1. Purpose of boiling Lassaigne’s extract with dilute $\mathrm{HNO_3}$ before halogen test

   In Lassaigne’s test for halogens, the sodium extract may contain not only sodium halides $(\mathrm{NaX})$ but also sodium cyanide $(\mathrm{NaCN})$ and sodium sulfide $(\mathrm{Na_2S})$ if nitrogen or sulfur are present in the organic compound.

2. Problem if $\mathrm{NaCN}$ and $\mathrm{Na_2S}$ are not removed

   On adding $\mathrm{AgNO_3}$ for the halogen test:

   • $\mathrm{CN^-}$ gives $\mathrm{AgCN}$ precipitate
   • $\mathrm{S^{2-}}$ gives $\mathrm{Ag_2S}$ precipitate

   These can interfere with the identification of halides.

3. Why boil with dilute $\mathrm{HNO_3}$?

   Dilute nitric acid decomposes $\mathrm{NaCN}$ and $\mathrm{Na_2S}$, removing $\mathrm{CN^-}$ and $\mathrm{S^{2-}}$ ions from the extract.

   Thus, after this treatment, only halide ions remain to react with $\mathrm{AgNO_3}$.

4. Check each option

   • A: Silver halides are soluble in $\mathrm{HNO_3}$.

     This is false. Silver halides such as $\mathrm{AgCl}$, $\mathrm{AgBr}$, and $\mathrm{AgI}$ are not soluble in dilute $\mathrm{HNO_3}$.

   • B: $\mathrm{AgCN}$ is soluble in $\mathrm{HNO_3}$.

     This is not the reason for boiling the extract before adding $\mathrm{AgNO_3}$. The purpose is to destroy $\mathrm{CN^-}$ before silver nitrate is added.

   • C: $\mathrm{Na_2S}$ and $\mathrm{NaCN}$ are decomposed by $\mathrm{HNO_3}$.

     This is correct.

   • D: $\mathrm{Ag_2S}$ is soluble in $\mathrm{HNO_3}$.

     This is false and also not the relevant reason.

5. Conclusion

   The correct reason is that dilute $\mathrm{HNO_3}$ decomposes $\mathrm{Na_2S}$ and $\mathrm{NaCN}$, preventing interference in the silver nitrate test for halogens.

Therefore, the correct option is C.