
Directions : (15) 
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 election2019} 
Two neighbours X and \[Y\in I\]. X exercised his voting right while Y did not caste her vote in general election2019. 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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Mr. 'X' and his wife 'W' both exercised their voting right in general election2019. 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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Three friends \[{{F}_{1}},\,{{F}_{2}}\] and \[{{F}_{3}}\] exercised their voting right in general election2019, 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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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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Mr. Shyam exercised his voting right in General Election2019, 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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Directions : (6  10) 
Sherlin and Danju are playing Ludo at home during Covid19. 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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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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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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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

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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Directions : (11  15) 
An organization conducted bike race under 2 different categoriesboys 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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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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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
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\[R\,:\,B\,\to G\] 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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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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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 \[y=x4\]. 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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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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The function \[f:\,R\to R\] defined by \[f\left( x \right)=x4\] 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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Let \[f\,:\,R\to R\] be defined by \[f\left( x \right)=x4\]. 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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Let \[R=\left\{ \left( {{L}_{1}},\,{{L}_{2}} \right)\,\,:\,\,{{L}_{1}} \right.\] is parallel to \[{{L}_{2}}\] and \[\left. {{L}_{1}}\,\,:\,\,\,y=x4 \right\}\] then which of the following can be taken as \[{{L}_{2}}\]?
A)
\[2x2y+5=0\] 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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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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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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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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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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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
View Solution play_arrow