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:

If $f : R \rightarrow R$ such that $f(x) = 5x - 3\cos x - 4\sin x$,then the function $f(x)$ is

Check the injectivity and surjectivity of the following function $f: N \rightarrow N$ defined by $f(x)=x^{2}$.

Consider the sets $A = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + y^2 = 25\}$,$B = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + 9y^2 = 144\}$,$C = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : x^2 + y^2 \leq 4\}$,and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:

Let $A \subseteq R, B \subseteq R$ and $f: A \rightarrow B$ be defined by $f(x)=x^2-3x+2$. If $f$ is a bijection,then

Which of the following statements is true?