JEE Mathematics / Practice

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JEE Main 2024 (Online) 30th January Evening ShiftQuestion 56

The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is $\_\_\_\_\_\_$ .

Sets, Relations and Function

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JEE Main 2022 (Online) 25th July Evening ShiftQuestion 57

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 58

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 2020 (Online) 3rd September Evening ShiftQuestion 59

Let $R_1$ and $R_2$ be two relations defined as follows : $R_1=\{(a,b)\in\mathbf{R}^2:a^2+b^2\in\mathbf{Q}\}$ and $R_2=\{(a,b)\in\mathbf{R}^2:a^2+b^2\notin\mathbf{Q}\}$, where $\mathbf{Q}$ is the set of all rational numbers. Then :

Sets, Relations and Function

$R_1$ and $R_2$ are both transitive.$R_1$ is transitive but $R_2$ is not transitive.$R_2$ is transitive but $R_1$ is not transitive.Neither $R_1$ nor $R_2$ is transitive.

JEE Main 2022 (Online) 27th July Evening ShiftQuestion 60

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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