Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $${{\sqrt x } \over 2}$$. Then, the value of x is _____________.

For the forward biased diode characteristics shown in the figure, the dynamic resistance at I_D = 3 mA will be __________ $$\Omega$$.

A series LCR circuit of R = 5$$\Omega$$, L = 20 mH and C = 0.5 $$\mu$$F is connected across an AC supply of 250 V, having variable frequency. The power dissipated at resonance condition is ______________ $$\times$$ 10² W.

One mole of an ideal gas at 27$$^\circ$$ is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be _________ $$\times$$ 10^$$-$$1 J. [Given : R = 8.3 J/mole K, ln2 = 0.6931] (Round off to the nearest integer)