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JEE Mains | PYQ

The mean free path of molecules of a certain gas at STP is \( 1500d \), where \( d \) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \( 373 \, \text{K} \) is approximately:

The output from a NAND gate having inputs A and B given below will be:

A passenger sitting in a train A moving at \( 90 \, \text{km/h} \) observes another train B moving in the opposite direction for \( 8 \, \text{s} \). If the velocity of the train B is \( 54 \, \text{km/h} \), then length of train B is:

An electron is moving along the positive \( x \)-axis. If the uniform magnetic field is applied parallel to the negative \( z \)-axis, then:
A. The electron will experience magnetic force along positive \( y \)-axis
B. The electron will experience magnetic force along negative \( y \)-axis
C. The electron will not experience any force in magnetic field
D. The electron will continue to move along the positive \( x \)-axis
E. The electron will move along circular path in magnetic field
Choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : A spherical body of radius \( (5 \pm 0.1) \, \text{mm} \) having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is \( 4\% \).
Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below:

A vehicle of mass \( 200 \, \text{kg} \) is moving along a levelled curved road of radius \( 70 \, \text{m} \) with angular velocity of \( 0.2 \, \text{rad/s} \). The centripetal force acting on the vehicle is :

In a Young’s double slits experiment, the ratio of amplitude of light coming from slits is \( 2 : 1 \). The ratio of the maximum to minimum intensity in the interference pattern is :

A particle executes SHM of amplitude \( A \). The distance from the mean position when it’s kinetic energy becomes equal to its potential energy is :

Given below are two statements :
Statements I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II : Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer from the options given below :

A \( 10 \, \mu \text{C} \) charge is divided into two parts and placed at \( 1 \, \text{cm} \) distance so that the repulsive force between them is maximum. The charges of the two parts are :

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative \( z \)-axis and magnetic field is along the positive \( x \)-axis. Then the direction of propagation of electromagnetic wave is :

To radiate EM signal of wavelength \( \lambda \) with high efficiency, the antennas should have a minimum size equal to:

The distance travelled by an object in time \( t \) is given by \( s = (2.5)t^{2} \). The instantaneous speed of the object at \( t = 5 \, \text{s} \) will be:

Two planets A and B of radii \( R \) and \( 1.5R \) have densities \( \rho \) and \( \dfrac{\rho}{2} \) respectively. The ratio of acceleration due to gravity at the surface of B to A is:

In the network shown below, the charge accumulated in the capacitor in steady state will be:

Give below are two statements:
Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.
In the light of above statements, choose the correct answer from the options given below.

The initial pressure and volume of an ideal gas are \( P_{o} \) and \( V_{o} \). The final pressure of the gas when the gas is suddenly compressed to volume \( \dfrac{V_{o}}{4} \) will be: (Given \( \gamma \) = ratio of specific heats at constant pressure and at constant volume)

In the equation \( \left[ X + \dfrac{a}{y^2} \right]\left[ Y - b \right] = RT \), \( X \) is pressure, \( Y \) is volume, \( R \) is universal gas constant and \( T \) is temperature. The physical quantity equivalent to the ratio \( \dfrac{a}{b} \) is :

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range \( 30 \) to \( 170 \).
Reason R: Nuclear force is short ranged.
In the light of above statements, choose the correct answer from the options given below:

A biconvex lens of focal length \( 10 \, \text{cm} \) is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _________ \( \text{D} \).

An insulated copper wire of \( 100 \) turns is wrapped around a wooden cylindrical core of the cross-sectional area \( 24 \, \text{cm}^2 \). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \( 12 \, \Omega \). If an externally applied uniform magnetic field in the core along its axis changes from \( 1.5 \, \text{T} \) in one direction to \( 1.5 \, \text{T} \) in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ____________ \( \text{mC} \).

An atom absorbs a photon of wavelength \( 500 \, \text{nm} \) and emits another photon of wavelength \( 600 \, \text{nm} \). The net energy absorbed by the atom in this process is \( n \times 10^{-4} \, \text{eV} \). The value of \( n \) is ________.
[Assume the atom to be stationary during the absorption and emission process]
(Take \( h=6.6\times 10^{-34} \, \text{J s} \) and \( c=3\times 10^{8} \, \text{m/s} \).)

Three point charges \( q \), \( -2q \) and \( 2q \) are placed on x-axis at a distance \( x=0 \), \( x=\dfrac{3}{4}R \) and \( x=R \) respectively from origin as shown. If \( q=2\times 10^{-6} \, \text{C} \) and \( R=2 \, \text{cm} \), the magnitude of net force experienced by the charge \( -2q \) is __________ \( \text{N} \).

A light rope is wound around a hollow cylinder of mass \( 5 \, \text{kg} \) and radius \( 70 \, \text{cm} \). The rope is pulled with a force of \( 52.5 \, \text{N} \). The angular acceleration of the cylinder will be __________ \( \text{rad s}^{-2} \).

A car accelerates from rest to \( u \, \text{m /s} \). The energy spent in this process is \( E \, \text{J} \). The energy required to accelerate the car from \( u \, \text{m /s} \) to \( 2u \, \text{m /s}\) is in \( E \, \text{J} \). The value of \( n \) is __________.

A straight wire \( AB \) of mass \( 40 \, \text{g} \) and length \( 50 \, \text{cm} \) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \( 0.40 \, \text{T} \) as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is __________ \( \text{A} \). \( \text{(Take } g = 10 \, \text{m s}^{-2} \text{)} \).

In an experiment with sonometer when a mass of \( 180 \, \text{g} \) is attached to the string, it vibrates with fundamental frequency of \( 30 \, \text{Hz} \). When a mass \( m \) is attached, the string vibrates with fundamental frequency of \( 50 \, \text{Hz} \). The value of \( m \) is __________ \( \text{g} \).

In the circuit shown, the energy stored in the capacitor is \( n \, \mu \text{J} \). The value of \( n \) is __________.

Two plates \( A \) and \( B \) have thermal conductivities \( 84 \, \text{W m}^{-1} \text{K}^{-1} \) and \( 126 \, \text{W m}^{-1} \text{K}^{-1} \) respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of \( A \) and \( B \) are kept at \( 100^{\circ}\text{C} \) and \( 0^{\circ}\text{C} \) respectively, then the temperature of the surface of contact in steady state is ________ \( ^{\circ}\text{C} \).