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GATE 2020 CE (CE1) – Question 13

Engineering Mathematics · Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs · 1 mark · Multiple choice

True ln(2) is 0.69. Estimate ln(2) by linear interpolation between ln(1) and ln(6). Find absolute percentage error, rounded to the nearest integer.

  1. 35
  2. 48
  3. 69
  4. 84

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Correct answer: (B) 48

Explanation

Linear interpolation gives $\ln1+(2-1)(\ln6-\ln1)/(6-1)=\ln6/5=0.358352$. Absolute percentage error is $|0.69-0.358352|/0.69\times100=48.065\%$. Rounded, **48%, B**.