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:

Let $A = \{1, 2, 3, \ldots, n\}$ and $B = \{a, b\}$. If the number of onto functions from $A$ to $B$ is $62$,then the number of subsets of $A$ containing exactly three elements is:

Let $f: R \to R$ be defined as $f(x) = x^3$. Then $f$ is . . . . . . .

Let $f: R \rightarrow R$ be defined as $f(x)=x^{4}$. Choose the correct answer.

$A$ mapping from $\mathbb{N}$ to $\mathbb{N}$ is defined as follows: $f: \mathbb{N} \rightarrow \mathbb{N}$ where $f(n) = (n+5)^2$ for all $n \in \mathbb{N}$ (where $\mathbb{N}$ is the set of natural numbers). Then:

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):