Engineering Mathematics-II Unit 3 – Sequence and Series: AKTU previous year questions
22 AKTU questions from Unit 3 (Sequence and Series) asked in 2019–2025, tagged by marks, year and topic. In short: about 27 marks of every paper come from this unit; the most asked topic is Fourier Series (10 times); 16 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
Unit 3 previous year questions
- Test the convergence of the following sequence: a_n = { 1 if n = 2^p for some p ∈ N; 1/n otherwise } (2 marks, 2025, Sequence and Series Basics)
- Test the convergence of the following series: ∑ [1·3·5…(2n−1) / 2·4·6…(2n)] x^(2n), n=1 to ∞ (7 marks, 2025, Tests for Convergence)
- Examine the convergence of the following series: 1 + (α+1)/(β+1) + (α+1)(2α+1)/[(β+1)(2β+1)] + (α+1)(2α+1)(3α+1)/[(β+1)(2β+1)(3β+1)] + … (7 marks, 2025, Tests for Convergence)
- Obtain the Fourier series for the function f(x) = x², −π ≤ x ≤ π. Hence, or otherwise show that 1/1² + 1/2² + 1/3² + 1/4² + … = ∑(1/n²) = π²/6 (7 marks, 2025, Fourier Series)
- What is the constant term (a₀) in the Fourier series expansion of f(x) = x² in (−π, π)? (2 marks, 2024, Fourier Series)
- Test the convergence of the series: ∑ [1 / (n log n)²] (7 marks, 2024, Tests for Convergence)
- Find half range Fourier sine series of f(x) = x(π − x) in (0, π). (7 marks, 2024, Fourier Series)
- Test convergence of the series: ∑ (n!)² / (2n)! using Raabe's test. (7 marks, 2024, Tests for Convergence)
- Discuss the convergence of sequence {uₙ}, where uₙ = sin(1/n). (2 marks, 2023, Sequence and Series Basics)
- Test the convergence of following series: 1/(1.2.3) + x/(4.5.6) + x²/(7.8.9) + ..., Where x is a real number. (7 marks, 2023, Tests for Convergence)
- Find a Fourier series to represent f(x) = x − x², −π ≤ x ≤ π. Hence, show that 1/1² − 1/2² + 1/3² − 1/4² + ... = π²/12. (7 marks, 2023, Fourier Series)
- Find the half range cosine series for the function f(x) = (x − 1)² in the interval (0, 1). Hence, prove that 1/1² + 1/3² + 1/5² + 1/7² + ... = π²/8. (7 marks, 2023, Fourier Series)
Most asked Unit 3 topics
- Fourier Series – asked 10 times
- Tests for Convergence – asked 8 times
- Sequence and Series Basics – asked 4 times
Unit 3 question pattern
- 2-mark questions: 7 asked in 2019–2025
- 7-mark questions: 9 asked in 2019–2025
- 10-mark questions: 6 asked in 2019–2025
- About 27 marks from Unit 3 in every paper
- 16 questions were asked again in a later year
Unit 3 questions year by year
- 2025: 4 Unit 3 questions asked (23 marks across that year's papers)
- 2024: 4 Unit 3 questions asked (23 marks across that year's papers)
- 2023: 4 Unit 3 questions asked (23 marks across that year's papers)
- 2022: 5 Unit 3 questions asked (34 marks across that year's papers)
- 2019: 5 Unit 3 questions asked (34 marks across that year's papers)