The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = P³ Q²√(RS) The maximum percentage error in the value of A will be: (a) 6.0% (b) 7.5% (c) 8.5% (d) 6.5%

Answer: (d). Official JEE form: A = (P³ Q²)/(√(R) S), so (Δ A)/(A) = 3(Δ P)/(P) + 2(Δ Q)/(Q) + 1/2(Δ R)/(R) + (Δ S)/(S) = 3(0.5) + 2(1) + 1/2(3) + 1.5 = 1.5 + 2 + 1.5 + 1.5 = 6.5% So the answer is (d) 6.5%.

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3%… | JEE Main 2018 (16 Apr, Shift 1)

Q98JEE Main 2018 · 16 APR · SHIFT 1Medium

Errors in Measurement

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = $\frac{P^{3} Q^{2}}{\sqrt{RS}}$

The maximum percentage error in the value of A will be:

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Answer: (d)

Official JEE form: $A = \frac{P^3 Q^2}{\sqrt{R}\, S}$ , so $\frac{\Delta A}{A} = 3\frac{\Delta P}{P} + 2\frac{\Delta Q}{Q} + \frac{1}{2}\frac{\Delta R}{R} + \frac{\Delta S}{S}$
$= 3(0.5) + 2(1) + \frac{1}{2}(3) + 1.5 = 1.5 + 2 + 1.5 + 1.5 = 6.5\%$
So the answer is (d) $6.5\%$ .

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Errors in Measurement question from JEE Main 2018 (16 Apr, Shift 1)

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