JEE Advanced 2018 Paper 1

Paragraph for next 2 questions If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. Forexample, consider the relation $z = \frac{x}{y}$ . If the errors in x,y and z are $\Delta x, \Delta y$ and $\Delta z$ ,respectively, thenThe series expansion for $\left(1 \pm \frac{\Delta y}{y}\right)^{-1}$ ,to first power in $\frac{\Delta y}{y}$ , is $1 \mp \frac{\Delta y}{y}$ .The relative errors in independent variables are always added. So the error in z will be $\Delta z = \left(\frac{\Delta x}{x} + \frac{\Delta y}{y}\right)$ The above derivation makes the assumption that $\frac{\Delta x}{x} \ll 1, \frac{\Delta y}{y} \ll 1$ . Therefore, the higher power of these quantities are neglected.