A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. Which of the following series of wave lengths will be emitted?

For  the given energy, 

Excitation of electron happens to the nth orbit. 

$13.6-12.5=\frac{13.6}{{\mathrm{n}}^2}$

$\Rightarrow \mathrm{n}=3$

From this we can say that the electron bean excited the electron in H atom from n = 1 to n = 3. During de-excitation the number of transitions possible is:
                                  - From n = 3 to n = 1 (Lyman series)
                                 - From n = 2 to n = 1 (Lyman series)
                                 - From n = 3 to n = 2 (Balmer series)