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 solve the question, we need to analyze both the assertion (A) and the reason (R) provided in the statement.

**Assertion (A): A unitless physical quantity must be dimensionless.**

1. **Understanding the Assertion**: A unitless physical quantity means that it does not have any associated units of measurement. For example, a ratio like speed (distance/time) can be unitless if we consider it in terms of ratios (e.g., comparing two speeds).

2. **Dimensionless Concept**: A dimensionless quantity is one that does not have any physical dimensions associated with it. This means it cannot be expressed in terms of fundamental quantities like length, mass, time, etc.

3. **Conclusion for Assertion**: If a quantity is unitless, it inherently does not have any dimensions. Therefore, the assertion is correct.

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**Reason (R): A pure number is always dimensionless.**

1. **Understanding the Reason**: A pure number refers to numerical values that do not have any physical units associated with them. Examples include integers (2, 3, 4) or mathematical constants (like π).

2. **Dimensionless Nature of Pure Numbers**: Pure numbers are indeed dimensionless because they do not represent any physical quantity that can be measured. They are simply numerical values used in calculations.

3. **Conclusion for Reason**: Since pure numbers do not have dimensions, this reason is also correct.

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**Final Evaluation**:

- Both the assertion and the reason are true.
- However, the reason does not provide a correct explanation for the assertion. The assertion is about unitless physical quantities being dimensionless, while the reason discusses pure numbers, which, although related, do not directly explain the assertion.

**Final Answer**: Both assertion and reason are true, but the reason is not the correct explanation of the assertion.

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