In hydrogen atom wavelength of second line of Balmer series is $\lambda ,$ which of the following statement(s) is/are correct:
A) The wavelength of the First line of Balmer series is $\left(\frac{27}{20}\right)\lambda$
B) The wavelength of the Third line of Balmer series is  $\left(\frac{20}{15}\right)\lambda$
C) The wavelength of the First line of Lyman series is  $\left(\frac{\lambda }{4}\right)$
D) The wavelength of the Second line of Lyman series is  $\left(\frac{25}{12}\right)\lambda$

$$\begin{gathered} \frac{1}{\lambda }\propto (\frac{1}{n_1^2}-\frac{1}{n_2^2}) \\ \Rightarrow \frac{{\lambda }_2}{{\lambda }_1}=\frac{{(1/n_1^2-1/n_2^2)}_i}{{(1/n_1^2-1/n_2^2)}_f} \\ \Rightarrow {\lambda }_2=\frac{(1/4-1/16)\lambda }{{(1/n_1^2-1/n_2^2)}_f} \\ \Rightarrow {\lambda }_2=\left(\frac{3}{16}\lambda \right)\left[\frac{1}{{(1/n_1^2-1/n_2^2)}_f}\right] \end{gathered}$$

A) For first line of Balmer series, 
  $n_1=2,n_2=3$
 $\Rightarrow {\lambda }_2=\left(\frac{27}{20}\right)\lambda$
B) For third line of Balmer series, 
  $n_1=2,n_2=5$
 $\Rightarrow {\lambda }_5=\left(\frac{25}{28}\right)\lambda$
C) For first line of Lyman series, 
  $n_1=1,n_2=2$
 $\Rightarrow {\lambda }_2=\frac{\lambda }{4}$
D) For second line of Lyman series, 

$n_1=2,n_2=3$

$\Rightarrow {\lambda }_2=\left(\frac{27}{128}\right)\lambda$