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JEE Mathematics / Practice

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JEE Main 2024 (Online) 30th January Morning ShiftQuestion 1
A group of $40$ students appeared in an examination of $3$ subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast one of the subjects, $20$ students passed in Mathematics, $25$ students passed in Physics, $16$ students passed in Chemistry, atmost $11$ students passed in both Mathematics and Physics, atmost $15$ students passed in both Physics and Chemistry, atmost $15$ students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is $\_\_\_\_\_\_$ .
Sets, Relations and Function
JEE Main 2022 (Online) 29th July Evening ShiftQuestion 2
If $[t]$ denotes the greatest integer $\le t$, then the number of points, at which the function $f(x)=4|2x+3|+9\left[x+\frac12\right]-12[x+20]$ is not differentiable in the open interval $(-20,20)$, is ________.
Sets, Relations and Function
JEE Main 2025 (Online) 7th April Morning ShiftQuestion 3
The number of relations on the set $A=\{1,2,3\}$, containing at most $6$ elements including $(1,2)$, which are reflexive and transitive but not symmetric, is $\_\_\_\_\_\_$ .
Sets, Relations and Function
JEE Main 2024 (Online) 30th January Morning ShiftQuestion 4
Let $A=\{1,2,3,\ldots,7\}$ and let $P(A)$ denote the power set of $A$. If the number of functions $f:A\to P(A)$ such that $a\in f(a)$, $\forall a\in A$ is $m^{n}$, $m$ and $n\in\mathbf{N}$ and $m$ is least, then $m+n$ is equal to $\_\_\_\_\_\_$ .
Sets, Relations and Function
JEE Main 2024 (Online) 30th January Evening ShiftQuestion 5
The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is $\_\_\_\_\_\_$ .
Sets, Relations and Function