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JEE Main 2017 (9 Apr, Shift 1) · Errors in Measurement

Errors in Measurement question from JEE Main 2017 (9 Apr, Shift 1)

Q101JEE Main 2017 · 9 APR · SHIFT 1Medium

Errors in Measurement

A physical quantity P is described by the relation

P = a1/21/2 b2 c3 d−4{}^{-4}

If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be:

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Answer: (c)

  1. P=a1/2b2c3d−4⇒ΔPP=12Δaa+2Δbb+3Δcc+4ΔddP = a^{1/2} b^2 c^3 d^{-4} \Rightarrow \frac{\Delta P}{P} = \frac{1}{2}\frac{\Delta a}{a} + 2\frac{\Delta b}{b} + 3\frac{\Delta c}{c} + 4\frac{\Delta d}{d}
  2. =12(2)+2(1)+3(3)+4(5)=1+2+9+20=32%= \frac{1}{2}(2) + 2(1) + 3(3) + 4(5) = 1 + 2 + 9 + 20 = 32\%
  3. So the answer is (c) 32%32\%.
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