Explanation

(d) For first line of Lyman series,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n_{1}$=1 and $n_{2}$=2
$\therefore\ \ \ \ \ \ \ \ \ \ \frac{1}{\lambda_{1}} = R\left( \frac{1}{1^{2}} - \frac{1}{2^{2}} \right) = R\left( 1 - \frac{1}{4} \right) = \frac{3R}{4}$
For first line of Paschen Series
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ n_{1}$=3 and $n_{2}$=4
$\therefore\ \ \ \ \ \ \ \ \ \frac{1}{\lambda_{2}} = R\left( \frac{1}{3^{2}} - \frac{1}{4^{2}} \right) = R\left( \frac{1}{9} - \frac{1}{16} \right) = \frac{7R}{144}$
$\therefore\ \ \ \ \ \frac{\lambda_{1}}{\lambda_{2}} = \ \frac{7R}{144}\ \times \ \frac{4}{3R} = \frac{7}{108}$