A body of mass 'm' is launched up on a rough inclined plane making an angle of 30$$^\circ$$ with the horizontal. The coefficient of friction between the body and plane is $${{\sqrt x } \over 5}$$ if the time of ascent is half of the time of descent. The value of x is __________.

In the given figure switches S₁ and S₂ are in open condition. The resistance across ab when the switches S₁ and S₂ are closed is _____________ $$\Omega$$.

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 __________ $$\Omega$$.