CUET Mathematics 2023 15 June Shift 2 PYQs

A and B are two sets such that $n(A) = 5$ and $n(B) = 7$. The number of one-one functions from A to B is

A relation $f: N \rightarrow N$ be defined by $f(x) = x^2$, $x \in N$ (Set of Natural numbers). Then $f(x)$ is

Which of the following statements are true?

(A) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = 3x$ is one-one onto.

(B) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = x^4$ is one-one and onto.

(C) $f:\mathbb{Z} \to \mathbb{Z}$ given by $f(x) = x^2$ is neither one-one nor onto.

(D) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = |x|$ is neither one-one nor onto.

(Where $\mathbb{R}$ is the set of all real numbers and $\mathbb{Z}$ is the set of all integers)

Choose the correct answer from the options given below: