A charge $\mathrm{Q} \mu \mathrm{C}$ is placed at the centre of a cube. The flux through two opposite faces of the cube is ( $\varepsilon_0=$ permittivity of free space)

The lengths of the two organ pipes open at both ends are ' L ' and $\left(\mathrm{L}+\mathrm{L}_1\right)$. If they are sounded together, the beat frequency will be ( $\mathrm{v}=$ velocity of sound in air)

Black bodies A and B radiate maximum energy with wavelength difference $4 \mu \mathrm{~m}$. The absolute temperature of body A is 3 times that of B. The wavelength at which body $B$ radiates maximum energy is

A monoatomic ideal gas, initially at temperature $\mathrm{T}_1$ is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature $\mathrm{T}_2$. If $\mathrm{L}_1$ and $\mathrm{L}_2$ are the lengths of the gas columns before and after expansion respectively, then $\left(T_2 / T_1\right)$ is given by