Two vectors $${\overrightarrow P }$$ and $${\overrightarrow Q }$$ have equal magnitudes. If the magnitude of $${\overrightarrow P + \overrightarrow Q }$$ is n times the magnitude of $${\overrightarrow P - \overrightarrow Q }$$, then angle between $${\overrightarrow P }$$ and $${\overrightarrow Q }$$ is :

Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is :

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 .................... $$\Omega$$.