The function $f(x) = \sec \left[ \log \left( x + \sqrt{1 + x^2} \right) \right]$ is

Let $S = \{1, 2, 3, 4, 5, 6\}$. Then the probability that a randomly chosen onto function $g: S \to S$ satisfies $g(3) = 2g(1)$ is:

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

For functions $f$ and $g$,where $f: [0, \frac{\pi}{2}] \rightarrow R$ with $f(x) = \sin x$ and $g: [0, \frac{\pi}{2}] \rightarrow R$ with $g(x) = \cos x$,which of the following is true?

Let $A = \{x_1, x_2, \dots, x_7\}$ and $B = \{y_1, y_2, y_3\}$ be two sets containing seven and three distinct elements respectively. The total number of onto functions $f : A \to B$ such that there exist exactly three elements $x$ in $A$ with $f(x) = y_2$ is equal to:

The number of one-one functions from the set $A = \{1, 2, 3, 4, 5\}$ to itself is . . . . . . .