List of top Questions asked in JEE Main

Let $ A = \{0,1,2,\ldots,9\} $. Let $ R $ be a relation on $ A $ defined by $(x,y) \in R$ if and only if $ |x - y| $ is a multiple of $3$. Given below are two statements:
Statement I: $ n(R) = 36 $.
Statement II: $ R $ is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below.

The sum of all values of $\alpha$, for which the shortest distance between the lines $\dfrac{x+1}{\alpha}=\dfrac{y-2}{-1}=\dfrac{z-4}{-\alpha}$ and $\dfrac{x}{\alpha}=\dfrac{y-1}{2}=\dfrac{z-1}{2\alpha}$ is $\sqrt{2}$, is

The mean and variance of the observations x, y, 5, 7, 9, 11, 13, 15 are 10 and 20 respectively. If x $>$ y, then the value of x - y is:

Find the sum of all real solutions of
$|x + 1|^2 - 4|x + 1| + 3 = 0$

If 3 balls are taken from a box without replacement and found to be all black. If all configurations of red balls and black balls are equally likely, then the probability that the box contained 1 red and 9 black balls is $\dfrac{p}{q}$ for some coprime natural numbers $p$ and $q$. Find $p+q$.

Let $z = (1+i)(1+2i)(1+3i)\cdots(1+ni)$ and $|z|^2 = 44200$. Find the value of $n$.

Let mirror image of parabola $x^2 = 4y$ in the line $x-y=1$ be $(y+a)^2 = b(x-c)$. Then the value of $(a+b+c)$ is

Let 4 integers $a_1, a_2, a_3, a_4$ are in A.P. with integral common difference $d$ such that $a_1+a_2+a_3+a_4=48$ and $a_1a_2a_3a_4+d^4=361$. Then the greatest term in this A.P. is

Let $S$ has 5 elements and $P(S)$ is the power set of $S$. Let an ordered pair $(A,B)$ is selected at random from $P(S)\times P(S)$. If the probability that $A\cap B=\varnothing$ is $\dfrac{3^m}{2^n}$, then the value of $(m+n)$ is

If domain of $f(x)=\sin^{-1}\!\left(\dfrac{1}{x^2-2x-2}\right)$ is $(-\infty,\alpha]\cup[\beta,\gamma]\cup[\delta,\infty)$, then $(\alpha+\beta+\gamma+\delta)$ is

Let

be a continuous function at $x=0$, then the value of $(a^2+b^2)$ is (where $[\ ]$ denotes greatest integer function).

Let \[ f(x)=\int \frac{7x^{10}+9x^8}{(1+x^2+2x^9)^2}\,dx \] and $f(1)=\frac14$. Given that

and $B=\operatorname{adj}(\operatorname{adj}A)$, if $|B|=81$, find the value of $\alpha^2$ (where $\alpha\in\mathbb{R}$).