JEE Mathematics / Practice

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JEE Main 2022 (Online) 25th July Evening ShiftQuestion 6

The sum of the maximum and minimum values of the function $f(x)=|5x-7|+[x^2+2x]$ in the interval $\left[\frac54,2\right]$, where $[t]$ is the greatest integer $\le t$, is ________.

Sets, Relations and Function

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JEE Main 2024 (Online) 1st February Morning ShiftQuestion 7

Let $A=\{1,2,3,\ldots,20\}$. Let $R_1$ and $R_2$ two relation on $A$ such that $R_1=\{(a,b):b$ is divisible by $a\}$, $R_2=\{(a,b):a$ is an integral multiple of $b\}$. Then, number of elements in $R_1-R_2$ is equal to $\_\_\_\_\_\_$ .

Sets, Relations and Function

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JEE Main 2022 (Online) 27th July Evening ShiftQuestion 8

The number of functions $f$, from the set $A=\{x\in\mathbf{N}:x^2-10x+9\le0\}$ to the set $B=\{n^2:n\in\mathbf{N}\}$ such that $f(x)\le(x-3)^2+1$, for every $x\in A$, is ________.

Sets, Relations and Function

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JEE Main 2023 (Online) 13th April Evening ShiftQuestion 9

Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R=\{(a,b)\in A\times A:b=|a|\text{ or }b^{2}=a+1\}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is $\_\_\_\_\_\_$ .

Sets, Relations and Function

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JEE Main 2021 (Online) 27th July Evening ShiftQuestion 10

Let $A=\{n\in\mathbf{N}\mid n^2\le n+10{,}000\}$, $B=\{3k+1\mid k\in\mathbf{N}\}$ and $C=\{2k\mid k\in\mathbf{N}\}$, then the sum of all the elements of the set $A\cap(B-C)$ is equal to ________.

Sets, Relations and Function

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