Which of the following series of transitions in the spectrum of hydrogen atom falls in the visible region?

The frequency of a certain line of the Lyman series of the atomic spectrum of the $H$ atom satisfies the following conditions:
$(i)$ It is the sum of the frequency of another Lyman line and a Balmer line.
$(ii)$ It is the sum of the frequency of a certain line,a Lyman line,and a Paschen line.
$(iii)$ It is the sum of the frequency of a Lyman and a Paschen line but no Brackett line.
To what transition does this frequency correspond?

If the wave number of radiation emitted for the electron transition from an excited state $n_2$ to the first excited state $(n_1 = 2)$ of a hydrogen atom is $\frac{5x}{36} \ m^{-1}$, the wave number of radiation absorbed for the electron transition from the same excited state $n_2$ to the next immediate higher excited state $(n_3 = n_2 + 1)$ in $m^{-1}$ is:

$A$ surface ejects electrons when hit by green light but not when hit by yellow light. Will electrons be ejected if the surface is hit by red light?

Based on equation $E = -2.178 \times 10^{-18} \ J \ \frac{Z^2}{n^2}$,certain conclusions are written. Which of them is not correct?

The velocity of an electron in the $3^{rd}$ excited state of $Be^{3+}$ is .......