Which of the following transitions in hydrogen atom emit photons of highest frequency? ( $\mathrm{n}=$ principle quantum number)

Two radioactive materials $A$ and $B$ having decay constant ' $7 \lambda$ ' and ' $\lambda$ ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is

The ratio of angular momentum of an electron in $\mathrm{n}^{\text {th }}$ orbit of hydrogen atom to the velocity of electron in $\mathrm{n}^{\text {th }}$ orbit is proportional to

In hydrogen atom spectrum, when an electron jumps from second excited state to the first excited state, the wavelength of radiation emitted is ' $\lambda$ '. If the electron jumps from the third excited state to the second orbit, the wavelength of radiation emitted will be $\frac{20 \lambda}{x}$. The value of $x$ is