Hydrogen Spectrum & Spectral Series question from MHT CET 2021 (24 Sep, Shift 1)

Answer: (c)

1. Balmer series: $n_1 = 2$.
2. Maximum ($3 \to 2$): $\frac{1}{\lambda_{max}} = R\left(\frac{1}{4}-\frac{1}{9}\right) = \frac{5R}{36}$
3. Minimum ($\infty \to 2$): $\frac{1}{\lambda_{min}} = \frac{R}{4}$
4. $\frac{\lambda_{max}}{\lambda_{min}} = \frac{36/5}{4} = \frac{9}{5}$
5. So the answer is (c) 9 : 5.