`(P)overset(Delta)(rarr)(Q)+(R )uarr+(S)uarr`
`(X)overset(Delta)(rarr)(Y)+(R )uarr+(S)uarr`
P and X are respectively

Options

A. `AgNO_3, LiNO_3`
B. `AgNO_3, Pb(NO_(3))_(2)`
C. `Hg_(2)(NO_(3))_(2),Ca(NO_3)_(2)`
D. `NaNO_(3), Zn(NO_3)_(2)`

Answer

To solve the question, we need to identify the compounds P and X based on the reactions provided. The reactions indicate that both P and X decompose upon heating to produce gases (NO2 and O2) and other products.

### Step-by-Step Solution:

1. **Identify the Reactions**:
- The first reaction is:
\[ P \xrightarrow{\Delta} Q + R + S \]
- The second reaction is:
\[ X \xrightarrow{\Delta} Y + R + S \]
Here, R and S are common products in both reactions.

2. **Analyze the Products**:
- From the video transcript, we know that both reactions produce gases (NO2 and O2). This suggests that both P and X are likely nitrates, as the decomposition of nitrates typically produces nitrogen dioxide (NO2) and oxygen (O2).

3. **Consider Common Nitrate Decompositions**:
- **For P**:
- Silver Nitrate (AgNO3) decomposes to give:
\[ 2AgNO3 \xrightarrow{\Delta} 2Ag + O2 + 2NO2 \]
- Lead Nitrate (Pb(NO3)2) decomposes to give:
\[ 2Pb(NO3)2 \xrightarrow{\Delta} 2PbO + 4NO2 + O2 \]
- Lithium Nitrate (LiNO3) decomposes to give:
\[ 4LiNO3 \xrightarrow{\Delta} 2Li2O + 4NO2 + O2 \]

- **For X**:
- Similar analysis can be done for other nitrates like Sodium Nitrate (NaNO3) and Zinc Nitrate (Zn(NO3)2).

4. **Match the Products**:
- From the reactions, we need to ensure that both P and X yield the same gases (NO2 and O2) upon heating.
- After analyzing the options:
- **P = Lead Nitrate (Pb(NO3)2)** and **X = Sodium Nitrate (NaNO3)** both yield NO2 and O2 upon decomposition.

5. **Conclusion**:
- Therefore, the compounds P and X that fit the criteria are:
- \( P = \text{Lead Nitrate (Pb(NO}_3\text{)}_2) } \)
- \( X = \text{Sodium Nitrate (NaNO}_3) \)

### Final Answer:
- \( P = \text{Lead Nitrate (Pb(NO}_3\text{)}_2) } \)
- \( X = \text{Sodium Nitrate (NaNO}_3) \)