A physical quantity C is related to four other quantities p, q, r and s as follows C=\fracp q^2r^3 \sqrts The percentage errors in the measurement of p, q, r and s are 1 \%, 2 \%, 3 \% and 2 \% , respectively. The percentage error in the measurement of C will be \underline\hspace2cm %

Units and Measurements PYQ — JEE Main 2025 · 3 Apr · Shift 2 · Q75 with Solution

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Correct answer: 15

C=\frac{p q^2}{r^3\sqrt{s}}=p^1 q^2 r^{-3} s^{-1/2}

For multiplication/division with powers, the maximum percentage error is the sum of absolute fractional errors multiplied by the powers:

\frac{\Delta C}{C}\times 100 = 1\left(\frac{\Delta p}{p}\times 100\right)+2\left(\frac{\Delta q}{q}\times 100\right)+3\left(\frac{\Delta r}{r}\times 100\right)+\frac{1}{2}\left(\frac{\Delta s}{s}\times 100\right)

For $p$ : $1\times 1\%=1\%$
For $q^2$ : $2\times 2\%=4\%$
For $r^3$ : $3\times 3\%=9\%$
For $\sqrt{s}=s^{1/2}$ in denominator: contribution is $\frac{1}{2}\times 2\%=1\%$

1+4+9+1=15

Hence,

\boxed{15\%}