(A) : Mass, Volume and time may be taken as fundamental quantities in a system.
(R) : Quantities which are independent of one another are called fundamental quantities.

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
C. (A) is true but (R) is false
D. Both (A) and (R) are false

Answer

To solve the question, we need to analyze both statements (A) and (R) and determine their validity and relationship.

### Step 1: Analyze Statement (A)
Statement (A) claims that mass, volume, and time may be taken as fundamental quantities in a system.

- **Fundamental Quantities**: These are basic physical quantities that cannot be defined in terms of other quantities. Common examples include mass, length, time, and electric current.
- **Volume**: Volume is derived from length (Volume = length × breadth × height), which means it is not a fundamental quantity but a derived quantity.

**Conclusion for (A)**: This statement is **False** because volume is not a fundamental quantity.

### Step 2: Analyze Statement (R)
Statement (R) states that quantities which are independent of one another are called fundamental quantities.

- **Independence of Quantities**: For a set of quantities to be considered fundamental, they must not be expressible in terms of one another. Mass and time are independent of each other, but volume is dependent on length.

**Conclusion for (R)**: This statement is **True** because it correctly defines fundamental quantities as those that are independent of each other.

### Step 3: Determine the Relationship Between (A) and (R)
Since (A) is false and (R) is true, we can conclude:

- (A) is incorrect as it incorrectly categorizes volume as a fundamental quantity.
- (R) is correct as it provides a valid definition of fundamental quantities.

### Final Conclusion
- (A) is False.
- (R) is True.
- The reason (R) does not correctly explain (A) since (A) itself is incorrect.

### Summary
- **Answer**: (A) is False, (R) is True, and (R) is not the correct explanation for (A).

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