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Question

Given A=xpyqzr. The percentage errors in measurement of x,y and z are 1 %, 0.5 % and 2% respectively. If p=3,q=2 and r=1 then the maximum percentage error in A is

A
5 %
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B
6 %
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C
3 %
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D
None of these
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Solution

The correct option is B 6 %
Given, A=xpyqzr
Take ln and then differentiate , ΔAA=±(pΔxx+qΔyy+rΔzz)
Thus the maximum percentage error in A:
ΔAA×100=pΔxx×100+qΔyy×100+rΔzz×100=(3×1)+(2×0.5)+(1×2)=6 %

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