(A): The order of accuracy of a measurement depends on the least count of the instrument.
(R): The smaller the least count, more number of significant figures are in the measured value.

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 the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion (A)
The assertion states: "The order of accuracy of a measurement depends on the least count of the instrument."

- **Explanation**: The least count of an instrument is the smallest increment that can be measured accurately with that instrument. A smaller least count indicates that the instrument can measure smaller differences, which generally leads to higher accuracy in measurements.

### Step 2: Understand the Reason (R)
The reason states: "The smaller the least count, more number of significant figures are in the measured value."

- **Explanation**: Significant figures are the digits in a number that contribute to its precision. When an instrument has a smaller least count, it can measure values with more precision, allowing for more significant figures in the final measurement. For example, if a ruler has a least count of 1 mm, you can measure to the nearest millimeter, but if it has a least count of 0.1 mm, you can measure to the nearest tenth of a millimeter, thus increasing the number of significant figures.

### Step 3: Evaluate the Truth of Both Statements
- **Assertion (A)**: True, because the accuracy of a measurement is indeed influenced by the least count of the measuring instrument.
- **Reason (R)**: True, because a smaller least count allows for more precise measurements, which results in more significant figures.

### Step 4: Determine the Relationship Between A and R
- Since both statements are true and the reason (R) correctly explains the assertion (A), we conclude that the correct answer is that both A and R are true, and R is the correct explanation of A.

### Final Conclusion
Both the assertion and the reason are true, and the reason is indeed the correct explanation for the assertion. Therefore, the answer is: **Both A and R are true, and R is the correct explanation of A.**

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