Which series of the hydrogen spectrum was observed first?

$A$ hydrogen atom in the ground state is excited by monochromatic radiation of $\lambda = 975 \; \mathring{A}$. The number of spectral lines in the resulting emission spectrum will be:

The shortest wavelength for the Lyman series is $912 \ \text{Å}$. The longest wavelength in the Paschen series is: (in $\text{Å}$)

The first member of the Balmer series of a hydrogen atom has a wavelength of $6561 \; \mathring{A}$. The wavelength of the second member of the Balmer series (in $nm$) is

The maximum number of emission lines for atomic hydrogen that you would expect to see with the naked eye if the only electronic levels involved are those shown in the figure,is

The frequencies for the series limit of the Balmer and Paschen series are $v_1$ and $v_3$ respectively. If the frequency of the first line of the Balmer series is $v_2$,then the relation between $v_1, v_2,$ and $v_3$ is: