A white sodium salt dissolves readily in water to give a solution which is neutral to litmus. When silver nitrate solution is added to the aforementioned solution, a white precipitate is obtained which does not dissolve in dil. nitric acid. The anion is:

We are given a white sodium salt, so let us represent it in general as $$\mathrm{NaX}$$ where $$\mathrm{X^-}$$ is the unknown anion. Being a sodium salt it dissolves completely in water, producing an aqueous solution of $$\mathrm{Na^+}$$ and $$\mathrm{X^-}$$ ions. We are told that this solution is neutral to litmus, so it is neither appreciably acidic nor basic.

Into this neutral solution silver nitrate is added. According to the general ionic reaction

$$\mathrm{Ag^+ + X^- \rightarrow AgX \downarrow}$$

a precipitate of $$\mathrm{AgX}$$ will form if $$\mathrm{AgX}$$ is insoluble in water. Experimentally a white precipitate appears. We next note the behaviour of this white precipitate toward dilute nitric acid. The observation states that the precipitate does not dissolve in dilute $$\mathrm{HNO_3}$$.

Now we check each anion one by one, recalling the well-known solubility properties of the corresponding silver salts in the presence of dilute nitric acid:

1. For carbonate: $$\mathrm{CO_3^{2-}}$$ gives $$\mathrm{Ag_2CO_3}$$, also white, but the carbonate decomposes in dilute acids due to the reaction $$\mathrm{CO_3^{2-} + 2\,H^+ \rightarrow CO_2 \uparrow + H_2O}$$. Therefore $$\mathrm{Ag_2CO_3}$$ dissolves in dilute $$\mathrm{HNO_3}$$ with brisk effervescence of $$\mathrm{CO_2}$$. This does not match the observation.

2. For sulfate: $$\mathrm{SO_4^{2-}}$$ gives $$\mathrm{Ag_2SO_4}$$. Silver sulfate is sparingly soluble in water but becomes appreciably soluble in dilute nitric acid because $$\mathrm{Ag_2SO_4 + 2\,H^+ \rightarrow 2\,Ag^+ + H_2SO_4}$$. Hence the precipitate would disappear on adding dilute $$\mathrm{HNO_3}$$. Again, this contradicts the observation.

3. For sulfide: $$\mathrm{S^{2-}}$$ produces $$\mathrm{Ag_2S}$$, which is characteristically black or dark brown, not white. The colour alone rules this out.

4. For chloride: $$\mathrm{Cl^-}$$ yields $$\mathrm{AgCl}$$ by the reaction $$\mathrm{Ag^+ + Cl^- \rightarrow AgCl \downarrow}$$, and silver chloride is well known to be a curdy white precipitate insoluble in dilute nitric acid. This behaviour exactly matches the experimental facts.

Because only chloride produces a white precipitate that remains unaffected by dilute $$\mathrm{HNO_3}$$, the anion must be $$\mathrm{Cl^-}$$.

Hence, the correct answer is Option D.