The number of air molecules per cm$$^3$$ increased from $$3\times10^{19}$$ to $$12\times10^{19}$$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the centre (O) of shell can be graphically represented as -

The radius of fifth orbit of the $$\mathrm{Li}^{++}$$ is __________ $$\times 10^{-12} \mathrm{~m}$$.

Take: radius of hydrogen atom $$ = 0.51\,\mathop A\limits^o $$

Two identical solid spheres each of mass $$2 \mathrm{~kg}$$ and radii $$10 \mathrm{~cm}$$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $$40 \mathrm{~cm}$$. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is __________ $$\times 10^{-3} \mathrm{~kg}~\mathrm{m}^{2}$$