JEE Maths PYQ Practice, chapter-wise

JEE Main 2022 (Online) 29th June Morning ShiftQuestion 26

Let a set $A=A_1\cup A_2\cup\ldots\cup A_k$, where $A_i\cap A_j=\phi$ for $i\neq j$, $1\le i,j\le k$. Define the relation $R$ from $A$ to $A$ by $R=\{(x,y):y\in A_i$ if and only if $x\in A_i,\ 1\le i\le k\}$. Then, $R$ is :

Sets, Relations and Function

reflexive, symmetric but not transitivereflexive, transitive but not symmetricreflexive but not symmetric and transitivean equivalence relation

JEE Main 2021 (Online) 27th July Evening ShiftQuestion 27

Let $\mathbf{N}$ be the set of natural numbers and a relation $R$ on $\mathbf{N}$ be defined by $R=\{(x,y)\in\mathbf{N}\times\mathbf{N}:x^3-3x^2y-xy^2+3y^3=0\}$. Then the relation $R$ is :

Sets, Relations and Function

reflexive and symmetric, but not transitivereflexive but neither symmetric nor transitivesymmetric but neither reflexive nor transitivean equivalence relation

JEE Main 2023 (Online) 8th April Evening ShiftQuestion 28

Let $A=\{1,2,3,4,5,6,7\}$. Then the relation $R=\{(x,y)\in A\times A:x+y=7\}$ is

Sets, Relations and Function

reflexive but neither symmetric nor transitivesymmetric but neither reflexive nor transitivetransitive but neither symmetric nor reflexivean equivalence relation

JEE Main 2022 (Online) 27th July Evening ShiftQuestion 29

The domain of the function $f(x)=\sin^{-1}[2x^2-3]+\log_2\left(\log_{\frac12}(x^2-5x+5)\right)$, where $[t]$ is the greatest integer function, is :

Sets, Relations and Function

$\left(-\sqrt{\frac52},\frac{5-\sqrt5}{2}\right)$$\left(\frac{5-\sqrt5}{2},\frac{5+\sqrt5}{2}\right)$$\left(1,\frac{5-\sqrt5}{2}\right)$$\left[1,\frac{5+\sqrt5}{2}\right)$

JEE Main 2022 (Online) 30th July Evening ShiftQuestion 30

Let $f:\mathbb{R}-\{5\}\to\mathbb{R}$ be defined as $f(x)=\frac{2x^2+3x-2}{x-5}$. Then $f$ is

Sets, Relations and Function

one-one and ontoone-one but not ontoonto but not one-oneneither one-one nor onto

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