Two bodies are projected from ground with same speeds $40 \mathrm{~ms}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is $\mathrm{m}$. (Given $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

The displacement equations of two interfering waves are given by

$y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega t+\sqrt{3} \cos \omega t] \mathrm{cm}$ respectively.

The amplitude of the resultant wave is _______ $\mathrm{cm}$.

For the given circuit, in the steady state, $\left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|=$ ________ V.

Two discs of same mass and different radii are made of different materials such that their thicknesses are $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$ respectively. The densities of materials are in the ratio $3: 5$. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$. The value of $x$ is ________.