The magnetic susceptibility of a material of a rod is 499. Permeability in vacuum is 4$$\pi$$ $$\times$$ 10^$$-$$7 H/m. Absolute permeability of the material of the rod is :

A zener diode having zener voltage 8 V and power dissipation rating of 0.5 W is connected across a potential divider arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance R_p is .................... $$\Omega$$.

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 _____________ $$\Omega$$.