A physical parameter $a$ can be determined by measuring the parameters b, c, d and e using the relation $a = b^{α} c^{β} / d^{γ} e^{δ}$ . If the maximum errors in the measurement of b, c, d and e are $b_{1} %, c_{1} %, d_{1} % and e_{1} %$ , then the maximum error in the value of $a$ determined by the experiment is

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$(b_{1} + c_{1} + d_{1} + e_{1}) %$

$(b_{1} + c_{1} - d_{1} - e_{1}) %$

$(α b_{1} + β c_{1} - γ d_{1} - δ e_{1}) %$

$(a b_{1} + β c_{1} + γ d_{1} + δ e_{1}) %$

answer is D.

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Detailed Solution

$a = b^{α} c^{β} / d^{γ} e^{δ}$

So, maximum error in $a$ is given by

$\begin{matrix} {(\frac{Δ a}{a} \times 100)}_{max} = α \cdot \frac{Δ b}{b} \times 100 + β \cdot \frac{Δ c}{c} \times 100 \\ + γ \cdot \frac{Δ d}{d} \times 100 + δ \cdot \frac{Δ e}{e} \times 100 \\ = (α b_{1} + β c_{1} + γ d_{1} + δ e_{1}) % \end{matrix}$