MHTCET 5 May 2025 Shift 2 Paper

Concept:The maximum percentage error in a quantity expressed as a product of powers is the sum of each exponent multiplied by the percentage error of the corresponding measured quantity.Explanation:The given relation is $X = a^2 b^3 c^{5/2} d^{-2}$.The general error formula is:$\frac{\Delta X}{X} \times 100 = 2\left(\frac{\Delta a}{a} \times 100\right) + 3\left(\frac{\Delta b}{b} \times 100\right) + \frac{5}{2}\left(\frac{\Delta c}{c} \times 100\right) + 2\left(\frac{\Delta d}{d} \times 100\right)$Errors always add up, so the negative exponent of $d$ contributes with its magnitude, which is $2$.Now substitute the given percentage errors:Contribution from $a$: $2 \times 1\% = 2\%$Contribution from $b$: $3 \times 2\% = 6\%$Contribution from $c$: $\frac{5}{2} \times 2\% = 5\%$Contribution from $d$: $2 \times 4\% = 8\%$Therefore, total percentage error in $X$ is:$\frac{\Delta X}{X} \times 100 = (2 + 6 + 5 + 8)\% = 21\%$Answer:The percentage error in the measurement of $X$ is $21\%$.Hence, the correct option is C.