An aqueous solution of a substance gives a white precipitate on treatment with $\mathrm{NaCl}$ solution, which dissolves on heating. When ${\mathrm{H}}_2\mathrm{S}$ gas is passed through it's hot acidic solution, a black precipitate is obtained. The cations which are not associated with this test are :

An aqueous solution of a substance gives a white precipitate on treatment with $\mathrm{NaCl}$ solution, which dissolves on heating. When ${\mathrm{H}}_2\mathrm{S}$ gas is passed through its hot acidic solution, a black precipitate is obtained. The cations which are not associated with this test are ${\mathrm{Mg}}^{2+}$, ${\mathrm{Ag}}^{+}$ and ${\mathrm{Hg}}_2^{2+}$.

The material is salt of ${\mathrm{Pb}}^{2+}$. I and II group contain lead. The reaction is having follows,

$\begin{array}{ccc}{\mathrm{Pb}}^{2+}+2\mathrm{HCl}\to {\mathrm{PbCl}}_2\downarrow & \stackrel{{\mathrm{H}}_2\mathrm{S}}{\to }& \mathrm{PbS}\downarrow \\ \text{ Whise ppt. }& & \text{ Black ppt }\\ \mathrm{dissolves} \mathrm{on}& & \\ \text{ boiling }& & \end{array}$

Hence, options A, B and C are correct.