To raise the temperature of a certain mass of gas by 50^oC at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100^oC at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

Concentric metallic hollow spheres of radii R and 4R hold charges Q₁ and Q₂ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :

A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $$\overrightarrow B $$ . Then the field inside the paramagnetic substance is :

The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is
$$\overrightarrow E = {E_0}\widehat j\cos \left( {\omega t - kx} \right)$$.
The magnetic field $$\overrightarrow B $$ , at the moment t = 0 is :