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JEE Main 2025 (8 Apr, Shift 2) · Errors in Measurement

Errors in Measurement question from JEE Main 2025 (8 Apr, Shift 2)

Q53JEE Main 2025 · 8 APR · SHIFT 2Medium

Errors in Measurement

A quantity Q is formulated as X−2Y+32Z−25X^{-2} Y^{+\frac{3}{2}} Z^{-\frac{2}{5}}. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is

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Answer: (c)

  1. Q=X−2Y3/2Z−2/5Q = X^{-2} Y^{3/2} Z^{-2/5}; magnitudes of powers multiply the fractional errors and add.
  2. ΔQQ=2(0.1)+32(0.2)+25(0.5)\frac{\Delta Q}{Q} = 2(0.1) + \frac{3}{2}(0.2) + \frac{2}{5}(0.5)
  3. =0.2+0.3+0.2=0.7= 0.2 + 0.3 + 0.2 = 0.7
  4. So the answer is (c) 0.7.
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