A wire of length $L,$ area of cross-section $A,$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young’s modulus is:

A ray is incident at an angle of incidence $i$ on one surface of a small-angle prism (with angle of prism $A$) and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$, then the angle of incidence is nearly equal to:

Two cylinders $A$ and $B$ of equal capacity are connected to each other via a stopcock. $A$ contains an ideal gas at standard temperature and pressure. $B$ is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. The process is:

An iron rod of susceptibility $599$ is subjected to a magnetizing field of $1200$ A/m. The permeability of the material of the rod is:$\quad (\mu_0 = 4\pi \times 10^{-7}$

The energy equivalent of $0.5$ g of a substance is:

A $40 \mu$F capacitor is connected to a $200$ V, $50$ Hz AC supply. The rms value of the current in the circuit is, nearly:

The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is: $(c =$speed of electromagnetic waves$)$

Two particles of mass $5$ kg and $10$ kg respectively are attached to the two ends of a rigid rod of length $1$ m with negligible mass. The center of mass of the system from the $5$ kg particle is nearly at a distance of:

A resistance wire connected in the left gap of a metre bridge balances a $10 \Omega$ resistance in the right gap at a point which divides the bridge wire in the ratio $3:2.$ If the length of the resistance wire is $1.5$ m, then the length of $1 \Omega$ of the resistance wire is:

In Young’s double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes:

A charged particle having drift velocity of $7.5 \times 10^{-4}$ m/s in an electric field of $3 \times 10^{-10}$ V/m, has a mobility in $$

A cylinder contains hydrogen gas at pressure of $249$ kPa and temperature $278 K.$ Its density is $(R = 8.3$ J mol$^{-1}$

Dimensions of stress are:

For which one of the following, Bohr model is not valid?

A series LCR circuit is connected to an AC voltage source. When L is removed from the circuit, the phase difference between current and voltage is $\frac{\pi}{3}.$ If instead C is removed from the circuit, the phase difference is again $\frac{\pi}{3}$

A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h.$ The mass of the water in the capillary is $5$ g. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is:

Assume that light of wavelength $600$ nm is coming from a star. The limit of resolution of a telescope whose objective has a diameter of $2$ m is:

The solids which have the negative temperature coefficient of resistance are:

The capacitance of a parallel plate capacitor with air as medium is $6 \mu F.$ With the introduction of a dielectric medium, the capacitance becomes $30 \mu F.$ The permittivity of the medium is:$\quad (\epsilon_0 = 8.85 \times 10^{-12}$

The energy required to break one bond in DNA is $10^{-20}$ J$.$ This value in eV is nearly:

The increase in the width of the depletion region in a p-n junction diode is due to:

The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_1$ and $r_2$ ($r_1 = 1.5 r_2$

Light with an average flux of $20$ W/cm$^2$ falls on a non-reflecting surface at normal incidence having surface area $20$ cm$^2.$ The energy received by the surface during a time span of 1 minute is:

For the logic circuit shown, the truth table is:

For transistor action, which of the following statements is correct?

In a guitar, two strings A and B made of the same material are slightly out of tune and produce beats of frequency $6$ Hz. When tension in B is slightly decreased, the beat frequency increases to $7$ Hz. If the frequency of A is $530$ Hz, the original frequency of B will be:

A short electric dipole has a dipole moment of $16 \times 10^{-9}$ C m. The electric potential due to the dipole at a point at a distance of $0.6$ m from the centre of the dipole, situated on a line making an angle of $60^{\circ}$

A body weighs $72$ N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

Which of the following graphs represents the variation of resistivity $(\rho)$ with temperature $(T)$ for copper?

In a certain region of space with volume $0.2$ m$^3,$ the electric potential is found to be $5$ V throughout. The magnitude of electric field in this region is:

The average thermal energy for a mono-atomic gas is:$\newline (k_B$ is Boltzmann constant and $T,$ absolute temperature$)$

Find the torque about the origin when a force of $3\hat{j}$ N acts on a particle whose position vector is $2\hat{k}$ m.

Light of frequency $1.5$ times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and intensity is doubled?

Two bodies of mass $4$ kg and $6$ kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is:

A long solenoid of $50$ cm length having $100$ turns carries a current of $2.5$ A. The magnetic field at the centre of the solenoid is:$\newline (\mu_0 = 4\pi \times 10^{-7}$

The Brewster’s angle $i_b$ for an interface should be:

An electron is accelerated from rest through a potential difference of $V$ volt. If the de Broglie wavelength of the electron is $1.227 \times 10^{-2}$ nm, the potential difference is:

Taking into account the significant figures, what is the value of $9.99$ m $- 0.0099$ m$?$

A screw gauge has a least count of $0.01$ mm and there are $50$ divisions on its circular scale. The pitch of the screw gauge is:

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

The mean free path for a gas, with molecular diameter $d$ and number density $n$ can be expressed as:

A ball is thrown vertically downward with a velocity of $20$ m/s from the top of a tower. It hits the ground after some time with a velocity of $80$ m/s. The height of the tower is $(g = 10$ m/s$^2):$

The color code of a resistance is given below. The values of resistance and tolerance, respectively, are:

When a uranium isotope ${}^{235}_{92}U$ is bombarded with a neutron, it generates ${}^{89}_{36}Kr$, three neutrons and:

A spherical conductor of radius $10$ cm has a charge of $3.2 \times 10^{-7}$ C distributed uniformly. What is the magnitude of the electric field at a point $15$ cm from the center of the sphere?$\newline (\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 { N m}^2{ C}^{-2})$