Verified Solution • 2025–26 Session moderate

QJEEM24Phb001: JEE Main 2024 Physics - Class 11 JEEM24Phb001 Solution: A physical quantity is found to depend on quantities by the…

A physical quantity QQ is found to depend on quantities a,b,ca, b, c by the relation Q=a4b3c2Q=\frac{a^4 b^3}{c^2} . The percentage error in a,ba, b and cc are 3%,4%3 \%, 4 \% and 5%5 \% respectively. Then, the percentage error in QQ is :

Multiple Choice Options

  • A 43%
  • B 34%
  • C 66%
  • D 14%

Step-by-Step Verified Solution

amp;Q=a4 b3c2amp;ΔQQ=4Δaa+3Δbb+2Δcc\begin{aligned}& \mathrm{Q}=\frac{\mathrm{a}^4 \mathrm{~b}^3}{\mathrm{c}^2} \\& \frac{\Delta \mathrm{Q}}{\mathrm{Q}}=4 \frac{\Delta \mathrm{a}}{\mathrm{a}}+3 \frac{\Delta \mathrm{b}}{\mathrm{b}}+2 \frac{\Delta \mathrm{c}}{\mathrm{c}}\end{aligned}

ΔQQ×100=4(Δaa×100)+3(Δbb×100)+2(Δcc×100)\frac{\Delta \mathrm{Q}}{\mathrm{Q}} \times 100=4\left(\frac{\Delta \mathrm{a}}{\mathrm{a}} \times 100\right)+3\left(\frac{\Delta \mathrm{b}}{\mathrm{b}} \times 100\right)+2\left(\frac{\Delta \mathrm{c}}{\mathrm{c}} \times 100\right)

% error in Qamp;=4×3%+3×4%+2×5%amp;=12%+12%+10%amp;=34%\begin{aligned}\% \text { error in } \mathrm{Q} & =4 \times 3 \%+3 \times 4 \%+2 \times 5 \% \\& =12 \%+12 \%+10 \% \\& =34 \%\end{aligned}

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