A solution contains $\left[{\mathrm{OH}}^{-}\right]$ equal to ${10}^{-6}\mathrm{M}$ .Which of the following hydroxides will get precipitated when this solution is added in an equal volume to a solution containing 0.1 M of metal ions?

$\mathrm{AgOH}\rightleftharpoons {\mathrm{Ag}}^{+}{\mathrm{OH}}^{-}$

${\mathrm{K}}_{\mathrm{Sp}}={\mathrm{S}}^2=5\times {10}^{-3}\Rightarrow \mathrm{S}=\sqrt{5\times {10}^{-3}}=6.7\times {10}^{-2}$

$\mathrm{Cd}{\left(\mathrm{OH}\right)}_2\rightleftharpoons {\mathrm{Cd}}^{+2}+2{\mathrm{OH}}^{-}$

     S              2S

${\mathrm{K}}_{\mathrm{Sp}}=4{\mathrm{S}}^2\Rightarrow \mathrm{S}=\sqrt[3]{\frac{{\mathrm{K}}_{\mathrm{Sp}}}{4}}=\sqrt[3]{2\times {10}^{-6}}=\sqrt[3]{2\times {10}^{-2}}$

$\left(\mathrm{iii}\right) \mathrm{Mg}{\left(\mathrm{OH}\right)}_2\Rightarrow \mathrm{S}=\sqrt[3]{7.5\times {10}^{-4}}$

$\left(\mathrm{iv}\right) \mathrm{Fe}{\left(\mathrm{OH}\right)}_2\rightleftharpoons {\mathrm{Fe}}^{+}+2{\mathrm{OH}}^{-}$

S          2S

${\mathrm{K}}_{\mathrm{Sp}}=4{\mathrm{S}}^2\Rightarrow \mathrm{S}=\sqrt[3]{\frac{{\mathrm{K}}_{\mathrm{Sp}}}{4}}$

$=\sqrt[3]{\frac{8\times {10}^{-6}}{4}}=\sqrt[3]{0.2\times {10}^{-5}}$

$\mathrm{Fe}{\left(\mathrm{OH}\right)}_2$