The peculiarity of sponges is

Let $f(x)=e^x$,$g(x)=\sin ^{-1} x$ and $h(x)=f(g(x))$,then $\frac{h^{\prime}(x)}{h(x)}$ is equal to

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2 = 8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$,then the locus of $P$ is:

$A$ vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300 \ K$. The ratio of the average rotational kinetic energy per $O_2$ molecule to that per $N_2$ molecule is

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is