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)

Two light waves having the same wavelength $$\lambda $$ in vacuum are in phase initially. Then the first wave travels a path L₁ through a medium of refractive index n₁ while the second wave travels a path of length L₂ through a medium of refractive index n₂ . After this the phase difference between the two waves 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 :

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $${{dB} \over {dt}}$$ = 0.032 Ts^–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 $$ \times $$ 10^–8 $$\Omega $$m)