The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :-

In a conductor, if the number of conduction electrons per unit volume is 8.5 × 10²⁸ m^–3 and mean free time is 25ƒs (femto second), it's approximate resistivity is :-
(m_e = 9.1 × 10^–31 kg)

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :-