**Explanation:**

To determine the correct option, let's analyze the observations for each sample.

1. **White ppt. with excess ammonia solution:**
- When excess ammonia solution (NH3) is added to a solution, it forms a complex with certain metal ions, resulting in the formation of a white precipitate.
- The most common metal ion that forms a white precipitate with excess ammonia is silver (Ag+). Therefore, the presence of a white ppt. with excess ammonia suggests the presence of the Ag+ ion.

2. **White ppt. with dil. NaCl solution:**
- When a solution containing certain metal ions is treated with dilute sodium chloride solution (NaCl), it forms a white precipitate.
- The most common metal ion that forms a white precipitate with dilute NaCl is lead (Pb2+). Therefore, the presence of a white ppt. with dilute NaCl suggests the presence of the Pb2+ ion.

3. **Black ppt. with H2S:**
- When hydrogen sulfide gas (H2S) is passed through a solution containing certain metal ions, it forms a black precipitate.
- The most common metal ion that forms a black precipitate with H2S is mercury (Hg2+). Therefore, the presence of a black ppt. with H2S suggests the presence of the Hg2+ ion.

Based on the above observations, we can conclude that the salt contains the Ag+, Pb2+, and Hg2+ ions.

Now, let's analyze the given options:

a) AgNO3 - This salt contains the Ag+ ion, which is consistent with the observation of a white ppt. with excess ammonia. However, it does not explain the formation of a white ppt. with dilute NaCl or a black ppt. with H2S.

b) Pb(NO3)2 - This salt contains the Pb2+ ion, which is consistent with the observation of a white ppt. with dilute NaCl. It also does not explain the formation of a black ppt. with H2S. Therefore, this option is correct.

c) Hg(NO3)2 - This salt contains the Hg2+ ion, which is consistent with the observation of a black ppt. with H2S. However, it does not explain the formation of a white ppt. with excess ammonia or dilute NaCl.

d) MnSO4 - This salt does not contain any of the ions mentioned in the observations. Therefore, it is not the correct option.

Hence, the correct option is **b) Pb(NO3)2** because it explains the formation of a white ppt. with dilute NaCl, which is consistent with the given observation.