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MHT CET 2025 (5 May, Shift 2) · Errors in Measurement

Errors in Measurement question from MHT CET 2025 (5 May, Shift 2)

Q46MHT CET 2025 · 5 MAY · SHIFT 2Medium

Errors in Measurement

A physical quantity ' X ' is related to four measurable quantities ' aa ', ' bb ', ' cc ' and ' dd ' as X=a2b3c5/2d−2X = a^{2} b^{3} c^{5/2} d^{-2}. The percentage error in the measurement of 'a', 'b', 'c' and 'd' are 1%, 2%, 2%1\%,\ 2\%,\ 2\% and 4%4\% respectively. The percentage error in measurement of quantity ' X ' is

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Answer: (c)

  1. For X=a2b3c5/2d−2X = a^2b^3c^{5/2}d^{-2}: ΔXX=2Δaa+3Δbb+52Δcc+2Δdd\frac{\Delta X}{X} = 2\frac{\Delta a}{a} + 3\frac{\Delta b}{b} + \frac{5}{2}\frac{\Delta c}{c} + 2\frac{\Delta d}{d}
  2. =2(1)+3(2)+52(2)+2(4)=2+6+5+8=21%= 2(1) + 3(2) + \frac{5}{2}(2) + 2(4) = 2 + 6 + 5 + 8 = 21\%
  3. So the answer is (c) 21%21\%.
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