Mathematics in Physics

JEE Main level, single correct, medium

57 of 121

Question 57 of 121

A quantity Q is formulated as X−2Y+32Z−25⋅X,Y\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y} and Z are independent parameters which have fractional errors of 0.1,0.20.1,0.2 and 0.5 , respectively in measurement. The maximum fractional error of Q is

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Answer: (C) 0.7

 Fractional error =2ΔXX+32ΔYY+25ΔZZ=2(0.1)+32(0.2)+25(0.5)=0.2+0.3+0.2=0.7\begin{aligned} & \text { Fractional error }=2 \frac{\Delta X}{X}+\frac{3}{2} \frac{\Delta Y}{Y}+\frac{2}{5} \frac{\Delta Z}{Z} \\ & =2(0.1)+\frac{3}{2}(0.2)+\frac{2}{5}(0.5) \\ & =0.2+0.3+0.2=0.7\end{aligned}

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