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Multiple Choice Questions Relations and Functions 1. Let R be the relation in the set of natural numbers N defined as R ( ) :3 11 . , N N x y xy × + Then 1 R - is given by i) ( ) ( ) ( ) ( ) { } , , , 0,11 1, 8 2, 5 3, 2 ( ) ( ) ( ) ( ) { } , , 1, 8 2, 5 3, 2 ii ( ) ( ) ( ) ( ) ( ) { } , , , 11, 0 8, 1 5, 2 2, 3 iii ( ) ( ) ( ) ( ) { } , , 8, 1 5, 2 2, 3 iv 2. A relation defined in a non-empty set A, having n elements, has () () ( ) 2 n relations 2 relations n relations i i iii ( ) 2 2 relations n iv 3. The relation R in the set of real numbers defined as R ( ) { } :1 >0 is , b R R ab a × + ( ) ( ) reflexive and transive symmetric and transitive i ii ( ) ( ) reflexive and symmetric equivalence relation iii iv 4. A relation R in human beings as R ( ) { } () ( ) ( ) ( ) : , human bengs ; a loves b is , reflexive symmetric and transitive equivalence neither of these ab ab i ii iii iv = 5. Let the function ' ' f be defined by ( ) 2 5 2, f x x + ' ' is f x . Then V R ' ' is f ( ) ( ) onto function one-one, onto function i ii

Relations and Functions tricks

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Page 1: Relations and Functions tricks

Multiple Choice Questions

Relations and Functions

1. Let R be the relation in the set of natural numbers N defined as R

( ) : 3 11 ., N N x yx y ∈ × + = =

Then 1R −

is given by

i) ( ) ( ) ( ) ( ){ } , , ,0,11 1,8 2,5 3,2 ( ) ( ) ( ) ( ){ } , ,1, 8 2, 5 3, 2ii

( ) ( ) ( ) ( ) ( ){ } , , , 11, 0 8, 1 5, 2 2, 3iii

( ) ( ) ( ) ( ){ } , , 8, 1 5, 2 2, 3iv

2. A relation defined in a non-empty set A, having n elements, has

( ) ( ) ( )2 n relations 2 relations n relationsi i iii

( )2

2 relationsniv

3. The relation R in the set of real numbers defined as R

( ){ }:1 > 0 is, b R R aba ∈ × +=

( ) ( ) reflexive and transive symmetric and transitivei ii

( ) ( ) reflexive and symmetric equivalence relationiii iv

4. A relation R in human beings as R

( ){ }

( ) ( )

( ) ( )

: , human bengs ; a loves b is ,

reflexive symmetric and transitive

equivalence neither of these

a ba b

i ii

iii iv

∈=

5. Let the function ' 'f be defined by ( )25 2, f xx += ' ' is f x . Then V R∈

' ' is f ( ) ( ) onto function one-one, onto functioni ii

Page 2: Relations and Functions tricks

( ) ( ) one-one function many-one, into functioniii iv

6. Let the function ' 'f be defined by

( ) 2 3, not belonging to x N. Then 'f' is f xx + ∈=

( ) ( ) into function bijective functioni ii

( ) ( ) many-one, into function none of theseiii iv

7. Let { } { }' ' : 2 1 be a function defined byf R R− → − ( )1, then 'f' is

2

xf x

x

−=

( ) ( )

( ) ( )

into function many one function

bijective function many one, into function

i ii

iii iv

8. If ( ) ( )3 and g cos 3 , f x x then fog isx x= =

( )3 x .cos 3xi ( )

2 cos 3xii ( )3 cos 3xiii ( )

3 3 cos xiv

9. Let function f:R R→ is defined as ( )3 12 1. Then ff x isx

−−=

( ) ( ) ( ) ( ) ( ) ( )

1/33 33 1

2x 1 1 2 1 22

xx xi ii iii iv

+ + + −

10 Let I be the set of integers. Define a binary operation

( ) ( ) ( ) in Z Ze as ,, , , b+da b c d a c∗ × ∗ += then binary operation ∗ is

( ) ( )

( ) ( )

not commutative not associative

commutative and associative does not have identity element

i ii

iii iv