List of top Questions asked in JEE Main

The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet color in non-luminous flame under hot condition in borax bead test is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below.

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 \[ \frac{x^2}{2} + \frac{y^2}{4} = 1. \]