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Mathematics in Physics

JEE Main level, single correct, medium

97 of 121

Question 97 of 121

A physical quantity z depends on four observables $a,b,c$ and $d$ , as $z=\dfrac{{a}^{2}{b}^{2/3}}{\sqrt{c}{d}^{3}}.$ The percentage of error in the measurement of $a,b,c$ and $d$ are $2%,1.5%,4%$ and $2.5%$ respectively. The percentage of error in $z$ is :

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Answer: (D) $14.5%$

\dfrac{\Delta t}{t}=\dfrac{2\Delta a}{a}+\dfrac{2}{3}\dfrac{\Delta b}{b}+\dfrac{1}{2}\dfrac{\Delta c}{c}+3\dfrac{\Delta d}{d}

=2\times 2+\dfrac{2}{3}\times 1.5+\dfrac{1}{2}\times 4+3\times 2.5

=4+1+2+7.5

=14.5%

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JEE Main 2025 Apr 2 Shift 1 question paper

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