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

Answer

B

Explanation

`x=(A^(2)B^(1/2))/(C^(1/3)D^(3))`
`(trianglex)/(x)=(2triangleA)/(A)+(1)/(2)(triangleB)/(B)+(1)/(3)(triangleC)/(C )xx3(triangleD)/(D)`
`(trianglex )/(x)xx100=2(1%)+(1)/(2)(2%)+(1)/(3)(3%)+3(4%)=16%`