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

Let $Z$ denote the set of integers. Define $f: Z \rightarrow Z$ by $f(x) = \begin{cases} \frac{x}{2}, & x \text{ is even} \\ 0, & x \text{ is odd} \end{cases}$. Then $f$ is:

Let $f: R \rightarrow R$ be defined by $f(x) = \left\{\begin{array}{cc} 2x, & x > 3 \\ x^2, & 1 < x \leq 3 \\ 3x, & x \leq 1 \end{array}\right.$. Then,the value of $f(-2) + f(3) + f(4)$ is:

Consider the following statements:
Statement-$I$ : $A$ function $f: A \rightarrow B$ is said to be one-one if and only if $f(x) \neq f(y) \Rightarrow x \neq y$.
Statement-$II$ : $A$ relation $f: A \rightarrow B$ is said to be a function if $x \neq y \Rightarrow f(x) \neq f(y)$.
Then which one of the following is true?

The function $f:[0,3] \rightarrow [1,29]$,defined by $f(x)=2x^3-15x^2+36x+1$,is

Let $R$ be the set of all real numbers and $f: R \rightarrow R$ be a continuous function. Suppose $|f(x) - f(y)| \geq |x - y|$ for all real numbers $x$ and $y$. Then,