During the qualitative analysis of salts using dilute acids,...

A. $CO_2$ gas turns lime water milky due to the formation of insoluble calcium carbonate ($CaCO_3$).
$Ca(OH)_2 + CO_2 \rightarrow CaCO_3 \downarrow + H_2O$
Thus, A matches with 4.

B. $H_2S$ gas turns lead acetate paper black due to the formation of black lead sulfide ($PbS$).
$(CH_3COO)_2Pb + H_2S \rightarrow PbS \downarrow + 2CH_3COOH$
Thus, B matches with 2.

C. $SO_2$ gas turns acidified potassium dichromate ($K_2Cr_2O_7$) paper green because it reduces $Cr^{6+}$ (orange) to $Cr^{3+}$ (green).
$K_2Cr_2O_7 + 3SO_2 + H_2SO_4 \rightarrow K_2SO_4 + Cr_2(SO_4)_3 + H_2O$
Thus, C matches with 1.

D. $NO_2$ gas acts as an oxidizing agent and oxidizes iodide ions to iodine, which turns starch-iodide paper blue.
$2NO_2 + 2KI \rightarrow 2KNO_2 + I_2$
$I_2 + \text{starch} \rightarrow \text{blue complex}$
Thus, D matches with 3.

The correct matching is A-4, B-2, C-1, D-3.

Answer: A-4, B-2, C-1, D-3