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JEE Main 3-April-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 3-April-2025 Paper - Shift 24 Marks
Question
A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows
$\mathrm{C}=\frac{\mathrm{pq}^{2}}{\mathrm{r}^{3} \sqrt{\mathrm{~s}}}$
The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \% 3 \%$ and $2 \%$ respectively.
The percentage error in the measurement of C will be __________ %.
✓

Answer

15
$\mathrm{C}=\mathrm{P}^{1} \mathrm{q}^{2} \mathrm{r}^{-3} \mathrm{~s}^{1 / 2}$
$\left(\frac{\mathrm{dC}}{\mathrm{C}}\right)_{\max }=\frac{\mathrm{dP}}{\mathrm{P}}+\frac{2 \mathrm{dq}}{\mathrm{q}}+\frac{3 \mathrm{dr}}{\mathrm{r}}+\frac{1}{2} \frac{\mathrm{ds}}{\mathrm{s}}$
$=\left(1+2 \times 2+3 \times 3+\frac{1}{2} \times 2\right) \%$
$=15 \%$

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