If $$x=a(t+\sin t), y=a(1-\cos t)$$, then $$\frac{d y}{d x}=$$

A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

In the arrangement of the capacitors as shown in figure, each capacitor is of 6 $$\mu$$F, then equivalent capacity between points A and B is

The relation obeyed by a perfect gas during an adiabatic process is $$\mathrm{PV}^{3 / 2}$$. The initial temperature of the gas is '$$\mathrm{T}$$'. When the gas is compressed to half of its Initial volume, the final temperature of the gas is