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Physics

Match List-I with List-II

Choose the correct answer from the options given below:

Electromagnetic waves travel in a medium with speed of \( 1.5 \times 10^{8} \, \text{m s}^{-1} \). The relative permeability of the medium is \( 2.0 \). The relative permittivity will be:

A bullet of mass \( 50 \, \text{g} \) is fired with a speed \( 100 \, \text{m/s} \) on a plywood and emerges with \( 40 \, \text{m/s} \). The percentage loss of kinetic energy is:

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \( 1 \, \text{mm} \) and circular scale reading is equal to \( 42 \) divisions. Pitch of screw gauge is \( 1 \, \text{mm} \) and it has \( 100 \) divisions on circular scale. The diameter of the wire is \( \dfrac{x}{50} \, \text{mm} \). The value of \( x \) is:

A small ball of mass \( m \) and density \( \rho \) is dropped in a viscous liquid of density \( \rho_{0} \). After sometime, the ball falls with constant velocity. The viscous force on the ball is:

\( \sigma \) is the uniform surface charge density of a thin spherical shell of radius \( R \). The electric field at any point on the surface of the spherical shell is:

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample is:

In photoelectric experiment energy of \( 2.48 \, \text{eV} \) irradiates a photo sensitive material. The stopping potential was measured to be \( 0.5 \, \text{V} \). Work function of the photo sensitive material is:

A light string passing over a smooth light pulley connects two blocks of masses \( m_{1} \) and \( m_{2} \) (where \( m_{2} > m_{1} \)). If the acceleration of the system is \( \frac{g}{\sqrt{2}} \), then the ratio of the masses \( \frac{m_{1}}{m_{2}} \) is:

Given below are two statements:
Statement I: In an LCR series circuit, current is maximum at resonance.
Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.
In the light of the above statements, choose the correct from the options given below:

The specific heat at constant pressure of a real gas obeying \( PV^{2}=RT \) equation is:

Which of the following phenomena does not explain by wave nature of light.
A. reflection
B. diffraction
C. photoelectric effect
D. polarization
Choose the most appropriate answer from the options given below:

To project a body of mass \( m \) from earth’s surface to infinity, the required kinetic energy is (assume, the radius of earth is \( R_E \), \( g \) = acceleration due to gravity on the surface of earth):

The value of unknown resistance \( (x) \) for which the potential difference between \( B \) and \( D \) will be zero in the arrangement shown, is:

The correct truth table for the following logic circuit is:

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is:

Four particles \( A, B, C, D \) of mass \( \dfrac{m}{2}, m, 2m, 4m \), have same momentum, respectively. The particle with maximum kinetic energy is:

An element \( \Delta l = \Delta x \, \hat{i} \) is placed at the origin and carries a large current \( I = 10 \, \text{A} \). The magnetic field on the \( y \)-axis at a distance of \( 0.5 \, \text{m} \) from the elements \( \Delta x \) of \( 1 \, \text{cm} \) length is:

A train starting from rest first accelerates uniformly up to a speed of \( 80 \, \text{km/h} \) for time \( t \), then it moves with a constant speed for time \( 3t \). The average speed for the train for the duration of journey will be (in \( \text{km/h} \)):

To find the spring constant \((k) \) of a spring experimentally, a student commits \( 2\% \) positive error in the measurement of time and \( 1\% \) negative error in measurement of mass. The percentage error in determining value of \( k \) is:

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _________ hours \( 30 \) minutes.

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point \( P \) is \( \dfrac{x \sigma}{\varepsilon_0} \). The value of \( x \) is _____ (all quantities are measured in SI units).

A big drop is formed by coalescing \( 1000 \) small droplets of water. The ratio of surface energy of \( 1000 \) droplets to that of energy of big drop is \( \dfrac{10}{x} \). The value of \( x \) is __________.

A particle is doing simple harmonic motion of amplitude \( 0.06 \, \text{m} \) and time period \( 3.14 \, \text{s} \). The maximum velocity of the particle is ______ cm/s.

For three vectors \( \vec{A} = (-x\hat{i} - 6\hat{j} - 2\hat{k}) \), \( \vec{B} = (-\hat{i} + 4\hat{j} + 3\hat{k}) \) and \( \vec{C} = (-8\hat{i} - \hat{j} + 3\hat{k}) \), if \( \vec{A}\cdot(\vec{B}\times\vec{C}) = 0 \), then value of \( x \) is ________.

Radius of a certain orbit of hydrogen atom is 8.48 Å . If energy of electron in this orbit is \( \frac{E}{x} \). then \( x = \) ________.
$(\text{Given } a_0 = 0.529\text{Å}, E = \text{energy of electron in ground state}).$

When a dc voltage of \( 100\,\text{V} \) is applied to an inductor a dc current of \( 5\,\text{A} \) flows through it. When an ac voltage of \( 200\,\text{V} \) peak value is connected to inductor, its inductive reactance is found to be \( 20\sqrt{3}\,\Omega \). The power dissipated in the circuit is ________ \( \text{W} \).

A circular coil having \( 200 \) turns, \( 2.5 \times 10^{-4}\, \text{m}^{2} \) area and carrying \( 100\,\mu\text{A} \) current is placed in a uniform magnetic field of \( 1\,\text{T} \). Initially the magnetic dipole moment \( (\vec{M}) \) was directed along \( \vec{B} \). Amount of work, required to rotate the coil through \( 90^\circ \) from its initial orientation such that \( \vec{M} \) becomes perpendicular to \( \vec{B} \) is ________ \( \mu \text{J} \).

A wire of resistance \( R \) and radius \( r \) is stretched till its radius became \( \frac{r}{2} \). If new resistance of the stretched wire is \( xR \), then value of \( x \) is ________.

The refractive index of prism is \( \mu = \sqrt{3} \) and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is ________.

JEE Main 2024 6th April Morning Shift

Mathematics Physics Chemistry

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A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample is: