| A physical quantity P is described by the relation \[P={{a}^{1/2}}\,{{b}^{2}}{{c}^{3}}{{d}^{-4}}\] |
| If the relative errors in the measurement of \[a,\,b,\,c\] and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be [JEE Online 09-04-2017] |
A) 12%
B) 8%
C) 25%
D) 32%
Correct Answer: D
Solution :
| [d] \[\frac{\Delta P}{P}=\frac{1}{2}\,\frac{\Delta a}{a}\,+2\,\frac{\Delta b}{b}\,+3\,\frac{\Delta c}{c}\,+4\,\frac{\Delta d}{d}\] |
| \[=\frac{1}{2}\,\times 2+2\times 1+3\times 3+4\times 5\] |
| \[=32%\] |
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