\] done clear
  B)
  \[{{2}^{(n)!}}\] done clear
  C)
  \[{{2}^{{{n}^{2}}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
  A)
  \[{{2}^{mn}}\] done clear
  B)
  \[{{2}^{mn}}-1\] done clear
  C)
  \[2mn\] done clear
  D)
  \[{{m}^{n}}\] done clear
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• question_answer19)
  Let R be a reflexive relation on a finite set A having            n-elements, and let there be m ordered pairs in R. Then
  A)
  \[m\ge n\] done clear
  B)
  \[m\le n\] done clear
  C)
  \[m=n\] done clear
  D)
  None of these done clear
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• question_answer20)
  The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : \[|{{x}^{2}}-{{y}^{2}}|<16\}\] is given by  
  A)
  {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} done clear
  B)
  {(2, 2), (3, 2), (4, 2), (2, 4)} done clear
  C)
  {(3, 3), (3, 4), (5, 4), (4, 3), (3, 1)} done clear
  D)
  None of these done clear
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• question_answer21)
  A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by \[xRy\Leftrightarrow x\] is relatively prime to y. Then domain of R is
  A)
  {2, 3, 5} done clear
  B)
  {3, 5} done clear
  C)
  {2, 3, 4} done clear
  D)
  {2, 3, 4, 5} done clear
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• question_answer22)
  Let R be a relation on N defined by \[x+2y=8\]. The domain of R is
  A)
  {2, 4, 8} done clear
  B)
  {2, 4, 6, 8} done clear
  C)
  {2, 4, 6} done clear
  D)
  {1, 2, 3, 4} done clear
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• question_answer23)
  If \[R=\{(x,\,y)|x,\,y\in Z,\,{{x}^{2}}+{{y}^{2}}\le 4\}\] is a relation in Z, then domain of R is
  A)
  {0, 1, 2} done clear
  B)
  {0, - 1, - 2} done clear
  C)
  {- 2, - 1, 0, 1, 2} done clear
  D)
  None of these done clear
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• question_answer24)
  R is a relation from {11, 12, 13} to {8, 10, 12} defined by \[y=x-3\]. Then \[{{R}^{-1}}\] is
  A)
  {(8, 11), (10, 13)} done clear
  B)
  {(11, 18), (13, 10)} done clear
  C)
  {(10, 13), (8, 11)} done clear
  D)
  None of these done clear
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• question_answer25)
  Let A = {1, 2, 3}, B = {1, 3, 5}. If relation R from A to B is given by R ={(1, 3), (2, 5), (3, 3)}. Then \[{{R}^{-1}}\] is
  A)
  {(3, 3), (3, 1), (5, 2)} done clear
  B)
  {(1, 3), (2, 5), (3, 3)} done clear
  C)
  {(1, 3), (5, 2)} done clear
  D)
  None of these done clear
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• question_answer26)
  Let R be a reflexive relation on a set A and I be the identity relation on A. Then
  A)
  \[R\subset I\] done clear
  B)
  \[I\subset R\] done clear
  C)
  \[R=I\] done clear
  D)
  None of these done clear
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• question_answer27)
  Let A = {1, 2, 3, 4} and R be a relation in A given by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)}. Then R is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
  Transitive done clear
  D)
  An equivalence relation done clear
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• question_answer28)
  An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is
  A)
  Reflexive and symmetric done clear
  B)
  Reflexive and transitive done clear
  C)
  Symmetric and transitive done clear
  D)
  Equivalence relation done clear
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• question_answer29)
  The relation R defined in N as \[aRb\Leftrightarrow b\] is divisible by a is 
  A)
  Reflexive but not symmetric done clear
  B)
  Symmetric but not transitive done clear
  C)
  Symmetric and transitive done clear
  D)
  None of these done clear
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• question_answer30)
  Let R be a relation on a set A such that \[R={{R}^{-1}}\], 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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• question_answer31)
  Let R = {(a, a)} be a relation on a set A. Then R is 
  A)
  Symmetric done clear
  B)
  Antisymmetric done clear
  C)
  Symmetric and antisymmetric done clear
  D)
  Neither symmetric nor anti-symmetric done clear
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• question_answer32)
  The relation "is subset of" on the power set P of a set A  is
  A)
  Symmetric done clear
  B)
  Anti-symmetric done clear
  C)
  Equivalency relation done clear
  D)
  None of these done clear
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• question_answer33)
  The relation R defined on a set A  is antisymmetric if \[(a,\,b)\in R\Rightarrow (b,\,a)\in R\] for
  A)
  Every (a, b) \[\in R\] done clear
  B)
  No \[(a,\,b)\in R\] done clear
  C)
  No \[(a,\,b),\,a\ne b,\,\in R\] done clear
  D)
  None of these done clear
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• question_answer34)
  In the set A = {1, 2, 3, 4, 5}, a relation R is defined by R = {(x, y)| x, y \[\in \] A and x < y}. Then R is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
  Transitive done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  Let A be the non-void set of the children in a family. The relation 'x is a brother of y' on A is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
  Transitive done clear
  D)
  None of these done clear
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• question_answer36)
  Let A = {1, 2, 3, 4} and let R= {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. 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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• question_answer37)
  The void relation on a set A is
  A)
  Reflexive done clear
  B)
  Symmetric and transitive done clear
  C)
  Reflexive and symmetric done clear
  D)
  Reflexive and transitive done clear
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• question_answer38)
  Let \[{{R}_{1}}\] be a relation defined by \[{{R}_{1}}=\{(a,\,b)|a\ge b,\,a,\,b\in R\}\]. Then \[{{R}_{1}}\] is                    [UPSEAT 1999]
  A)
  An equivalence relation on R done clear
  B)
  Reflexive, transitive but not symmetric done clear
  C)
  Symmetric, Transitive but not reflexive done clear
  D)
  Neither transitive not reflexive but symmetric done clear
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• question_answer39)
  Which one of the following relations on R  is an equivalence relation
  A)
  \[a\,{{R}_{1}}\,b\Leftrightarrow |a|=|b|\] done clear
  B)
  \[a{{R}_{2}}b\Leftrightarrow a\ge b\] done clear
  C)
  \[a{{R}_{3}}b\Leftrightarrow a\text{ divides }b\] done clear
  D)
  \[a{{R}_{4}}b\Leftrightarrow a<b\] done clear
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• question_answer40)
  If R is an equivalence relation on a set A, then \[{{R}^{-1}}\] is
  A)
  Reflexive only done clear
  B)
  Symmetric but not transitive done clear
  C)
  Equivalence done clear
  D)
  None of these done clear
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• question_answer41)
  R is a relation over the set of real numbers and it is given by \[nm\ge 0\]. Then R is
  A)
  Symmetric and transitive done clear
  B)
  Reflexive and symmetric done clear
  C)
  A partial order relation done clear
  D)
  An equivalence relation done clear
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• question_answer42)
  In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R  [Karnataka CET 1990]
  A)
  Is reflexive done clear
  B)
  Is symmetric done clear
  C)
  Is transitive done clear
  D)
  Possesses all the above three properties done clear
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• question_answer43)
  The relation "congruence modulo m" is
  A)
  Reflexive only done clear
  B)
  Transitive only done clear
  C)
  Symmetric only done clear
  D)
  An equivalence relation done clear
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• question_answer44)
  Solution set of \[x\equiv 3\] (mod 7), \[p\in Z,\] is given by
  A)
  {3} done clear
  B)
  \[\{7p-3:p\in Z\}\] done clear
  C)
  \[\{7p+3:p\in Z\}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer45)
  Let R and S be two equivalence relations on a set A. Then
  A)
  \[R\text{ }\cup \text{ }S\] is an equivalence relation on A done clear
  B)
  \[R\text{ }\cap \text{ }S\] is an equivalence relation on A done clear
  C)
  \[R-S\] is an equivalence relation on A done clear
  D)
  None of these done clear
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• question_answer46)
  Let R and S be two relations on a set A. Then
  A)
  R and S are transitive, then \[R\text{ }\cup \text{ }S\] is also transitive done clear
  B)
  R and S are transitive, then \[R\text{ }\cap \text{ }S\] is also transitive done clear
  C)
  R and S are reflexive, then \[R\text{ }\cap \text{ }S\]  is also reflexive done clear
  D)
  R and S are symmetric then \[R\text{ }\cup \text{ }S\] is also symmetric done clear
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• question_answer47)
  Let R = {(1, 3), (2, 2), (3, 2)} and S = {(2, 1), (3, 2), (2, 3)} be two relations on set A = {1, 2, 3}. Then RoS =
  A)
  {(1, 3), (2, 2), (3, 2), (2, 1), (2, 3)} done clear
  B)
  {(3, 2), (1, 3)} done clear
  C)
  {(2, 3), (3, 2), (2, 2)} done clear
  D)
  {(2, 3), (3, 2)} done clear
  View Solution play_arrow

• question_answer48)
  Let L denote the set of all straight lines in a plane. Let a relation R be defined by \[\alpha R\beta \Leftrightarrow \alpha \bot \beta ,\,\alpha ,\,\beta \in L\]. 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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• question_answer49)
  Let R be a relation over the set N × N and it is defined by \[(a,\,b)R(c,\,d)\Rightarrow a+d=b+c.\] Then R is
  A)
  Reflexive only done clear
  B)
  Symmetric only done clear
  C)
  Transitive only done clear
  D)
  An equivalence relation done clear
  View Solution play_arrow

• question_answer50)
  Let n be a fixed positive integer. Define a relation R on the set Z of integers by, \[aRb\Leftrightarrow n|a-b\]|. Then R is
  A)
  Reflexive done clear
  B)
  Symmetric done clear
  C)
  Transitive done clear
  D)
  Equivalence done clear
  View Solution play_arrow

• question_answer51)
  Let\[R=\{(3,\,3),\ (6,\ 6),\ (9,\,9),\ (12,\,12),\ (6,\,12),\ (3,\,9),(3,\,12),\,(3,\,6)\}\] be a relation on the set \[A=\{3,\,6,\,9,\,12\}\]. The relation is [AIEEE 2005]
  A)
  An equivalence relation done clear
  B)
  Reflexive and symmetric only done clear
  C)
  Reflexive and transitive only done clear
  D)
  Reflexive only done clear
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• question_answer52)
  \[{{x}^{2}}=xy\] is a relation which is [Orissa JEE 2005]
  A)
  Symmetric done clear
  B)
  Reflexive done clear
  C)
  Transitive done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer53)
  Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is [AIEEE 2004]
  A)
  Reflexive done clear
  B)
  Transitive done clear
  C)
  Not symmetric done clear
  D)
  A function done clear
  View Solution play_arrow

• question_answer54)
  The number of reflexive relations of a set with four elements is equal to [UPSEAT 2004]
  A)
  \[{{2}^{16}}\] done clear
  B)
  \[{{2}^{12}}\] done clear
  C)
  \[{{2}^{8}}\] done clear
  D)
  \[{{2}^{4}}\] done clear
  View Solution play_arrow

• question_answer55)
  Let S be the set of all real numbers. Then the relation R = {(a, b) : 1 + ab > 0} on S is [NDA 2003]
  A)
  Reflexive and symmetric but not transitive done clear
  B)
  Reflexive and transitive but not symmetric done clear
  C)
  Symmetric, transitive but not reflexive done clear
  D)
  Reflexive, transitive and symmetric done clear
  E)
  None of the above is true done clear
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• question_answer56)
  If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is [NDA 2003]
  A)
  \[{{2}^{9}}\] done clear
  B)
  \[{{9}^{2}}\] done clear
  C)
  \[{{3}^{2}}\] done clear
  D)
  \[{{2}^{9-1}}\] done clear
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