List of top Questions asked in JEE Main

An electron is released in the field generated by a non-conductivity sheet of uniform surface charge density $ \sigma $. The rate of change of de-Broglie wavelength associated with the electron varies inversely as the $ n $th power of the distance travelled. Find the value of $ n $.
Given $ \lambda = 2 \, \text{nC/m} $ (linear charge density) for a wire passing through the body diagonal of a closed cube with side length $ \sqrt{3} \, \text{cm} $, find the flux through the cube.
A monoatomic gas is stored in a thermally insulated container. The gas is suddenly compressed to $ \frac{1}{8} $th of its initial volume. Find the ratio of final pressure to initial pressure.
Two balls are projected with the same speed at different angles. If the maximum height of the 1st ball is 8 times the maximum height of the 2nd ball, find the ratio of their time of flight.
A uniform disc of radius $ r $ is rotating about an axis passing through its diameter with angular speed 800 rpm. A torque of magnitude $ 25\pi \, \text{Nm} $ is applied on the disc for 40 sec. If the final angular speed of the disc is 2100 rpm, find the diameter of the disc if its mass is 1 kg.
For a nucleus of mass number $ A $ and radius $ R $, mass density is $ \rho $. Then choose the correct option.
There are two charged spheres of radius $ R $ and $ 3R $. When the spheres are made to touch each other and then separate, the surface charge density becomes $ \sigma_1 $ and $ \sigma_2 $ respectively. Find the ratio $ \frac{\sigma_1}{\sigma_2} $.
A fractional error in $ x $, $ y $, and $ z $ are 0.1, 0.2, and 0.5 respectively. Find the maximum fractional error in $ x^{-2} y^{3/2} z^{-2/5} $.

Find output voltage in the given circuit.

In 3, 3-dimethylhex-1-en-4-yne, the number of sp, sp² and sp³ carbon atoms, respectively are:
A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be \( \frac{x}{100} \), where \( x \) is:

Nature of compounds TeO₂ and TeH₂ is___________ and ______________respectively.

Let $ A = [a_{ij}] $ be a $3 \times 3 $ matrix such that: $$ A = \begin{bmatrix} 0 & 0 & 4 \\ 1 & 0 & 0 \\ 0 & 1 & 3 \\ \end{bmatrix}, A^{-1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 3 & 0 \\ 2 & 1 & 0 \end{bmatrix}. $$ Then $ a_{23} $ equals:

For the reaction, $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$

Attainment of equilibrium is predicted correctly by: 


 
 

In YDSE, light of intensity 4I and 9I passes through two slits respectively. The difference of maximum and minimum intensity of the interference pattern is:
Let $f: [0, 3] \to A$ be defined by $f(x) = 2x^3 - 15x^2 + 36x + 7$ and $g: [0, \infty) \to B$ be defined by $g(x) = \frac{x}{x^{2025} + 1}$. If both functions are onto and $S = \{ x \in \mathbb{Z} : x \in A \text{ or } x \in B \}$, then $n(S)$ is equal to:
Total number of nucleophiles from the following is: $NH_3$, $PhSH$, $(H_3C_2S)_2$, $H_2C=CH_2$, $OH^-$, $H_3O^+$, $(CH_3)_2CO$, $NCH_3$

1.24 g of $ {AX}_2 $ (molar mass 124 g mol$^{-1}$) is dissolved in 1 kg of water to form a solution with boiling point of 100.105$^\circ$C, while 2.54 g of $ {AY}_2 $ (molar mass 250 g mol$^{-1}$) in 2 kg of water constitutes a solution with a boiling point of 100.026$^\circ$C. $ K_{b(H_2O)} = 0.52 \, \text{K kg mol}^{-1} $. Which of the following is correct?

The figure shows a circular portion of radius \( \frac{R}{2} \) removed from a disc of mass \( m \) and radius \( R \). The moment of inertia about an axis passing through the centre of mass of the disc and perpendicular to the plane is:
The heat of formation of \( \text{SO}_2(g) \) is given by: $$ S(g) + \frac{3}{2} O_2(g) \rightarrow SO_3(g) + 2x \, \text{kcal} $$ $$ SO_2(g) + \frac{1}{2} O_2(g) \rightarrow SO_3(g) + y \, \text{kcal} $$ 
Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + 7\hat{j} + 3\hat{k}$.
Let $$ L_1 : \vec{r} = (-\hat{i} + 2\hat{j} + \hat{k}) + \lambda \vec{a}, \quad \lambda \in \mathbb{R} $$ and $$ L_2 : \vec{r} = (\hat{j} + \hat{k}) + \mu \vec{b}, \quad \mu \in \mathbb{R} $$ be two lines. If the line $L_3$ passes through the point of intersection of $L_1$ and $L_2$, and is parallel to $\vec{a} + \vec{b}$, then $L_3$ passes through the point:
For the reaction, $$ H_2(g) + I_2(g) \rightleftharpoons 2HI(g) $$ Attainment of equilibrium is predicted correctly by: 
If the equation of the parabola with vertex $\left( \frac{3}{2}, 3 \right)$ and the directrix $x + 2y = 0$ is $$ ax^2 + by^2 - cxy - 30x - 60y + 225 = 0, \text{ then } \alpha + \beta + \gamma \text{ is equal to:} $$
If the square of the shortest distance between the lines $$ \frac{x-2}{1} = \frac{y-1}{2} = \frac{z+3}{-3} \quad \text{and} \quad \frac{x+1}{2} = \frac{y+3}{4} = \frac{z+5}{-5}, $$ is $ \frac{m}{n} $, where $m, n$ are coprime numbers, then $m+n$ is equal to:

A body of mass $100 \;g$ is moving in a circular path of radius $2\; m$ on a vertical plane as shown in the figure. The velocity of the body at point A is $10 m/s.$ The ratio of its kinetic energies at point B and C is: (Take acceleration due to gravity as $10 m/s^2$)

A body of mass 100 g is moving in a circular