If $f(x)$ is a function satisfying $f(x + y) = f(x)f(y)$ for all $x,\;y \in N$ such that $f(1) = 3$ and $\sum\limits_{x = 1}^n {f(x) = 120} $. Then the value of $n$ is

Suppose that a function $f: R \rightarrow R$ satisfies $f(x+y)=f(x) f(y)$ for all $x, y \in R$ and $f(1)=3 .$ If $\sum \limits_{i=1}^{n} f(i)=363,$ then $n$ is equal to

Let $f(x)=\frac{x-1}{x+1}, x \in R-\{0,-1,1)$. If $f^{a+1}(x)=f\left(f^{n}(x)\right)$ for all $n \in N$, then $f^{\prime}(6)+f(7)$ is equal to

The number of functions $f$, from the set$A=\left\{x \in N: x^{2}-10 x+9 \leq 0\right\}$ to the set $B=\left\{n^{2}: n \in N\right\}$ such that $f(x) \leq(x-3)^{2}+1$, for every $x \in A$, is.

Which pair $(s)$ of function $(s)$ is/are equal ?

where $\{x\}$ and $[x]$ denotes the fractional part $\&$ integral part functions.

If the domain of the function $f(x)=\log _e\left(4 x^2+11 x+6\right)+\sin ^{-1}$ $(4 x+3)+\cos ^{-1}\left(\frac{10 x+6}{3}\right) \text { is }(\alpha, \beta]$ Then $36|\alpha+\beta|$ is equal to :