If the set $x$ contains $7$ elements and set $y$ contains $8$ elements,then the number of bijections from $x$ to $y$ is

Let $A \subseteq R, B \subseteq R$ and $f: A \rightarrow B$ be defined by $f(x)=x^2-3x+2$. If $f$ is a bijection,then

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements,and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then ...... .

$f: N \rightarrow N$,is defined by $f(x)=x^6$ then, . . . . . . .

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injections that can be defined from $A$ to $B$ is

The function $f(x) = \sin (\log (x + \sqrt {x^2 + 1}))$ is