List of top Questions asked in JEE Main

For the reaction given below at 25°C: \[ \text{A}_2 \rightleftharpoons 2\text{A} \] Find \( K_p \). Given \( \Delta G^\circ_A = -50.384 \, \text{kJ/mol} \) and \( \Delta G^\circ_{A_2} = -100 \, \text{kJ/mol} \).
Statement-I: Sucrose is dextrorotatory and upon hydrolysis, it becomes laevorotatory. Statement-II: Sucrose on hydrolysis gives glucose and fructose such that the laevorotation of glucose is more than dextrorotation of fructose. Which of the following is correct?
Which of the following statement is correct regarding the nature and directive influence of \( \text{NO}_2 \) group in nitrobenzene?
Bohr’s radius of H-atom is \( 2.12 \times 10^{-10} \) m. Calculate the energy of electron at this level.
Which of the following statement is correct regarding an element having atomic number 79?
Sodium extract of organic compound of 0.1 g is treated with chlorine water and \( \text{CCl}_4 \) which dissolves in organic solvent to produce a violet colour. Upon treatment with \( \text{AgNO}_3 \), a yellow ppt. of 0.12 g is produced. Calculate the percentage of halide in the organic compound.
The number of values of \( x \) satisfying \( \tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6} \) and \( x<\left[ \frac{-1}{2\sqrt{6}} , \frac{1}{2\sqrt{6}} \right] \) is:
The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{1}{\left\lfloor x \right\rfloor + 4} \, dx \] where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function, is:
If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5\beta}}{2} \] then the value of \( (\alpha + \beta) \) is:
If \[ \int \left( \cos x \right)^{-\frac{5}{2}} \left( \sin x \right)^{-\frac{1}{2}} \, dx \] \[ = \frac{P_1}{q_1} \left( \cot x \right)^{\frac{3}{2}} + \frac{P_2}{q_2} \left( \cot x \right)^{\frac{3}{2}} + \frac{P_3}{q_3} \left( \cot x \right)^{\frac{1}{2}} + \frac{P_4}{q_4} \left( \cot x \right)^{-\frac{3}{2}} + c \] (where \( c \) is the constant of integration), then value of \[ \frac{15P_1P_2P_3P_4}{q_1q_2q_3q_4} \] is:
If the image of the point \( P(3, 2, a) \) reflected about the line \[ \frac{x-3}{2} = \frac{y-5}{5} = \frac{z-2}{-2} \] is \( (5, b, c) \), then the value of \( \sigma^2 + b^2 + c^2 \) is:
If \[ A = \begin{pmatrix} 2 & 3 \\ 3 & 5 \end{pmatrix} \] then the value of \[ |A^{2025} - 3A^{2024} + A^{2023}| \] is:
If the area of the region \( \{ (x, y) : x^2 + 1 \leq y \leq 3 - x \} \) is divided by the line \( x = -1 \) in the ratio \( m : n \) (where \( m \) and \( n \) are coprime natural numbers), then the value of \( m + n \) is:

All are cylindrical rods having radius of cross-section $R$ and mass of each rod $\dfrac{M}{4}$. Find the moment of inertia about $yy'$ axis:

$A$ and $B$ are identical point masses. $A$ is released as shown in the diagram at an angle $60^\circ$ from the vertical. Find $R$ if $B$ is able to reach point $C$ after elastic impact. 

Among the given options choose the correct energy of transition:

Masses $m$ and $2m$ are connected by a massless rod of length $d$. If angular momentum about an axis passing through centre of mass and perpendicular to the rod is $L$, then the angular speed $(\omega)$ of the system is:

A screw gauge has a least count of $0.01$ mm. Using this screw gauge a measurement was done. When nothing was present in the jaw, zero of circular scale was above reference line by $3$ units. When a sphere was kept between the jaws, main scale reads $1$ mm and $51^{\text{st}$ division of circular scale coincides with reference line. Find the actual diameter of the ball:}

The stress v/s strain graph of a material is as shown. Find the Young's modulus of the material. 

A set of measurements of a certain parameter is: $20.00,\; 19.75,\; 18.25,\; 17.01$. Find the relative error for the set of measurements.
Figure beside represents strain versus stress graph for four materials $A, B, C$ and $D$. Which material has maximum Young's modulus?
Find de-Broglie wavelength of an oxygen molecule at $27^\circ$C. Molar mass of oxygen molecule is $32$ g/mole.
A projectile is projected with speed $v$ at an angle $60^\circ$ with the horizontal. Find the ratio of the difference of kinetic energies at point $C$ (at ground) and point $B$ (at highest point) with the kinetic energy at point $C$ as shown in the diagram:
Find the area bounded by \( y = \max \{ \sin x, \cos x \} \) when \( x \in \left[ 0, \frac{3\pi}{2} \right] \) with the x-axis:
If \[ \begin{vmatrix} 0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} = \begin{vmatrix} 1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} \] then the value of \( \cos^2 \alpha + \cos^3 \beta + \cos^2 \gamma \) is: