List of top Questions asked in JEE Main

If the system of equations \[ x + 2y - 3z = 2 \] \[ 2x + \lambda y + 5z = 5 \] \[ 4x + 3y + \mu z = 33 \] has infinite solutions, then \( \lambda + \mu \) is equal to
When ethane-1,2-diamine is progressively added to aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be:
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
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?
Given that the arithmetic mean \( S_{12} = 57 \), \( S_{40} = 1030 \), find \( S_{30} - S_{10} \)?
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?
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):
\[ \text{S(s)} + \text{O}_2 \text{(g)} \to \text{SO}_2 \text{(g)} \]
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?
By using relation \( \Delta G = \Delta H - T \Delta S \), which of the following is incorrect for a spontaneous reaction at a given temperature?
If a square is divided into \( 4 \times 4 \) squares. If two squares are chosen randomly, then the probability that the squares don't share a common side is:
There are 5 boys and 4 girls. The sum of the number of ways to sit them such that all boys sit together and the number of ways such that no boys sit together is equal to:
Find the variance of the numbers 8, 21, 34, ..., 320.
81 g of Al reacts with 128 g of \( O_2 \). Calculate the amount of \( Al_2O_3 \) produced.
Find the wavelength in (nm) of incident radiation where the work function is 4.12 eV and the stopping potential is 4V. Given that \( h \nu = 1242 \, \text{eV} \cdot \text{nm} \).
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 value of \( E_0 \) is 9.3 V/m and \( c \) is \( 3 \times 10^8 \, \text{m/s} \). Find the value of \( B_0 \).
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 \[ A_{11} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \quad A_{14} = \begin{bmatrix} 4 & 1 \\ 3 & 0 \end{bmatrix}, \quad A_{21} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \quad A_{23} = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}, \quad \text{find} \, a_{23}. \]