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- Mathematics in Physics
NEET · Physics · Mathematics in Physics
Given below are two statements: one is labelled as Assertion (A)...
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The mean of three length measurements , , and is correctly reported as .
Reason (R): The integer 3 used for division is an exact number with infinite significant figures, so the decimal places in the final result are determined by the addition rule applied to the original measurements.
In the light of the above statements, choose the most appropriate answer from the options given below:
Assertion (A): The mean of three length measurements , , and is correctly reported as .
Reason (R): The integer 3 used for division is an exact number with infinite significant figures, so the decimal places in the final result are determined by the addition rule applied to the original measurements.
In the light of the above statements, choose the most appropriate answer from the options given below:
Options
- ABoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- CAssertion (A) is true but Reason (R) is false.
- DAssertion (A) is false but Reason (R) is true.
Correct answer
B. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Step-by-step solution
Assertion (A) is true: The sum of the measurements is . The raw mean is . Since the original measurements have one decimal place, the mean should also be rounded to one decimal place. Rounding to one decimal place gives .
Reason (R) is true and correctly explains the Assertion: When calculating an average, the number of observations (3) is an exact number with infinite significant figures. Therefore, it does not restrict the precision of the result. The precision is governed by the sum of the measurements, which follows the addition rule (retaining the least number of decimal places present in the original data).
Hence, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
Answer: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Reason (R) is true and correctly explains the Assertion: When calculating an average, the number of observations (3) is an exact number with infinite significant figures. Therefore, it does not restrict the precision of the result. The precision is governed by the sum of the measurements, which follows the addition rule (retaining the least number of decimal places present in the original data).
Hence, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
Answer: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).