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 calorimeter of water equivalent 20 g contains 180 g of water at 25^oC. ‘m’ grams of steam at 100^oC is mixed in it till the temperature of the mixure is 31^oC. The value of ‘m’ is close to :
(Latent heat of water = 540 cal g^–1, specific heat of water = 1 cal g^{–1 o}C^–1)

An massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $${N \over {20}}$$ ma² where N is an integer. The value of N 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 :