GATE EE 2020 Set 1 — Question 12
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumDefinite & Improper IntegralsCalculusEngineering MathematicsFourier Series
Engineering Mathematics → Calculus → Definite & Improper Integrals
Last updated
Question
Which of the following is true for all possible non-zero choices of integers , or all possible non-zero choices of real numbers , as applicable?
Correct answer
(C) (1)/(2π) ∫_(-π)^(π) sin pθ cos qθ dθ = 0
Solution
Check each option against all admissible choices; one counterexample is enough to rule an option out.(A) are non-zero integers with , but is allowed. Then andSo (A) is not true for all choices.(B) Take , . The integrand is even, soSo (B) is false.(C) satisfies , so it is odd for every real . The integral of an odd function over the symmetric interval is zero:This holds for all admissible , so (C) is always true.(D) Take (allowed, since ). Then , whose average over tends to as , not 0. So (D) is false.Answer: (C)
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 EE 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.
More questions on Calculus
2026 Set 1 Q14Consider the following differential equation:…2026 Set 1 Q30Two matrices and have a common eigenvalue , and the same corresponding…2026 Set 1 Q32Given that , the integral…2026 Set 1 Q35 is an skew-symmetric matrix with real-valued entries, and is an…2026 Set 1 Q36A time-limited waveform is specified as follows:…