Assertion (A): The error in measurement of radius of the sphere is 0.3%. The permissible error in its surface area is 1.2%.
Reason (R): Area of sphere, \(A = 4\pi r^2 \Rightarrow \frac{\Delta A}{A} = 4\frac{\Delta r}{r}\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The surface area of a sphere is \(A = 4\pi r^2\), which gives the fractional error relation as \(\frac{\Delta A}{A} = 2\frac{\Delta r}{r}\). Thus, the error in area is \(2 \times 0.3% = 0.6%\), making both statements false.
Assertion (A): Mean absolute error of a measurement is always positive.
Reason (R): Mean absolute error is defined as the magnitude of difference between true value and measured value.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Mean absolute error is the arithmetic mean of all absolute errors and is always positive. The definition given in the reason describes individual absolute error rather than the mean absolute error, so R is false.
Assertion (A): If the measuring instruments used are perfect, then measurements made will be perfect.
Reason (R): Measurements depend upon only on the instruments.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Even with perfect instruments, errors due to observation, environmental factors, or experimental setup can occur. Both statements are false.