$(a)\;2,3\qquad(b)\;3,1\qquad(c)\;3,2\qquad(d)\;1,2$

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For $He^+,\large\frac{1}{\lambda}$$=R_Hz^2\bigg[\large\frac{1}{2^2}-\frac{1}{4^2}\bigg]$

For $H,\large\frac{1}{\lambda}$$=R_H\bigg[\large\frac{1}{n_1^2}-\frac{1}{n_2^2}\bigg]$

Since $\lambda$ is same

$\therefore Z^2\bigg[\large\frac{1}{2^2}-\frac{1}{4^2}\bigg]=\bigg[\large\frac{1}{n_1^2}-\frac{1}{n_2^2}\bigg]$

$z=2$

$\bigg[\large\frac{1}{1^2}-\frac{1}{2^2}\bigg]=\bigg[\large\frac{1}{n_1^2}-\frac{1}{n_2^2}\bigg]$

$n_1=1$ and $n_2=2$

Hence (d) is the correct answer.

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