A body starts falling freely from height $$H$$ hits an inclined plane in its path at height $$h$$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $$\frac{H}{h}$$ for which the body will take the maximum time to reach the ground is __________.

A particle performs simple harmonic motion with amplitude $$A$$. Its speed is increased to three times at an instant when its displacement is $$\frac{2 A}{3}$$. The new amplitude of motion is $$\frac{n A}{3}$$. The value of $$n$$ is ___________.

The mass defect in a particular reaction is $$0.4 \mathrm{~g}$$. The amount of energy liberated is $$n \times 10^7 \mathrm{~kWh}$$, where $$n=$$ __________. (speed of light $$\left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$$

A small square loop of wire of side $$l$$ is placed inside a large square loop of wire of side $$L\left(L=l^2\right)$$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $$\sqrt{x} \times 10^{-7} \mathrm{H}$$, where $$x=$$ _________.