If the set $x$ contains $7$ elements and set $y$ contains $8$ elements,then the number of bijections from $x$ to $y$ is

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

The number of functions $f: \{1, 2, 3, 4\} \to \{a, b, c\}$, which are not onto, is:

Let $f: N \to N$ be defined by $f(x) = x^2 + x + 1$,where $x \in N$. Then $f$ is:

If $f: Z \rightarrow N$ is defined by $f(n) = \begin{cases} 2n, & \text{if } n > 0 \\ 1, & \text{if } n = 0 \\ -2n-1, & \text{if } n < 0 \end{cases}$, then the function $f$ is:

The number of functions $f: \{1, 2, \ldots, 100\} \rightarrow \{0, 1\}$ that assign $1$ to exactly one of the positive integers less than or equal to $98$ is equal to $\qquad$.