Physics · Units, Dimensions & Error Analysis

JEE Main 2025 — 8 April, Evening Shift — Question 55

A quantity $Q$ is formulated as $X^{-2} Y^{+\frac{3}{2}} Z^{-\frac{2}{5}}, X, Y$ and $Z$ are independent parameters which have fractional errors of $0.1,0.2$ and 0.5 , respectively in measurement. The maximum fractional error of $Q$ is

Option A:
0.1
Option B:
0.6
Option C:
0.7
Correct
Option D:
0.8

Answer: C

Step-by-step solution

$\frac{\Delta Q}{Q}=-2 \frac{( \pm \Delta x)}{x}+\frac{3}{2} \frac{( \pm \Delta y)}{y}-\frac{2}{5} \frac{( \pm \Delta z)}{z}$

For maximum fractional error $\begin{aligned} \frac{\Delta Q}{Q} & =\frac{2 \Delta x}{x}+\frac{3}{2} \frac{\Delta y}{y}+\frac{2}{5} \frac{\Delta z}{z} \\ & =2 \times 0.1+\frac{3}{2} \times 0.2+\frac{2}{5} \times 0.5 \end{aligned}$ $=0.7$

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Exam: JEE Main 2025
Paper: 8 April, Evening Shift
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Significant Figures and Error Analysis