JEE Maths PYQ Practice, chapter-wise

JEE Main 2022 (Online) 29th July Morning ShiftQuestion 16

Let $R$ be a relation from the set $\{1,2,3,\ldots,60\}$ to itself such that $R=\{(a,b):b=pq$, where $p,q\ge3$ are prime numbers$\}$. Then, the number of elements in $R$ is :

Sets, Relations and Function

$600$$660$$540$$720$

JEE Main 2022 (Online) 25th June Evening ShiftQuestion 17

Let $A=\{x\in\mathbf{R}:|x+1|<2\}$ and $B=\{x\in\mathbf{R}:|x-1|\ge2\}$. Then which one of the following statements is NOT true ?

Sets, Relations and Function

$A-B=(-1,1)$$B-A=\mathbf{R}-(-3,1)$$A\cap B=(-3,-1]$$A\cup B=\mathbf{R}-[1,3)$

JEE Main 2024 (Online) 8th April Morning ShiftQuestion 18

Let $[t]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of $2310$ and $f:A\to\mathbb{Z}$ be the function $f(x)=\left[\log_2\left(x^{2}+\left[\frac{x^{3}}{5}\right]\right)\right]$. The number of one-to-one functions from $A$ to the range of $f$ is

Sets, Relations and Function

$20$$24$$120$$25$

JEE Main 2023 (Online) 10th April Evening ShiftQuestion 19

Let $A=\{2,3,4\}$ and $B=\{8,9,12\}$. Then the number of elements in the relation $R=\{((a_1,b_1),(a_2,b_2))\in(A\times B,A\times B):a_1\text{ divides }b_2\text{ and }a_2\text{ divides }b_1\}$ is

Sets, Relations and Function

$12$$18$$24$$36$

JEE Main 2022 (Online) 29th June Evening ShiftQuestion 20

The probability that a relation $R$ from $\{x,y\}$ to $\{x,y\}$ is both symmetric and transitive, is equal to

Sets, Relations and Function

$\frac{5}{16}$$\frac{9}{16}$$\frac{11}{16}$$\frac{13}{16}$

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