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

When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column, and the temperature remains constant while surface tension is neglected, what is the depth of the lake (in $m$)?

Which one of the following reactions does not form a gaseous product?

Four charges are placed at the circumference of a dial clock as shown in the figure. If the clock has only an hour hand, then the resultant force on a charge $q_0$ placed at the center points in the direction which shows the time as: (in $.30$)

The distance between the lines represented by $4x^2 + 20xy + 25y^2 + 2x + 5y - 12 = 0$ is equal to

Three rings,each having equal radius $R$,are placed mutually perpendicular to each other and each having its centre at the origin of the coordinate system. If current $I$ is flowing through each ring,then the magnitude of the magnetic field at the common centre is