When $Z$ is doubled in an atom,which of the following statements are consistent with Bohr's theory?

For the Balmer series in the spectrum of $H$ atom,$\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$,the correct statements among $(I)$ to $(IV)$ are:
$(I)$ As wavelength decreases,the lines in the series converge.
$(II)$ The integer $n_{1}$ is equal to $2$.
$(III)$ The lines of longest wavelength corresponds to $n_{2}=3$.
$(IV)$ The ionization energy of hydrogen can be calculated from wave number of these lines.

Angular momentum of an electron in the $n^{th}$ orbit of a hydrogen atom is given by

For the hydrogen emission spectrum,the energy change $E$ (in Joules) is given by $\Delta E = 2.18 \times 10^{-18} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \ J$,where $n_1 = 1, 2, 3, \dots$ and $n_2 = 2, 3, 4, \dots$. Which of the following corresponds to the Paschen series?

Which one of the following corresponds to the wavelength of a line in the Balmer series of the $H$ atom spectrum? $(R =$ Rydberg constant$)$

The Ritz combination principle states that: