If $f(x) = [8x] - 3$,where $[x]$ is the greatest integer function of $x$,then $f(\pi) = $

$f: X \rightarrow R$, where $X = \{x \mid 0 < x < 1\}$, is defined as $f(x) = \frac{2x-1}{1-|2x-1|}$. Then:

If $f: N \times N \rightarrow N$ defined by $f(m, n) = mn$,then $f$ is . . . . . . .

$A$ mapping from $\mathbb{N}$ to $\mathbb{N}$ is defined as follows: $f: \mathbb{N} \rightarrow \mathbb{N}$ where $f(n) = (n+5)^2$ for all $n \in \mathbb{N}$ (where $\mathbb{N}$ is the set of natural numbers). Then:

If set $A$ has $5$ elements and set $B$ has $7$ elements,then the number of many-one functions that can be defined from $A$ to $B$ is:

Let $f(x) = \cos(\sqrt{P}x),$ where $P = [\lambda]$ and $[.]$ denotes the Greatest Integer Function. If the period of $f(x)$ is $\pi$,then: