A 12.5 eV electron beam is used to bombard gaseous hydrogen at room...

If we assume electron in hydrogen atom takes energy $12.09 \mathrm{eV}$ from the incoming radiation, the maximum excited state of electron will be $n=3$. So, number of spectral lines is $\frac{3(3-1)}{2}=3$.
Here we assume some part of energy $12.5 \mathrm{eV}-12.09 \mathrm{eV}=0.41 \mathrm{eV}$ get lost due to collision.