33
MCQ (Single Correct Answer)
If $A=\{1,2,3\}$ and consider the relation
$$R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$$
Then, $R$ is
A
reflexive but not symmetric
B
reflexive but not transitive
C
symmetric and transitive
D
neither symmetric nor transitive
34
MCQ (Single Correct Answer)
The identity element for the binary operation $*$ defined on $Q-\{0\}$ as $a * b=\frac{a b}{2}, \forall a, b \in Q-\{0\}$ is
A
1
B
0
C
2
D
None of these
35
MCQ (Single Correct Answer)
If the set $A$ contains 5 elements and the set $B$ contains 6 elements, then the number of one-one and onto mappings from $A$ to $B$ is
A
720
B
120
C
0
D
None of these
36
MCQ (Single Correct Answer)
If $A=\{1,2,3, \ldots, n\}$ and $B=\{a, b\}$. Then, the number of surjections from $A$ into $B$ is
A
${ }^n P_2$
B
$2^n-2$
C
$2^n-1$
D
None of these
37
MCQ (Single Correct Answer)
If $f: R \rightarrow R$ be defined by $f(x)=\frac{1}{x}, \forall x \in R$. Then, $f$ is
A
one-one
B
onto
C
bijective
D
$f$ is not defined