In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = \(\frac{A^2 B^{1/2}}{C^{1/3} D^3}\) will be : 

16%

X = \(\frac{A^2B^{\frac{1}{2}}}{C^{\frac{1}{3}}{D^3}}\)

% Error : \(\frac{\Delta X}{X} × 100\) = \(2\frac{\Delta A}{A} × 100\) + \(\frac{1}{2} \frac{\Delta B}{B} × 100\) + \(\frac{1}{3} \frac{\Delta C}{C} × 100\) +  \(3\frac{\Delta D}{D} × 100\)

\(\frac{\Delta X}{X} × 100\) = 2 x 1% + \(\frac{1}{2}\) x 2% + \(\frac{1}{3}\) x 3% 3 x 4% = 16%