JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 11th April Evening ShiftQuestion 6

Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let $R$ be a relation defined on $A\times B$ such that $R=\{((a_1,b_1),(a_2,b_2)):a_1\le b_2\text{ and }b_1\le a_2\}$. Then the number of elements in the set $R$ is

Sets, Relations and Function

$26$$52$$160$$180$

JEE Main 2025 (Online) 3rd April Evening ShiftQuestion 7

Let $A=\{-2,-1,0,1,2,3\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $y=\max\{x,1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to

Sets, Relations and Function

$11$$12$$13$$14$

JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 8

Let $A=\{1,2,3,\ldots,100\}$ and $R$ be a relation on $A$ such that $R=\{(a,b):a=2b+1\}$. Let $(a_1,a_2),(a_2,a_3),(a_3,a_4),\ldots,(a_k,a_{k+1})$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer $k$, for which such a sequence exists, is equal to :

Sets, Relations and Function

$5$$6$$7$$8$

JEE Main 2025 (Online) 8th April Evening ShiftQuestion 9

Let $A=\{0,1,2,3,4,5\}$. Let $R$ be a relation on $A$ defined by $(x,y)\in R$ if and only if $\max\{x,y\}\in\{3,4\}$. Then among the statements $(S_1)$ : The number of elements in $R$ is $18$, and $(S_2)$ : The relation $R$ is symmetric but neither reflexive nor transitive

Sets, Relations and Function

both are trueboth are falseonly $(S_1)$ is trueonly $(S_2)$ is true

JEE Main 2024 (Online) 1st February Evening ShiftQuestion 10

Consider the relations $R_1$ and $R_2$ defined as $aR_1b\Leftrightarrow a^{2}+b^{2}=1$ for all $a,b\in\mathbf{R}$ and $(a,b)R_2(c,d)\Leftrightarrow a+d=b+c$ for all $(a,b),(c,d)\in\mathbf{N}\times\mathbf{N}$. Then

Sets, Relations and Function

Only $R_1$ is an equivalence relationOnly $R_2$ is an equivalence relation$R_1$ and $R_2$ both are equivalence relationsNeither $R_1$ nor $R_2$ is an equivalence relation