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GATE 2026 MN – Question 29

Engineering Mathematics · Calculus · 1 mark · Multiple select

For Fourier series on a symmetric interval, which statements are correct?

  1. An even function’s series contains only cosine terms.
  2. An odd function’s series contains only cosine terms.
  3. An odd function’s series contains only sine terms.
  4. An even function’s series contains only sine terms.

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Correct answer: (A) An even function’s series contains only cosine terms.; (C) An odd function’s series contains only sine terms.

Explanation

Integrating an even function times an odd sine over a symmetric interval gives zero, so its sine coefficients vanish. An odd function has zero mean and zero cosine coefficients, leaving sine terms. Therefore A,C; the constant term is included with the even/cosine part.

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