In fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $t$ second. The frequency of vibration of air column is
($\lambda$ = wavelength of the wave)

A sonometer wire is vibrating in third overtone. There are

A charge 'Q' C is placed at the centre of a cube. The electric flux through two opposite faces of the cube is
($\epsilon_0$ = permittivity of free space)

The capacitance of a capacitor becomes $\dfrac{7}{6}$ times the original value if dielectric slab of thickness $t = \dfrac{2d}{3}$ is introduced between the plates, where 'd' is the distance of separation between the plates. The dielectric constant of the slab is