Relations & Functions (Basic) JEE Main PYQs, 2020 to 2025

Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements

(S₁): The number of elements in R is 18, and

(S₂): The relation R is symmetric but neither reflexive nor transitive

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

Let $f, g:(1, \infty) \rightarrow \mathbb{R}$ be defined as $f(x)=\frac{2 x+3}{5 x+2}$ and $g(x)=\frac{2-3 x}{1-x}$. If the range of the function fog: $[2,4] \rightarrow \mathbb{R}$ is $[\alpha, \beta]$, then $\frac{1}{\beta-\alpha}$ is equal to

Let $[x]$ denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function $f(x)=[x]+|x-2|,-2< x<3$, is not continuous and not differentiable. Then $\mathrm{m}+\mathrm{n}$ is equal to :

Let $f:R \to R$ be a function such that $f(x) = {{{x^2} + 2x + 1} \over {{x^2} + 1}}$. Then