In the measurement of a physical quantity `X = (A^(2) B)/(C^(1//3) D^(3))`. The percentage erros introduced in the measurments of the quantities `A,B,C` and `D` are `2%,2%,4%` and `5%` respectively. Then the minimum amount of percentage of error in the meaurement fo `X` is contributed by

Explanation

`X=(A^(2)B)/(C^(1/3)D^(3))`
`(DeltaA)/(A)%=2%,(DeltaB)/(B)%=2%,`
`(DeltaC)/(C)%=4%,(DeltaD)/(D)%=5%`
`(DeltaX)/(X)=2(DeltaA)/(A)÷(DeltaB)/(B)+(1)/(3)(DeltaC)/(C)+3(DeltaD)/(D)`
Percentage error in `X=(DeltaX)/(X) xx 100`
`=2(DeltaA)/(A) xx 100+(DeltaB)/(B) xx 100+(1)/(3)(DeltaC)/(C)+3 xx (DeltaD)/(D)`
`=(2 xx 2)+2+((1)/(3) xx 4)+(3 xx 5)=22.34%`
`:.` The minimum amount of error is contributed.