Engineering Mathematics-II Unit 5 – Complex Variable – Integration: AKTU previous year questions
24 AKTU questions from Unit 5 (Complex Variable – Integration) asked in 2019–2025, tagged by marks, year and topic. In short: about 28 marks of every paper come from this unit; the most asked topic is Complex Integration (9 times); 19 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 5 previous year questions
- Find the residue at the simple pole of the following function: f(z) = 8z³ / [(z−1)(z+1)³] (2 marks, 2025, Residues and Residue Theorem)
- Evaluate the following integral using contour integration: ∫_c (12z−7) / [(z−1)²(2z+3)] dz where c is the circle |z| = 2. (7 marks, 2025, Complex Integration)
- State Cauchy's Integral Theorem. Verify Cauchy's theorem for f(z) = e^(iz) integrated along the boundary of the rectangle 1−i, 1+i, −1+i, −1−i in counterclockwise direction. (7 marks, 2025, Complex Integration)
- Use contour integral to evaluate: ∫₀^(2π) cos 2θ / (5 + 4cosθ) dθ (7 marks, 2025, Residues and Residue Theorem)
- Find the residue of f(z) = cos z / [z(z+5)] at z = 0 (2 marks, 2024, Residues and Residue Theorem)
- Evaluate ∫_C (z² + 1) / (z² − 1) dz using Cauchy Integral Formula where C: |z − 1| = 1 (2 marks, 2024, Complex Integration)
- Define Laurent's series. (2 marks, 2024, Taylor and Laurent Series)
- Evaluate ∮_C e^(2z) / [(z−1)(z−2)] dz where C: |z| = 3 using Cauchy Integral Formula. (7 marks, 2024, Complex Integration)
- Expand f(z) = (z² − 1) / [(z + 2)(z + 3)] in Laurent's series valid for |z| > 3. (7 marks, 2024, Taylor and Laurent Series)
- Evaluate ∮_C (z + 4) / (z² + 2z + 5) dz where C: |z + 1 − i| = 2 using Cauchy Integral Formula. (7 marks, 2024, Complex Integration)
- Classify the singularity of f(z) = e^(1/z) / z. (2 marks, 2023, Taylor and Laurent Series)
- Using Cauchy-integral formula, evaluate ∮_C sin 2z / [(z + 3)(z + 1)²] dz, where C is a rectangle with vertices at 3 ± i, −2 ± i. (7 marks, 2023, Complex Integration)
Most asked Unit 5 topics
- Complex Integration – asked 9 times
- Taylor and Laurent Series – asked 8 times
- Residues and Residue Theorem – asked 7 times
Unit 5 question pattern
- 2-mark questions: 9 asked in 2019–2025
- 7-mark questions: 9 asked in 2019–2025
- 10-mark questions: 6 asked in 2019–2025
- About 28 marks from Unit 5 in every paper
- 19 questions were asked again in a later year
Unit 5 questions year by year
- 2025: 4 Unit 5 questions asked (23 marks across that year's papers)
- 2024: 6 Unit 5 questions asked (27 marks across that year's papers)
- 2023: 4 Unit 5 questions asked (23 marks across that year's papers)
- 2022: 5 Unit 5 questions asked (34 marks across that year's papers)
- 2019: 5 Unit 5 questions asked (34 marks across that year's papers)