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GATE 2016 ME (ME2) – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Which curve represents $y=\ln(|e^{[|\sin(|x|)|]}|)$ for $|x|<2\pi$? Here x is the abscissa and y the ordinate.

Diagram for GATE 2016 ME (ME2) question 10
  1. Curve A
  2. Curve B
  3. Curve C
  4. Curve D

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Show answer and explanation

Correct answer: (C) Curve C

Explanation

The exponential is positive, so its outer absolute value has no effect. Logarithm cancels the exponential, leaving |sin(|x|)|=|sinx|. The function is nonnegative, even, zero at integer multiples ofπ and peaks at odd multiples ofπ/2. This is graph **C**.