List of top Questions asked in JEE Main

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

Let $f(x)$ be a differentiable function satisfying \[ f(x)=e^x+\int_0^1 (y+xe^x)f(y)\,dy \] Find $f(0)+e$, where $e$ is Napier's constant.

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

Evaluate \[ \left(\frac{4}{7}+\frac{1}{3}\right)+\left(\frac{4}{7}+\frac{4}{3}\right)\left(\frac{1}{3}\right) +\left(\frac{4}{7}+\frac{4}{3}\right)^2\left(\frac{1}{3}\right)^2+\cdots \]

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).

If the equation \[ x^4-ax^2+9=0 \] has four real and distinct roots, then the least possible integral value of $a$ is

If dataset $A=\{1,2,3,\ldots,19\}$ and dataset $B=\{ax+b;\,x\in A\}$. If mean of $B$ is $30$ and variance of $B$ is $750$, then sum of possible values of $b$ is

If $f(a)$ is the area bounded in the first quadrant by $x=0$, $x=1$, $y=x^2$ and $y=|ax-5|-|1-ax|+ax^2$, then find $f(0)+f(1)$.

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 $\alpha\in\mathbb{R}$).

Find the number of solutions of the equation \[ \tan(x+100^\circ)=\tan(x+50^\circ)\tan(x-50^\circ) \] where $x\in(0,\pi)$.

Let $P$ and $Q$ be any two $3\times3$ matrices where $P=[p_{ij}]_{3\times3}$, $Q=[q_{ij}]_{3\times3}$ such that $q_{ij}=2^{\,i+j-1}p_{ij}$. Find $|\operatorname{adj}(\operatorname{adj}P)|$.

Let the ellipse \[ E=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] have eccentricity equal to the greatest value of the function \[ f(t)=-\frac34+2t-t^2 \] and the length of its latus rectum is $30$. Find the value of $a^2+b^2$.

If two lines drawn from a point $P(2,3)$ intersect the line $x+y=6$ at a distance $\sqrt{\dfrac{2}{3}}$, then the angle between the lines is

If shortest distance between the lines \[ \frac{x+1}{\alpha}=\frac{y-2}{-2}=\frac{z-4}{-2\alpha} \quad \text{and} \quad \frac{x}{\alpha}=\frac{y-1}{1}=\frac{z-1}{\alpha} \] is $\sqrt{2}$, then find the sum of all possible values of $\alpha$.

Let a function $f(x)$ satisfy \[ 3f(x)+2f\!\left(\frac{m}{19x}\right)=5x \] where $m=\sum_{i=1}^{9} i^2$. Find $f(5)+f(2)$.

The correct order of electron gain enthalpy (magnitude only) for group 16 elements is:

Find magnetic field at midpoint O. Rings have radius $R$ and direction of current is in opposite sense.

Resistance of each side is $R$. Find equivalent resistance between two opposite points as shown in the figure.

In case of meter bridge experiment balance length for $2\Omega$ and $3\Omega$ is $\ell$ and for $x\Omega$ and $3\Omega$ is $(\ell + 10)$ cm. Find $x$.

A cylindrical object of density $600\,\text{kg/m}^3$ and height $8$ cm is floating in a liquid of density $900\,\text{kg/m}^3$. Find height of cylinder inside liquid.

When rod becomes horizontal find its angular velocity. It is pivoted at point A as shown.

A soap bubble of diameter $7$ cm, its diameter is increased to $14$ cm. If change in its surface energy is $(15000 - x)\,\mu$J, find $x$. (Given surface tension = $0.04$ N/m)

Select correct truth table.

On a surface, if photon of wavelength $\lambda$ is incident, the stopping potential is $3.2$ V. If the wavelength incident is $2\lambda$, stopping potential is $0.7$ V. Find $\lambda$.