Explanation

(a)
${Bi}_{2}S_{3} \rightleftharpoons 2{Bi}^{3 +} + 3S^{2 -}$
$2s$ $3s$
$K_{sp} = (2s)^{2}(3s)^{3} = 108s^{5}$
$108s^{5} = 1 \times 10^{- 17}$
$s = \left( \frac{1 \times 10^{- 17}}{108} \right)^{\frac{1}{5}} = 1.56 \times 10^{- 4}$
$MnS \rightleftharpoons {Mn}^{2 +} + S^{2 -}$
$s$ $s$
$K_{sp} = s^{2}$
$s = \sqrt{K_{sp}} = \sqrt{7 \times 10^{- 16}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ = 2.64 \times 10^{- 8}$
$CuS \rightleftharpoons {Cu}^{2 +} + S^{2 -}$
$s$ $s$
$K_{sp} = s^{2}$
$8 \times 10^{- 37} = s^{2}$
$s = \sqrt{8 \times 10^{- 37}} = 0.89 \times 10^{- 18}$
${Ag}_{2}S \rightleftharpoons 2{Ag}^{+} + S^{2 -}$
$2s$ $s$
$K_{sp} = 4s^{3}or\ 4s^{3} = 6 \times 10^{- 51}$
$s = \sqrt[3]{\frac{6 \times 10^{- 51}}{4}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sqrt[3]{1.5 \times 10^{- 51}} = 1.14 \times 10^{- 17}$
The solubility of ${Bi}_{2}S_{3}$ is maximum. Hence, it is the most soluble.