JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions JEE PYQ - Mathematical Tools Units and Dimensions

The percentage errors in quantities P, Q, R and S are \[0.5%,1%,3%\]and\[1.5%\] respectively in the measurement of a physical quantity.\[A=\frac{{{P}^{3}}{{Q}^{2}}}{\sqrt{RS}}.\] The maximum percentage error in the value of will be

A) \[8.5%\]

B) \[6.0%\]

C) \[7.5%\]

D) \[6.5%\]

Correct Answer: D

Solution :

[d] Percentage error

\[\frac{\Delta \Alpha }{A}\times 100=3\frac{\Delta P}{P}\times 100+\]

\[2\frac{\Delta Q}{Q}+\frac{1}{2}\frac{\Delta R}{R}\times 100+\frac{\Delta S}{S}\times 100\]

\[=3\times 0.5+2\times 1+0.5\times 3+1.5=6.5\]