Question:
Statement-I: When two quantities are multiplied, the relative error in the result is the sum of the relative errors in the quantities.
Statement-II: When two quantities are divided, the relative error in the result is the difference of the relative errors in the quantities.
Statement-I: When two quantities are multiplied, the relative error in the result is the sum of the relative errors in the quantities.
Statement-II: When two quantities are divided, the relative error in the result is the difference of the relative errors in the quantities.
Statement-II: When two quantities are divided, the relative error in the result is the difference of the relative errors in the quantities.
Show Hint
In error analysis:
\[
\text{Relative errors add for multiplication and division.}
\]
Never subtract them.
Updated On: Jun 18, 2026
- Both statements I and II are correct
- Both statements I and II are not correct
- Statement I is correct, but statement II is not correct
- Statement I is not correct, but statement II is correct
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
For experimental measurements:
If
\[
Z=AB,
\]
then
\[
\frac{\Delta Z}{Z}
=
\frac{\Delta A}{A}
+
\frac{\Delta B}{B}.
\]
Similarly, if
\[
Z=\frac{A}{B},
\]
then
\[
\frac{\Delta Z}{Z}
=
\frac{\Delta A}{A}
+
\frac{\Delta B}{B}.
\]
Relative errors are always added irrespective of multiplication or division.
Step 1: Analyze Statement-I.
For multiplication, \[ Z=AB. \] Therefore, \[ \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B}. \] Hence Statement-I is correct.
Step 2: Analyze Statement-II.
For division, \[ Z=\frac{A}{B}. \] Relative errors are still added: \[ \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B}. \] They are not subtracted. Hence Statement-II is incorrect.
Step 3: Select the correct option.
\[ \boxed{\text{Statement I is correct but Statement II is not correct.}} \]
Step 1: Analyze Statement-I.
For multiplication, \[ Z=AB. \] Therefore, \[ \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B}. \] Hence Statement-I is correct.
Step 2: Analyze Statement-II.
For division, \[ Z=\frac{A}{B}. \] Relative errors are still added: \[ \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B}. \] They are not subtracted. Hence Statement-II is incorrect.
Step 3: Select the correct option.
\[ \boxed{\text{Statement I is correct but Statement II is not correct.}} \]
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