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

Let $f: R \rightarrow R$ be defined by $f(x) = 5^{-|x|} + \operatorname{sgn}(5^{-x})$,where $\operatorname{sgn}(x)$ denotes the signum function of $x$. Then $f$ is

Let $f: R \rightarrow R$ be a function defined by $f(x) = \frac{e^{|x|} - e^{-x}}{e^x + e^{-x}}$,then

If a set $A$ has $n$ elements,then the number of functions defined from $A$ to $A$ that are not one-one is

The number of onto functions from the set $\{1, 2, \ldots, 11\}$ to the set $\{1, 2, \ldots, 10\}$ is

Let $X$ and $Y$ be subsets of $R$,the set of all real numbers. The function $f:X \to Y$ defined by $f(x) = x^2$ for $x \in X$ is one-one but not onto if (Here $R^+$ is the set of all positive real numbers):