The ratio of specific heats of a gas is $\gamma$. The change in internal energy of one mole of the gas,when the volume changes from $V$ to $2 V$ at constant pressure $p$ is

$A$ disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$,the height to which the disc will rise will be:

Which of the following statements about the Bohr model of the hydrogen atom is false?

If $u=\sin ^{-1}\left(\frac{x^2+y^2}{x+y}\right)$ then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to:

$A$ wire of length $10 \, cm$ translates in a direction making an angle of $60^\circ$ with its length. The plane of motion is perpendicular to a uniform magnetic field of $1.0 \, T$ that exists in the space. Find the $emf$ induced between the ends of the rod if the speed of translation is $20 \, cm/s.$

When a ceiling fan is switched on,it makes $10$ rotations in the first $3 \, s$. How many rotations will it make in the next $3 \, s$ (Assume uniform angular acceleration)?