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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 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
( ) ( ) 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