A physical quantity Q is found to depend on quantities a, b, c by the relation Q=frac{a^4 b^3}{c^2}. The percentage error in a, b and

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

c $ \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}} $ $ \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) $ $ \% \text { error in } \mathrm{Q}=4 \times 3 \%+3 \times 4 \%+2 \times 5 \% $ $=12 \%+12 \%+10 \% $ $=34 \%$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

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

A $66 \%$
B $43 \%$
C $34 \%$
D $14 \%$

JEE MAIN 2024, Diffcult

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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