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^2B^(1//2))/(C^(1//3) D^3)`
In X = 2ln `A +1/2 lnB -1/3 ln C -3ln D`
Differentiating `((dX)/X)_("max") =2(dA)/A+1/2(dB)/B+1/3(dC)/C+(3dC)/D`
Error `X_("max") = 2xx1 +2/2 +1/3 xx 3 + 3 xx 4 = 16%`