Engineering Mathematics-II Unit 5 – Complex Variable – Integration: important questions for AKTU
Unit 5 (Complex Variable – Integration) questions that AKTU repeats most often. This unit carries about 28 marks per paper. Start with the repeated questions, then the most asked topics.
Most repeated Unit 5 questions
- Use contour integral to evaluate: ∫₀^(2π) cos 2θ / (5 + 4cosθ) dθ (7 marks, 2025, Residues and Residue Theorem) – also asked in 2019, 2022, 2023, 2024
- Expand f(z) = (z² − 1) / [(z + 2)(z + 3)] in Laurent's series valid for |z| > 3. (7 marks, 2024, Taylor and Laurent Series) – also asked in 2019, 2022, 2023, 2025
- 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) – also asked in 2022, 2023, 2024
Most important Unit 5 topic
- Complex Integration (Unit 5: Complex Variable – Integration) – asked 9 times in 2019, 2022, 2023, 2024, 2025
Most asked Unit 5 topics
- Complex Integration – asked 9 times
- Taylor and Laurent Series – asked 8 times
- Residues and Residue Theorem – asked 7 times
More 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)
- 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)
- 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)
Unit 5 syllabus topics
- Complex Integration
- Taylor and Laurent Series
- Residues and Residue Theorem