In an experiment four quantities $a$, $b$, $c$ and $d$ are measured with percentage error $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{a^3 b^2}{cd}$. The percentage error in $P$ is

Given the physical quantity $P = \frac{a^3 b^2}{cd}$. The maximum percentage error in $P$ is determined by the sum of the percentage errors of the individual quantities multiplied by their respective powers. The formula for percentage error is: $\frac{\Delta P}{P} \times 100 = 3\left(\frac{\Delta a}{a} \times 100\right) + 2\left(\frac{\Delta b}{b} \times 100\right) + \left(\frac{\Delta c}{c} \times 100\right) + \left(\frac{\Delta d}{d} \times 100\right)$ Given the percentage errors are: $\frac{\Delta a}{a} \times 100 = 1\%$ $\frac{\Delta b}{b} \times 100 = 2\%$ $\frac{\Delta c}{c} \times 100 = 3\%$ $\frac{\Delta d}{d} \times 100 = 4\%$ Substituting these values into the error equation: $\% \text{ Error in } P = 3(1\%) + 2(2\%) + 1(3\%) + 1(4\%)$ $\% \text{ Error in } P = 3\% + 4\% + 3\% + 4\% = 14\%$.