In an experiment, the percentage of error occurred in the 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=(A^(2)B^(1//2))/(C^(1//3)D^(3))`, will be

Options

A. `10%`
B. `((3)/(13))%`
C. `16%`
D. `-10%`

Answer

C

Explanation

`x=(A^(2)B^(1//2))/(C^(1//3)D^(3))`
`lnx=2lnA+(1)/(2)lnB-(1)/(3)lnC-2lnD`
Differenting
`((dx)/x)_(max)=2(dA)/(A)+(1)/(2)(dB)/(B)+(1)/(3)(dC)/(C)+(3dD)/(D)`
error xmas `=2xx1+(2)/(2)+(1)/(3)xx3+3xx4=+16%`