List of top Questions asked in JEE Main

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).

Three identical spheres of the same mass undergo one-dimensional motion as shown in the figure with initial velocities \( v_A = 5 \, \text{m/s}, v_B = 2 \, \text{m/s}, v_C = 4 \, \text{m/s} \). If we wait sufficiently long for elastic collision to happen, then \( v_A = 4 \, \text{m/s}, v_B = 2 \, \text{m/s}, v_C = 5 \, \text{m/s} \) will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. In light of the above statements, choose the correct answer from the options given below:

A capacitor, \( C_1 = 6 \, \mu F \), is charged to a potential difference of \( V_1 = 5 \, \text{V} \) using a 5V battery. The battery is removed and another capacitor, \( C_2 = 12 \, \mu F \), is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges \( q_1 \) and \( q_2 \) on the capacitors \( C_1 \) and \( C_2 \) when equilibrium condition is reached?

Three equal masses \( m \) are kept at vertices (A, B, C) of an equilateral triangle of side \( a \) in free space. At \( t = 0 \), they are given an initial velocity \( \vec{V_A} = V_0 \hat{AC}, \, \vec{V_B} = V_0 \hat{BA}, \, \vec{V_C} = V_0 \hat{CB} \).

Here, \( \hat{AC}, \hat{CB}, \hat{BA} \) are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is:

Match List-I with List-II.

Choose the correct answer from the options given below:

Match List-I with List-II.

Choose the correct answer from the options given below:

The truth table for the circuit given below is:

Choose the correct answer from the options given below:

The magnetic field inside a 200 turns solenoid of radius 10 cm is \( 2.9 \times 10^{-4} \) Tesla. If the solenoid carries a current of 0.29 A, then the length of the solenoid is:

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is \( 7 \times 10^6 \, \text{V/s} \), then the integer value of the distance between the parallel plates is:

Two planets, A and B are orbiting a common star in circular orbits of radii \( R_A \) and \( R_B \), respectively, with \( R_B = 2R_A \). The planet B is \( \sqrt{2} \) times more massive than planet A. The ratio \( \frac{L_B}{L_A} \) of angular momentum (\( L \)) of planet B to that of planet A (\( L_A \)) is closest to integer:

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time \( t = 0 \), for the first time. The maximum possible number of crossing(s) (including the crossing at \( t = 0 \)) is:

Given below are two statements:
Statement (I): In partition chromatography, the stationary phase is a thin film of liquid present in the inert support.
Statement (II): In paper chromatography, the material of paper acts as a stationary phase.
In light of the above statements, choose the correct answer from the options given below:

Given below are two statements:
Statement (I): On nitration of m-xylene with \( \text{HNO}_3 \), \( \text{H}_2\text{SO}_4 \), followed by oxidation, 4-nitrobenzene-1, 3-dicarboxylic acid is obtained as the major product.
Statement (II): CH\(_3\) group is o/p-directing while NO\(_2\) group is m-directing group.
In the light of the above statements, choose the correct answer from the options given below:

Match List-I with List-II:

Choose the correct answer from the options given below:

If \[ \text{C(diamond)} \rightarrow \text{C(graphite)} + X \, \text{kj mol}^{-1} \] \[ \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Y \, \text{kj mol}^{-1} \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Z \, \text{kj mol}^{-1} \] At constant temperature. Then:

Given below are two statements:
Statement (I): It is impossible to specify simultaneously with arbitrary precision, the linear momentum and the position of a particle.
Statement (II): If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is \( \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2m} \).
In the light of the above statements, choose the correct answer from the options given below:

Drug X becomes ineffective after 50% decomposition. The original concentration of drug in a bottle was 16 mg/mL which becomes 4 mg/mL in 12 months. The expiry time of the drug in months is ____ . Assume that the decomposition of the drug follows first order kinetics.