Assertion : Molecular mass of A is `M/4` if the molecular mass of B is M.
Reason : Vapour density of A four times that of B.

Options

A. If both assertion and reason are true and the reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If assertion is true but reason is false.
D. If the assertion and reason both are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that the molecular mass of A is \( \frac{M}{4} \) if the molecular mass of B is \( M \).

- If the molecular mass of B is \( M \), then according to the assertion, the molecular mass of A is \( \frac{M}{4} \).

### Step 2: Understand the Reason
The reason states that the vapor density of A is four times that of B.

- Vapor density (VD) is defined as the mass of a certain volume of gas compared to the mass of an equal volume of hydrogen at the same temperature and pressure. It can also be calculated using the formula:
\[ \text{Vapor Density} = \frac{\text{Molecular Mass}}{2} \]

### Step 3: Calculate the Vapor Densities
1. **Calculate the vapor density of B:**
- Given the molecular mass of B is \( M \):
\[ \text{VD}_B = \frac{M}{2} \]

2. **Calculate the vapor density of A:**
- Given the molecular mass of A is \( \frac{M}{4} \):
\[ \text{VD}_A = \frac{\frac{M}{4}}{2} = \frac{M}{8} \]

### Step 4: Compare the Vapor Densities
Now, we need to check if the vapor density of A is indeed four times that of B:
- From our calculations:
- Vapor density of A \( \text{VD}_A = \frac{M}{8} \)
- Vapor density of B \( \text{VD}_B = \frac{M}{2} \)

To find out if \( \text{VD}_A \) is four times \( \text{VD}_B \):
\[ \text{VD}_A = 4 \times \text{VD}_B \implies \frac{M}{8} = 4 \times \frac{M}{2} \]
Calculating the right side:
\[ 4 \times \frac{M}{2} = \frac{4M}{2} = 2M \]

Clearly, \( \frac{M}{8} \neq 2M \). Therefore, the reason is false.

### Conclusion
- The assertion is true: the molecular mass of A is \( \frac{M}{4} \) if the molecular mass of B is \( M \).
- The reason is false: the vapor density of A is not four times that of B.

### Final Answer
- Assertion: True
- Reason: False