12th Class Mathematics Relations and Functions Question Bank

done Case Based (MCQs) - Relations and Functions Total Questions - 25

• question_answer1)

  Directions : (1-5)

  A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67% the highest ever.

  Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation 'R' is defined on I as follows :

  \[R=\left\{ \left( {{V}_{1}},\,{{V}_{2}} \right) \right.\,:\,{{V}_{1}},\,{{V}_{2}}\,\in \,\,I\]and both use their voting right in general election-2019}

  Two neighbours X and \[Y\in I\]. X exercised his voting right while Y did not caste her vote in general election-2019. Which of the following is true ?
  A)
  \[\left( X,\,Y \right)\in R\] done clear
  B)
  \[\left( Y,\,X \right)\in R\] done clear
  C)
  \[\left( X,\,X \right)\,\notin R\] done clear
  D)
  \[\left( X,\,Y \right)\,\notin R\] done clear
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• question_answer2)
  Mr. 'X' and his wife 'W' both exercised their voting right in general election-2019. Which of the following is true ?
  A)
  both (X, W) and \[\left( W,\,X \right)\in R\] done clear
  B)
  \[\left( X,\,W \right)\in R\] but \[\left( W,\,X \right)\notin R\] done clear
  C)
  both (X, W) and \[\left( W,\,X \right)\notin R\] done clear
  D)
  \[\left( W,\,X \right)\in R\] but \[\left( X,\,W \right)\,\notin R\] done clear
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• question_answer3)
  Three friends \[{{F}_{1}},\,{{F}_{2}}\] and \[{{F}_{3}}\] exercised their voting right in general election-2019, then which of the following is true ?
  A)
  \[\left( {{F}_{1}},\,{{F}_{2}} \right)\in R,\,\left( {{F}_{2}},\,{{F}_{3}} \right)\in R\] and \[\left( {{F}_{1}},\,{{F}_{3}} \right)\in R\] done clear
  B)
  \[\left( {{F}_{1}},\,{{F}_{2}} \right)\in R,\,\left( {{F}_{2}},\,{{F}_{3}} \right)\in R\] and \[\left( {{F}_{1}},\,{{F}_{3}} \right)\notin R\] done clear
  C)
  \[\left( {{F}_{1}},\,{{F}_{2}} \right)\in R,\,\left( {{F}_{2}},\,{{F}_{2}} \right)\in R\] not \[\left( {{F}_{3}},\,{{F}_{3}} \right)\notin R\] done clear
  D)
  \[\left( {{F}_{1}},\,{{F}_{2}} \right)\notin R,\,\left( {{F}_{2}},\,{{F}_{3}} \right)\notin R\] and \[\left( {{F}_{1}},\,{{F}_{3}} \right)\notin R\] done clear
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• question_answer4)
  The above defined relation R is
  A)
  Symmetric and transitive but not reflexive done clear
  B)
  Universal relation done clear
  C)
  Equivalence relation done clear
  D)
  Reflexive but not symmetric and transitive. done clear
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• question_answer5)
  Mr. Shyam exercised his voting right in General Election-2019, then Mr. Shyam is related to which of the following?
  A)
  All those eligible voters who cast their votes done clear
  B)
  Family members of Mr. Shyam done clear
  C)
  All citizens of India done clear
  D)
  Eligible voters of India. done clear
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• question_answer6)

  Directions : (6 - 10)

  Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin's sister Raji observed and noted the possible outcomes of the throw every time belongs to set \[\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\]. Let A be the set of players while B be the set of all possible outcomes.

  \[A=\left\{ S,\,D \right\},\,B=\left\{ 1,\,2,\,3,\,4,\,5,\,6 \right\}\]

  Let \[R\,\,:\,B\to B\] be defined by \[R=\left\{ \left( x,\,y \right) \right.:y\] is divisible by x} is
  A)
  Reflexive and transitive but not symmetric done clear
  B)
  Reflexive and symmetric and not transitive done clear
  C)
  Not reflexive but symmetric and transitive done clear
  D)
  Equivalence done clear
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• question_answer7)
  Raji wants to know the number of functions from A to B. How many number of functions are possible ?
  A)
  \[{{6}^{2}}\] done clear
  B)
  \[{{2}^{6}}\] done clear
  C)
  6! done clear
  D)
  \[{{2}^{12}}\] done clear
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• question_answer8)
  Let R be a relation on B defined by \[R=\left\{ \left( 1,\,2 \right),\,\left( 2,\,2 \right),\,\left( 1,\,3 \right),\,\left( 3,\,4 \right),\,\left( 3,\,1 \right),\,\left( 4,\,3 \right),\,\left( 5,\,5 \right) \right\}\]. Then R is
  A)
  Symmetric done clear
  B)
  Reflexive done clear
  C)
  Transitive done clear
  D)
  None of these three done clear
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• question_answer9)
  Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?
  A)
  \[{{6}^{2}}\] done clear
  B)
  \[{{2}^{6}}\] done clear
  C)
  6! done clear
  D)
  \[{{2}^{12}}\] done clear
  View Solution play_arrow

• question_answer10)
  Let \[R\,\,:\,\,B\to B\] be defined by \[R=\left\{ \left( 1,\,1 \right),\,\left( 1,\,2 \right),\,\left( 2,\,2 \right),\,\left( 3,\,3 \right),\,\left( 4,\,4 \right),\,\left( 5,\,5 \right),\,\left( 6,\,6 \right) \right\}\], then R is
  A)
  Symmetric done clear
  B)
  Reflexive and Transitive done clear
  C)
  Transitive and symmetric done clear
  D)
  Equivalence done clear
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• question_answer11)

  Directions : (11 - 15)

  An organization conducted bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project.

  Let \[B=\left\{ {{b}_{1}},\,{{b}_{2}},\,{{b}_{3}} \right\}\] \[G=\left\{ {{g}_{1}},\,{{g}_{2}} \right\}\] where B represents the set of boys selected and G the set of girls who were selected for the final race.

  Ravi decides to explore these sets for various types of relations and functions

  Ravi wishes to form all the relations possible from B to G. How many such relations are possible?
  A)
  \[{{2}^{6}}\] done clear
  B)
  \[{{2}^{5}}\] done clear
  C)
  0 done clear
  D)
  \[{{2}^{3}}\] done clear
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• question_answer12)
  Let \[R\,\,:\,\,B\,\to \,B\] be defined by \[R=\left\{ \left( x,\,y \right) \right.\,:\,\]x and y are students of same sex}. Then this relation R is
  A)
  Equivalence done clear
  B)
  Reflexive only done clear
  C)
  Reflexive and symmetric but not transitive done clear
  D)
  Reflexive and transitive but not symmetric done clear
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• question_answer13)
  Ravi wants to know among those relations how many functions can be formed from B to G?
  A)
  \[{{2}^{2}}\] done clear
  B)
  \[{{2}^{12}}\] done clear
  C)
  \[{{3}^{2}}\] done clear
  D)
  \[{{2}^{3}}\] done clear
  View Solution play_arrow

• question_answer14)
  \[R\,:\,B\,\to G\] be defined by \[R=\left\{ \left( {{b}_{1}},\,{{g}_{1}} \right),\,\left( {{b}_{2}},\,{{g}_{2}} \right),\,\left( {{b}_{3}},\,{{g}_{3}} \right) \right\}\,\], then R is
  A)
  Injective done clear
  B)
  Surjective done clear
  C)
  Neither Surjective nor Injective done clear
  D)
  Surjective and Injective. done clear
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• question_answer15)
  Ravi wants to find the number of injective functions from B to G. How many numbers of injective functions are possible?
  A)
  0 done clear
  B)
  2! done clear
  C)
  3! done clear
  D)
  0! done clear
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• question_answer16)

  Directions : (16 - 20)

  Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line \[y=x-4\]. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

  Answer the following using the above information.

  Let relation R be defined by \[R=\left\{ \left( {{L}_{1}},\,{{L}_{2}} \right) \right.\,:\,{{L}_{1}}\,|\,\,|\,\,{{L}_{2}}\] where \[\left. {{L}_{1}},\,{{L}_{2}}\,\in L \right\}\] then R is ............ relation
  A)
  Equivalence done clear
  B)
  Only reflexive done clear
  C)
  Not reflexive done clear
  D)
  Symmetric but not transitive done clear
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• question_answer17)
  Let \[R=\left\{ \left( {{L}_{1}},\,{{L}_{2}} \right)\,:\,{{L}_{1}}\,\bot {{L}_{2}}, \right\}\] where \[{{L}_{1}},\,{{L}_{2}}\in L\] which of the following is true ?
  A)
  R is Symmetric but neither reflexive nor transitive done clear
  B)
  R is Reflexive and transitive but not symmetric done clear
  C)
  R is Reflexive but neither symmetric nor transitive done clear
  D)
  R is an Equivalence relation. done clear
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• question_answer18)
  The function \[f:\,R\to R\] defined by \[f\left( x \right)=x-4\] is
  A)
  Bijective done clear
  B)
  Surjective but not injective done clear
  C)
  Injective but not Surjective done clear
  D)
  Neither Surjective nor Injective. done clear
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• question_answer19)
  Let \[f\,:\,R\to R\] be defined by \[f\left( x \right)=x-4\]. Then the range of f (x) is
  A)
  R done clear
  B)
  Z done clear
  C)
  W done clear
  D)
  Q done clear
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• question_answer20)
  Let \[R=\left\{ \left( {{L}_{1}},\,{{L}_{2}} \right)\,\,:\,\,{{L}_{1}} \right.\] is parallel to \[{{L}_{2}}\] and \[\left. {{L}_{1}}\,\,:\,\,\,y=x-4 \right\}\] then which of the following can be taken as \[{{L}_{2}}\]?
  A)
  \[2x-2y+5=0\] done clear
  B)
  \[2x+y=5\] done clear
  C)
  \[2x+2y+7=0\] done clear
  D)
  \[x+y=7\] done clear
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• question_answer21)

  Directions : (21 - 25)

  Raji visited the Exhibition along with their family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by \[y={{x}^{2}}\].

  Answer the following questions using the above information.

  Let \[f\,:\,R\to R\] be defined by \[f\left( x \right)={{x}^{2}}\]is
  A)
  Neither Surjective nor Injective done clear
  B)
  Surjective done clear
  C)
  Injective done clear
  D)
  Bijective done clear
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• question_answer22)
  Let \[f\,\,:\,\,N\,\,\to \,\,N\] be defined by \[f\left( x \right)={{x}^{2}}\] is
  A)
  Surjective but not Injective done clear
  B)
  Surjective done clear
  C)
  Injective done clear
  D)
  Bijective done clear
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• question_answer23)
  Let \[f:\left\{ 1,\,2,\,3\,.... \right\}\to \left\{ 1,\,4,\,9,\,... \right\}\]be defined by \[f\left( x \right)={{x}^{2}}\]is
  A)
  Bijective done clear
  B)
  Surjective but not Injective done clear
  C)
  Injective but Surjective done clear
  D)
  Neither Surjective nor Injective. done clear
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• question_answer24)
  Let : \[N\to R\] be defined by \[f\left( x \right)={{x}^{2}}\]. Range of the function among the following is
  A)
  \[\left\{ 1,\text{ }4,\text{ }9,\text{ }16,\text{ }... \right\}\] done clear
  B)
  \[\left\{ 1,\text{ }4,\text{ }8,\text{ }9,\text{ }10,\text{ }... \right\}\] done clear
  C)
  \[\left\{ 1,4,\text{ }9,\text{ }15,\text{ }16,\text{ }... \right\}\] done clear
  D)
  \[\left\{ 1,\text{ }4,\text{ }8,\text{ }16,\text{ }... \right\}\] done clear
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• question_answer25)
  The function : \[Z\to Z\] defined by \[f\left( x \right)={{x}^{2}}\] is
  A)
  Neither Injective nor Surjective done clear
  B)
  Injective done clear
  C)
  Surjective done clear
  D)
  Bijective done clear
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