List of top Questions asked in JEE Main

A liquid drop of radius R is divided into 27 identical drops. If the surface tension of the drops is T, then find work done in this process.

A uniform magnetic field of \( 2 \times 10^{-3} \, \text{T} \) acts along positive Y-direction. A rectangular loop of sides 20 cm and 10 cm with current of 5 A is in the Y-Z plane. The current is in anticlockwise sense with reference to the negative X-axis. Magnitude and direction of the torque is:

Total number of stereo isomers possible for the given structure :

Major product of the following reaction is -

Average force exerted on a non-reflecting surface at normal incidence is $2.4\times10^{-4}\ N$. If $360\ W/cm^2$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

Let $A=I_2-2MM^T$, where $M$ is a real matrix of order $2\times1$ such that the relation $M^TM=I_1$ holds. If $\lambda$ is a real number such that the relation $AX=\lambda X$ holds for some non-zero real matrix $X$ of order $2\times1$, then the sum of squares of all possible values of $\lambda$ is equal to ____________ .

Projectiles A and B are thrown at angles of $45^{\circ}$ and $60^{\circ}$ with vertical respectively from top of a $400\ m$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $v_A:v_B$ is :
[Take $g=10\ ms^{-2}$]

Let $A$ be a $3\times3$ real matrix such that $A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix},\ A\begin{pmatrix}-1\\0\\1\end{pmatrix}=4\begin{pmatrix}-1\\0\\1\end{pmatrix},\ A\begin{pmatrix}0\\1\\0\end{pmatrix}=2\begin{pmatrix}0\\1\\0\end{pmatrix}$.
Then, the system $(A-3I)\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix}$ has :

Let $R=\begin{pmatrix}x&0&0\\0&y&0\\0&0&z\end{pmatrix}$ be a non-zero $3\times3$ matrix, where $x\sin\theta=y\sin\left(\theta+\dfrac{2\pi}{3}\right)=z\sin\left(\theta+\dfrac{4\pi}{3}\right)\ne0,\ \theta\in(0,2\pi)$. For a square matrix $M$, let trace $(M)$ denote the sum of all the diagonal entries of $M$. Then, among the statements:
(I) Trace $(R)=0$
(II) If trace $(\operatorname{adj}(\operatorname{adj}(R)))=0$, then $R$ has exactly one non-zero entry.

$\displaystyle\lim_{x\to\frac{\pi}{2}}\left(\frac{1}{\left(x-\frac{\pi}{2}\right)^2}\int_{x^3}^{\left(\frac{\pi}{2}\right)^3}\cos\left(t^{1/3}\right)dt\right)$ is equal to

If $f(x)=\begin{cases}2+2x, & -1\le x<0\\ 1-\dfrac{x}{3}, & 0\le x\le 3\end{cases}$ ; $g(x)=\begin{cases}-x, & -3\le x\le 0\\ x, & 0<x\le 1\end{cases}$, then the range of $(f\circ g)(x)$ is

For $0<a<1$, the value of the integral $\displaystyle\int_0^{\pi}\frac{dx}{1-2a\cos x+a^2}$ is :

De Broglie wavelength of proton = \(λ\) and that of an a particle \(2λ\). The ratio of velocity of proton to that of \(\alpha\) particle is 

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become.

The parabola \( y^2 = 4x \) divides the area of the circle \( x^2 + y^2 = 5 \) in two parts. The area of the smaller part is equal to:

In a given circuit, an ideal battery is connected with four resistances as shown. Find current \(i\) as mentioned in the diagram.

The effective resistance between A and B, if resistance of each resistor is R, will be

Let a variable line passing through the centre of the circle x² + y² – 16x – 4y = 0, meet the positive co-ordinate axes at the point A and B. Then the minimum value of OA + OB, where O is the origin, is equal to

A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons ?

The correct nomenclature for the following compound is:

The 20^th term from the end of the progression \[ 20, 19, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \ldots, -129 \frac{1}{4} \] is:

A galvanometer (G) of $2 \, \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is:

Which of the following are aromatic?

For \( x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \), if\[y(x) = \int \frac{\csc x + \sin x}{\csc x \sec x + \tan x \sin^2 x} \, dx\]and\[\lim_{x \to -\frac{\pi}{2}} y(x) = 0\]then \( y\left(\frac{\pi}{4}\right) \) is equal to