List of top Questions asked in JEE Main

The equation of chord of the ellipse \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \) with (3, 1) as mid-point is

The conditions and consequences that favour the \( t_{2g}^6 e_g^1 \) configuration in a metal complex are

A solid sphere rolls without slipping on a horizontal plane. What is the ratio of translational kinetic energy to the rotational kinetic energy of the sphere?

A solid sphere and hollow sphere roll down purely equal distances on the same inclined plane (starting from rest) in time \( t_1 \) and \( t_2 \). Then

If \( 7 = 5 + \frac{1}{7}(5 + \alpha) + \frac{1}{7^2}(5 + 2\alpha) + \cdots \infty \text{ terms}, \) then \( \alpha \) is equal to

The temperature in a city is measured to be 30°C. What is the corresponding temperature in Fahrenheit?

Sulfur undergoes oxidation to form sulfur trioxide (SO$_3$) and sulfur dioxide (SO$_2$) in the following reactions:
1. \( \text{S} + \text{O}_2 \to \text{SO}_2 \)
2. \( 2\text{SO}_2 + \text{O}_2 \to 2\text{SO}_3 \)
Given that sulfur (S) is oxidized to SO$_2$, and SO$_2$ is further oxidized to SO$_3$, calculate the change in oxidation states of sulfur in both reactions.

In Young's Double Slit Experiment, monochromatic light of wavelength \( \lambda \) is used. The slits are separated by a distance \( d \), and the screen is placed at a distance \( D \) from the slits. If the fringe width is observed to be \( \beta \), and the distance between the slits and the screen is doubled, what will be the new fringe width?

Two charges +7 mC and -4 mC at coordinates (-7, 0, 0) and (7, 0, 0), respectively, find the electrostatic potential energy. \[ \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2}. \]

The system of equations: \[ x + y + z = 6, \quad x + 2y + 5z = 9, \quad x + 5y + \lambda z = \mu, \] has no solution if:

Given the matrix \[ A = (a_{ij}), \] where \[ A_{11} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \quad A_{14} = \begin{bmatrix} 4 & 1 \\ 3 & 0 \end{bmatrix}, \quad A_{21} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \quad A_{23} = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}, \quad \text{find} \, a_{23}. \]

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:

Find the charge on the capacitor in the steady state. \vspace{1cm} \includegraphics[width=0.7\textwidth]{a.png}

Find the area bounded between two curves: \[ x^2 + y^2 = 25 \quad \text{and} \quad y = |x - 1|. \]

If \[ (7 + e^{2x}) dy - (1 + 2e^{2x})(y + 3) dx = 0, \quad y(0) = 5, \] then \( y(n2) = \)?