In which of the following is lead sulfate $(PbSO_4)$ soluble?

$A$ solution prepared in conc. $HCl$ sometimes gives white turbidity even in the absence of $1^{st}$ group,when water is added to it. It is due to the presence of

$A$ laboratory reagent imparts green colour to the flame. On heating with solid $K_2Cr_2O_7$ and conc. $H_2SO_4$,it evolves a red gas. Identify the reagent.

Match List-$I$ with List-$II$:

List-$I$ ($Test$/$reagent$)	List-$II$ ($Radical$ $identified$)
$A$. Lake Test	$I$. $NO_3^{-}$
$B$. Nessler's Reagent	$II$. $Fe^{3+}$
$C$. Potassium thiocyanate	$III$. $Al^{3+}$
$D$. Brown Ring Test	$IV$. $NH_4^{+}$

Choose the correct answer from the options given below:

An aqueous solution of a mixture of two inorganic salts,when treated with dilute $HCl$,gave a precipitate $(P)$ and a filtrate $(Q)$. The precipitate $P$ was found to dissolve in hot water. The filtrate $(Q)$ remained unchanged when treated with $H_2S$ in a dilute mineral acid medium. However,it gave a precipitate $(R)$ with $H_2S$ in an ammoniacal medium. The precipitate $R$ gave a coloured solution $(S)$ when treated with $H_2O_2$ in an aqueous $NaOH$ medium.
$1.$ The precipitate $P$ contains
$(A)$ $Pb^{2+}$ $(B)$ $Hg_2^{2+}$ $(C)$ $Ag^{+}$ $(D)$ $Hg^{2+}$
$2.$ The coloured solution $S$ contains
$(A)$ $Fe_2(SO_4)_3$ $(B)$ $CuSO_4$ $(C)$ $ZnSO_4$ $(D)$ $Na_2CrO_4$

$A$ colorless aqueous solution contains nitrates of two metals,$X$ and $Y$. When it was added to an aqueous solution of $NaCl$,a white precipitate was formed. This precipitate was found to be partly soluble in hot water to give a residue $P$ and a solution $Q$. The residue $P$ was soluble in aqueous $NH_3$ and also in excess sodium thiosulfate. The hot solution $Q$ gave a yellow precipitate with $KI$. The metals $X$ and $Y$,respectively,are