A) (\[{{b}_{1}}\,+\,{{c}_{1}}\,+\,{{d}_{1}}\,+\,{{e}_{1}}\])%
B) (\[{{b}_{1\,}}\,+\,{{c}_{1}}\,-\,{{d}_{1}}\,-\,{{e}_{1}}\])%
C) (\[\alpha {{b}_{1}}\,+\,\beta {{c}_{1}}\,-\,\gamma {{d}_{1}}\,-\delta {{e}_{1}}\])%
D) (\[\alpha {{b}_{1}}+\,\beta {{c}_{1}}\,+\,\gamma {{d}_{1}}\,+\,\delta {{e}_{1}}\])%
Correct Answer: D
Solution :
\[a={{b}^{\alpha }}\,{{c}^{\beta }}/{{d}^{\gamma }}\,{{e}^{\delta }}\] So maximum error in a is given by \[{{\left( \frac{\Delta a}{a}\times 100 \right)}_{\max }}=\alpha \,.\,\frac{\Delta b}{b}\times 100+\beta \,.\,\frac{\Delta c}{c}\times 100\]\[+\gamma \,.\,\frac{\Delta d}{d}\times 100+\delta \,.\,\frac{\Delta e}{e}\times 100\] \[=\left( \alpha {{b}_{1}}+\beta {{c}_{1}}+\gamma {{d}_{1}}+\delta {{e}_{1}} \right)%\]
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