$A$ light wave has a frequency of $4 \times 10^{14} \text{ Hz}$ and a wavelength of $5 \times 10^{-7} \text{ m}$ in a medium. The refractive index of the medium is

$\sum_{k=1}^{2n+1} (-1)^{k-1} k^2$ is equal to

The motion of planets in the solar system is an example of the conservation of

The catalyst used for the polymerization of olefins is....

An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \, g/cm^3$) standing initially $20 \, cm$ from the bottom in each arm. An immiscible liquid of density $4.0 \, g/cm^3$ is added to one arm until a layer $5 \, cm$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?

In which of the following reactions is benzaldehyde formed from benzoyl chloride and hydrogen in the presence of $Pd/BaSO_4$?