b
\(C{r_2}{(S{O_4})_3} \rightleftharpoons \mathop {2C{r^{ + 3 }}}\limits_{2s}  + \mathop {3S{O_4}^{ -  - }}\limits_{3s} \)

\({K_{sp}} = {(2s)^2}{(3s)^2} = 4{s^2} \times 27{s^3} = 108{s^5}\)

\(s = {\left( {\frac{{{K_{sp}}}}{{108}}} \right)^{1/5}}\)

\(H{g_2}C{l_2} \rightleftharpoons \mathop {2H{g^{2 + }}}\limits_{2s}  + \mathop {2C{l^ - }}\limits_{2s} \)

\({K_{sp}} = {(2s)^2} \times {(2s)^2} = 16{x^4}\)

\(s = {\left( {\frac{{{K_{sp}}}}{{16}}} \right)^{1/4}}\)

\(BaS{O_4} \rightleftharpoons \mathop {B{a^{ + 2 }}}\limits_s  + \mathop {S{O_4}^{ -  - }}\limits_s \)

\({K_{sp}} = {s^2}\)

\(s = \sqrt {{K_{sp}}} \)

\(CrC{l_3} \rightleftharpoons \mathop {C{r^{3 + }}}\limits_s  + \mathop {3C{l^ - }}\limits_{3s} \)

\({K_{sp}} = s \times {(3s)^3} = 27\,{s^4}\)

\(s = {\left( {\frac{{{K_{sp}}}}{{27}}} \right)^{1/4}}\)

Hence the correct order of solubilities of salts is

\(\sqrt {{K_{sp}}}  > {\left( {\frac{{{K_{sp}}}}{{16}}} \right)^{1/4}} > {\left( {\frac{{{K_{sp}}}}{{27}}} \right)^{1/4}} > {\left( {\frac{{{K_{sp}}}}{{108}}} \right)^{1/5}}\)