Select the correct statement(s):

Options

A. White ppt of `BaCO_(3)` and `CaOC_(3)` and `CaCO_(3)` is soluble in dil `HNO_(3)` dil `HCI,CH_(3)COOH` and soda water
B. White ppt of `PbCO_(3)`is soluble in dil `HNO_(3)` dil`CH_(3)COOH`
C. White ppt of `AgCO_(3)` is soluble in dil `HNO_(3)`and `NH_(3)` soluble
D. `HCN` and `H_(2)HO_(3)` are stranger acids than `H_(2)CO_(3)`

Answer

To solve the question, we need to evaluate each statement provided and determine whether they are correct or not. Let's analyze each option step by step.

### Step-by-Step Solution:

**Step 1: Evaluate Option 1**
- **Statement**: "White PPT of barium carbonate and calcium carbonate is soluble in dilute HNO3, HCl, acetic acid, and soda water."
- **Analysis**: Both barium carbonate (BaCO3) and calcium carbonate (CaCO3) react with dilute acids such as HNO3 (nitric acid) and HCl (hydrochloric acid), leading to the formation of soluble barium and calcium salts, respectively. They are also soluble in acetic acid. However, soda water (which contains carbonic acid) does not dissolve them significantly. Therefore, this statement is **partially correct** but not entirely true for soda water.

**Step 2: Evaluate Option 2**
- **Statement**: "White precipitate of lead carbonate is soluble in dilute HNO3 and dilute acetic acid."
- **Analysis**: Lead carbonate (PbCO3) is indeed soluble in dilute nitric acid and acetic acid. When added to these acids, it dissolves, forming lead salts. Thus, this statement is **correct**.

**Step 3: Evaluate Option 3**
- **Statement**: "White PPT of AgCO3 is soluble in dilute HNO3 and NH3."
- **Analysis**: Silver carbonate (Ag2CO3) is soluble in dilute nitric acid and also in ammonia (NH3). The reaction with nitric acid leads to the formation of soluble silver nitrate, and ammonia can complex with silver ions, increasing solubility. Therefore, this statement is **correct**.

**Step 4: Evaluate Option 4**
- **Statement**: "HCN and H2CO3 are stronger acids."
- **Analysis**: Hydrocyanic acid (HCN) is indeed a stronger acid than carbonic acid (H2CO3). The dissociation constant (Ka) of HCN is greater than that of H2CO3, indicating that HCN dissociates more completely in solution. Therefore, this statement is **correct**.

### Conclusion:
After evaluating all the options, we find that:
- Option 1 is partially correct (not entirely true for soda water).
- Options 2, 3, and 4 are correct.

### Final Answer:
The correct statements are:
- Option 2: Correct
- Option 3: Correct
- Option 4: Correct