Which of the following gives a precipitate with $Pb(NO_3)_2$ but not with $Ba(NO_3)_2$?

$S^{2-}$ and $SO_3^{2-}$ can be distinguished by using

The solution of a chemical compound $X$ reacts with $AgNO_3$ solution to form a white precipitate of $Y$,which dissolves in $NH_4OH$ to give a complex $Z$. When $Z$ is treated with dilute $HNO_3$,$Y$ reappears. The chemical compound $X$ can be:

Molar mass of the salt from $NaBr$,$NaNO_3$,$KI$,and $CaF_2$ which does not evolve coloured vapours on heating with concentrated $H_2SO_4$ is . . . . . . $g \ mol^{-1}$. (Molar mass in $g \ mol^{-1}$: $Na: 23$,$N: 14$,$K: 39$,$O: 16$,$Br: 80$,$I: 127$,$F: 19$,$Ca: 40$)

$[X] +$ dil. $H_{2}SO_{4} \longrightarrow [Y]:$
Colourless, suffocating gas
$[Y] + K_{2}Cr_{2}O_{7} + H_{2}SO_{4} \longrightarrow$
Green colouration of solution
Then, $[X]$ and $[Y]$ are

When $Y$ is treated with $KMnO_4$,then the final precipitate is of:
$'X' \xrightarrow[BaCl_{2} \text{ solution}]{} 'Y' \quad (\text{White ppt., insoluble in dil. } HCl)$
$'X' \xrightarrow[\text{Flame test}]{} \text{Golden yellow flame}$