Consider the function $f(x) = x^3 - 8x^2 + 20x - 13$. The function $f: R \rightarrow R$ is:

The number of bijective functions $f : \{1, 3, 5, 7, \ldots, 99\} \rightarrow \{2, 4, 6, 8, \ldots, 100\}$ such that $f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \geq f(99)$ is:

Consider the identity function $I_{N}: N \rightarrow N$ defined as $I_{N}(x) = x$ for all $x \in N$. Show that although $I_{N}$ is onto,the function $I_{N} + I_{N}: N \rightarrow N$ defined as $(I_{N} + I_{N})(x) = I_{N}(x) + I_{N}(x) = x + x = 2x$ is not onto.

Let $g: N \rightarrow N$ be defined as
$g(3n+1)=3n+2$
$g(3n+2)=3n+3$
$g(3n+3)=3n+1, \text{ for all } n \geq 0$
Then which of the following statements is true?

If a set $A$ has $m$ elements and set $B$ has $n$ elements and the number of injections from $A$ to $B$ is $2520$. Then,$m$ is equal to

Consider the following statements:
Statement-$I$ : $A$ function $f: A \rightarrow B$ is said to be one-one if and only if $f(x) \neq f(y) \Rightarrow x \neq y$.
Statement-$II$ : $A$ relation $f: A \rightarrow B$ is said to be a function if $x \neq y \Rightarrow f(x) \neq f(y)$.
Then which one of the following is true?