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

The function $f: C \rightarrow C$ defined by $f(x) = \frac{ax + b}{cx + d}$ for $x \in C$,where $ad - bc \neq 0$,reduces to a constant function if:

Let $A = \{1, 2, 3, \ldots, 7\}$ and let $P(A)$ denote the power set of $A$. If the number of functions $f: A \rightarrow P(A)$ such that $a \in f(a)$ for all $a \in A$ is $m^n$,where $m, n \in N$ and $m$ is the least possible value,then $m + n$ is equal to . . . . . . .

If a set $A$ has $m$ elements and the set $B$ has $n$ elements,then the number of injections from $A$ to $B$ is

$A$ function $f$ from the set of natural numbers $\mathbb{N}$ to the set of integers $\mathbb{Z}$ is defined by $f(n) = \begin{cases} \frac{n-1}{2}, & \text{if } n \text{ is odd} \\ -\frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$. The function $f$ is:

Let $f : R \rightarrow R$ be a function such that $f(x) = \frac{x^2+2x+1}{x^2+1}$. Then