A current $$I=10 \sin (100 \pi t)$$ ampere, is passed in a coil which induces a maximum emf $$5 \pi$$ volt in neighbouring coil. The mutual inductance of two coils is

The average density of the earth is [g is acceleration due to gravity]

Two bar magnets '$$\mathrm{P}$$' and '$$\mathrm{Q}$$' are kept in uniform magnetic field '$$\mathrm{B}$$' with magnetic moments '$$\mathrm{M_P}$$' and '$$\mathrm{M_Q}$$' respectively. Magnet 'P' is oscillating with frequency twice that of magnet 'Q'. If the moment of inertia of the magnet 'P' is twice that of magnet 'Q' then

Which one of the following is NOT a correct expression for an ideal gas?

[$$\mathrm{C_p}=$$ Molar specific heat of a gas at constant pressure,

$$\mathrm{C_v}=$$ Molar specific heat of a gas at constant volume,

$$\mathrm{Y}=$$ Ratio of two specific heats of a gas,

$$\mathrm{R}=$$ Universal gas constant]