List of top Mathematics Questions asked in JEE Main

The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :
Let $y=y(x)$ be the solution curve of the differential equation $\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log _e x\right)\right), x>0, y(1)=3$ Then $\frac{y^2(x)}{9}$ is equal to :
If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to
The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively Later, the marks of one of the students is increased from 8 to 12 If the new mean of the marks is $10.2$, then their new variance is equal to :
Let $A= \begin{pmatrix} m & n \\ p & q\end{pmatrix}, d=|A| \neq 0$ and $|A-d(\operatorname{Adj} A)|=0$ Then
If $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2 a$, then the value of $\left(a+\frac{1}{a}\right)$ is :
Let $\vec{a}$ and $\vec{b}$ be two vectors, Let $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$ If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$, then the value of $\vec{b} \cdot \vec{c}$ is
Let $A$ be a point on the $x$-axis Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16 x$ If one of these tangents touches the two curves at $Q$ and $R$, then $(Q R)^2$ is equal to
If $[ t ]$ denotes the greatest integer $\leq t$, then the value of $\frac{3( e -1)}{ e } \int\limits_1^2 x^2 e^{[x]+\left[x^3\right]} dx$ is :
Let $y=x+2,4 y=3 x+6$ and $3 y=4 x+1$ be three tangent lines to the circle $(x-h)^2+(y- k )^2= r ^2$ Then $h + k$ is equal to :
If $a_n=\frac{-2}{4 n^2-16 n+15}$, then $a_1+a_2+\ldots \ldots+a_{25}$ is equal to:
The coefficient of $x^{301}$ in $(1+x)^{500}+x(1+x)^{499}+x^2(1+x)^{498}+\ldots \ldots +x^{500}$ is :
The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c)\}$ on the set $\{ a , b , c \}$ so that it becomes symmetric and transitive is :
If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is:

Let the plane $P : 8 x+\alpha_1 y+\alpha_2 z+12=0$ be parallel to the line $L : \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}$. If the intercept of $P$ on the $y$-axis is 1 , then the distance between $P$ and $L$ is :

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then
A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then
If $P ( h , k )$ be a point on the parabola $x=4 y^2$, which is nearest to the point $Q (0,33)$, then the distance of $P$ from the directrix of the parabola $y^2=4(x+y)$ is equal to :
Consider the following statements: 
P : I have fever 
Q: I will not take medicine 
R : I will take rest 
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:
Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a_1, a_2, a_3, \ldots , a_{100}$ is $25$ Then $S$ is
Let $a_1=1, a_2, a_3, a_4, \ldots $ be consecutive natural numbersThen $\tan ^{-1}\left(\frac{1}{1+a_1 a_2}\right)+\tan ^{-1}\left(\frac{1}{1+a_2 a_3}\right)+\ldots +\tan ^{-1}\left(\frac{1}{1+a_{2021} a_{2022}}\right)$ is equal to

Let\( S={x∈R:0<x<1 and\ 2 tan−1\frac{(1+x)}{(1−x​)}=cos^{−1}\frac{(1-x^2)}{(1+x^2​)}}\). If n(S) denotes the number of elements in S then :

Let \(9 =\) \(x_1​<x_2​<…<x_7​\) be in an A.P. with common difference d. If the standard deviation of \(x_1​,x_2​ …,x_7\)​ is 4 and the mean is \(\bar x\), then \(\bar x+x_6\)​ is equal to :

The absolute minimum value, of the function $f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right]$, where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is:

In a binomial distribution $B(n, p)$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $6(n+p-q)$ is equal to