$A$ particle moving with a uniform acceleration travels $24 \,m$ and $64 \,m$ in the first two consecutive intervals of $4 \,sec$ each. Its initial velocity is............$m/sec$.

If $\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=f(x)-\log \left(1+x^2\right)$ then $f(x)$ is equal to

Which of the following is an essential amino acid?

If $u=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)$,then the value of $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is

What is the $IUPAC$ name of the following compound?

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