Which of the following is a biodegradable polymer?

If $u=\sin ^{-1}\left(\frac{x^2+y^2}{x+y}\right)$ then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to:

The major product of the following reaction is:

If a gas is compressed isothermally,then the r.m.s. velocity of the molecules

The equation of the normal to the curve $y^4=ax^3$ at $(a, a)$ is

$A$ circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is