A physical quantity A can be determined by measuring parameters B, C, D and E using the relation A = Bα CβDγ Eδ. If the maximum errors in the measurement are b%, c%, d% and e% then maximum error in the value of A is (a) (α b + β c - γ d - δ e)% (b) (b + c - d - e)% (c) (α b + β c + γ d + δ e)% (d) (b + c + d + e)%

Answer: (c). For A = Bα CβDγ Eδ, maximum relative errors always add, each multiplied by its power. (Δ A)/(A) = α(Δ B)/(B) + β(Δ C)/(C) + γ(Δ D)/(D) + δ(Δ E)/(E) Errors in the denominator are also added, never subtracted. So the answer is (c) (α b + β c + γ d + δ e)%.

A physical quantity A can be determined by measuring parameters B, C… | MHT CET 2025 (21 Apr, Shift 1)

Q50MHT CET 2025 · 21 APR · SHIFT 1Medium

Errors in Measurement

A physical quantity A can be determined by measuring parameters $B, C, D$ and E using the relation $A = \frac{B^{\alpha} C^{\beta}}{D^{\gamma} E^{\delta}}$ . If the maximum errors in the measurement are $b\%,\ c\%,\ d\%$ and $e\%$ then maximum error in the value of A is

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Answer: (c)

For $A = \frac{B^{\alpha} C^{\beta}}{D^{\gamma} E^{\delta}}$ , maximum relative errors always add, each multiplied by its power.
$\frac{\Delta A}{A} = \alpha\frac{\Delta B}{B} + \beta\frac{\Delta C}{C} + \gamma\frac{\Delta D}{D} + \delta\frac{\Delta E}{E}$
Errors in the denominator are also added, never subtracted.
So the answer is (c) $(\alpha b + \beta c + \gamma d + \delta e)\%$ .

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Errors in Measurement question from MHT CET 2025 (21 Apr, Shift 1)

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