According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

A conducting metal circular-wire-loop of radius \(r\) is placed perpendicular to a magnetic field which varies with time as \(B = {B_0}{e^{\frac{{ - t}}{\tau }}}\) , where \(B_0\) and \(\tau \) are constants, at time \(t = 0\). If the resistance of the loop is \(R\) then the heat generated in the loop after a long time \(\left( {t \to \infty } \right)\) is

In Young's double slit experiment the two slits are \(0.6 \; mm\) distance apart. Interference pattern is observed on a screen at a distance \(80 \; cm\) from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be \(\dots \; nm .\)

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be \(\dots \;\)%

For extrinsic semiconductors; when doping level is increased;

The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is

In a hydrogen atom the electron makes a transition from \(( n +1)^{\text {th }}\) level to the \(n ^{\text {th }}\) level. If \(n>>1,\) the frequency of radiation emitted is proportional to

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are \(0.1 \;kg - m ^{2}\) and \(10\; rad \,s^{-1}\) respectively while those for the second one are \(0.2 \;kg - m ^{2}\) and \(5\; rad \,s ^{-1}\) respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is ...........\(J\)

A moving coil galvanometer allows a full scale current of \(10^{-4}\, A\). A series resistance of \(2\, M\,\Omega \) is required to convert the above galvanometer into a voltmeter of range \(0 -5\, V\). Therefore the value of shunt resistance required to convert the above galvanometer into a ammeter of range \(0-10\, mA\) is....\(\Omega \)

The electric current through a wire varies with time as \(I=I_0+\beta t\). where \(I_0=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed. Reason \(R:\) A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. In the light of the above statements, choose the most appropriate answer from the options given below