GATE CE 2023 Set 1 — Question 25
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+1 / -0MediumFourier SeriesPartial Differential EquationsEngineering Mathematics
Engineering Mathematics → Partial Differential Equations → Fourier Series
Last updated
Question
The following function is defined over the interval :If it is expressed as a Fourier series,which options amongst the following are true?
Correct answer
(B) aₙ, n = 1, 2, …, ∞ depend on q; (C) bₙ, n = 1, 2, …, ∞ depend on p
Solution
The function is defined on .
1.The term is an even function.
2.The term is an odd function.
In a Fourier series:- The sine coefficients are given by . Since is an odd function, the integral of (even odd) is zero, and the integral of (odd odd) is non-zero. Thus, depends only on the odd part of , which is . Therefore, depends on .
- The cosine coefficients are given by . Since is an even function, the integral of (even even) is non-zero, and the integral of (odd even) is zero. Thus, depends only on the even part of , which is . Therefore, depends on .
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.