If Z = (A²B³)/(C⁴), then the relative error in Z will be: (a) (Δ A)/(A) + (Δ B)/(B) + (Δ C)/(C) (b) (2Δ A)/(A) + (3Δ B)/(B) - (4Δ C)/(C) (c) (2Δ A)/(A) + (3Δ B)/(B) + (4Δ C)/(C) (d) (Δ A)/(A) + (Δ B)/(B) - (Δ C)/(C)

Answer: (c). For a product or quotient, relative errors always add, each multiplied by the magnitude of its power. Z = (A²B³)/(C⁴) ⇒ (Δ Z)/(Z) = (2Δ A)/(A) + (3Δ B)/(B) + (4Δ C)/(C) So the answer is (c).

If Z = (A²B³)/(C⁴), then the relative error in Z will be: | JEE Main 2022 (25 Jun, Shift 1)

Q74JEE Main 2022 · 25 JUN · SHIFT 1Easy

Errors in Measurement

If $Z = \frac{A^2B^3}{C^4}$ , then the relative error in Z will be:

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Answer: (c)

For a product or quotient, relative errors always add, each multiplied by the magnitude of its power.
$Z = \frac{A^2B^3}{C^4} \Rightarrow \frac{\Delta Z}{Z} = \frac{2\Delta A}{A} + \frac{3\Delta B}{B} + \frac{4\Delta C}{C}$
So the answer is (c).

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