JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Units & Measurement

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

Answer: (C)

Solution

For a product

Q = X^{a} Y^{b} Z^{c}

the maximum fractional error adds the magnitudes of the powers times the individual fractional errors:

\frac{Δ Q}{Q} = ∣ a ∣ \frac{Δ X}{X} + ∣ b ∣ \frac{Δ Y}{Y} + ∣ c ∣ \frac{Δ Z}{Z}

. Substituting the given exponents and errors,

\frac{Δ Q}{Q} = 2 (0.1) + \frac{3}{2} (0.2) + \frac{2}{5} (0.5) = 0.2 + 0.3 + 0.2

. The maximum fractional error in

Q

0.7

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option