A salt solution which gives a reddish-brown precipitate with NaOH and a white precipitate with BaCl 2 solution is:

Fe₂(SO₄)₃

Reason —

Reddish-brown ppt with NaOH indicates Fe³⁺ ions.
$\text{Fe}^{3+} + 3\text{OH}^- \rightarrow \text{Fe(OH)}_3 \downarrow \space (\text{reddish-brown})$

White ppt with BaCl₂ indicates SO₄^2- ions (forms insoluble BaSO₄)
$\text{Ba}^{2+} + \text{SO}_4^{2-} \rightarrow \text{BaSO}_4 \downarrow \space (\text{white})$

So the salt must contain Fe³⁺ and SO₄^2-, which is Fe₂(SO₄)₃.