A : A unitless physical quantity must be dimensionless.
R : A pure number is always dimensionless.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To analyze the statements given in the question, we need to evaluate both the assertion (A) and the reason (R) provided.

### Step 1: Understanding the Assertion (A)
The assertion states: "A unitless physical quantity must be dimensionless."

- A physical quantity is defined as something that can be measured and has both magnitude and unit.
- If a physical quantity is unitless, it means that it does not have any associated units of measurement.
- Since dimensions are derived from units, if there are no units, there can be no dimensions assigned to that quantity.
- Therefore, a unitless physical quantity must indeed be dimensionless.

**Conclusion for Step 1**: The assertion (A) is correct.

### Step 2: Understanding the Reason (R)
The reason states: "A pure number is always dimensionless."

- A pure number is a number that does not have any physical units associated with it.
- Examples of pure numbers include counting numbers (like 1, 2, 3) or ratios (like 1/2, 3/4) that do not depend on any unit of measurement.
- Since pure numbers do not have units, they are inherently dimensionless.

**Conclusion for Step 2**: The reason (R) is also correct.

### Step 3: Evaluating the Relationship Between A and R
Now, we need to determine if the reason (R) correctly explains the assertion (A).

- The assertion (A) claims that a unitless physical quantity must be dimensionless, and the reason (R) states that a pure number is always dimensionless.
- Since a unitless physical quantity can be considered a pure number (as it has only magnitude and no units), the reason does indeed explain the assertion.

### Final Conclusion
Both the assertion (A) and the reason (R) are correct, and the reason correctly explains the assertion. Therefore, the answer is:

**Option 1: Both A and R are correct, and R is the correct explanation of A.**

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