When the rms velocity of a gas is denoted by '$$v$$', which one of the following relations is true?

($$\mathrm{T}=$$ Absolute temperature of the gas.)

A parallel plate air capacitor has a uniform electric field 'E' in the space between the plates. Area of each plate is A and the distance between the plates is '$$\mathrm{d}$$'. The energy stored in the capacitor is $$\left[\varepsilon_0=\right.$$ permittivity of free space)

Two massless springs of spring constant $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ are connected one after the other forming a single chain, suspended vertically and certain mass is attached to the free end. If '$$e_1$$' and '$$e_2$$' are their respective extensions and '$$\mathrm{f}$$' is their stretching force, the total extension produced is

The time taken by a particle executing simple harmonic motion of period '$$\mathrm{T}$$', to move from the mean position to half the maximum displacement is