List of top Questions asked in JEE Main

If \( A \) and \( B \) are binomial coefficients of the 30\(^\text{th}\) and 12\(^\text{th}\) terms of the binomial expansion \( (1 + x)^{2n-1} \), and \( 2A = 5B \), then the value of \( n \) is

Consider the following reaction:
\[ \text{S(s)} + \frac{3}{2} \text{O}_2 \text{(g)} \to \text{SO}_3 \text{(g)} + 2x \text{ K} \] \[ \text{SO}_2 \text{(g)} + \frac{1}{2} \text{O}_2 \text{(g)} \to \text{SO}_3 \text{(g)} + y \text{ K} \] Calculate \( \Delta H \) for the following reaction (K):
\[ \text{S(s)} + \text{O}_2 \text{(g)} \to \text{SO}_2 \text{(g)} \]

There is a group A of 5 boys and 3 girls and another group B of 5 boys and 6 girls. How many ways can we invite 4 boys and 4 girls for a party with 5 from group A and 3 from group B?

If the acceleration due to gravity on the surface of Earth is \( g \), then the acceleration due to gravity on a planet whose diameter is \( \frac{1}{3} \) of that of Earth and same mass as that of Earth is \( g' = ng \), where \( n \) is

When ethane-1,2-diamine is progressively added to aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be:

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

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?

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

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

Given that the arithmetic mean \( S_{12} = 57 \), \( S_{40} = 1030 \), find \( S_{30} - S_{10} \)?

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.

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

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

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

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

Find the length of the chord whose midpoint is \( \left( \frac{3}{2}, 0 \right) \) of the ellipse \[ \frac{x^2}{2} + \frac{y^2}{4} = 1. \]