Engineering Mathematics-II Unit 4 – Complex Variable – Differentiation: AKTU previous year questions
22 AKTU questions from Unit 4 (Complex Variable – Differentiation) 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 Analytic Functions (15 times); 15 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 4 previous year questions
- Show that the following function is harmonic: h(x, y) = x² + xy − y² (2 marks, 2025, Analytic Functions)
- If f(z) = u + iv is analytic, and u − v = (e^y − cos x + sin x) / (cosh y − cos x), find f(z) such that f(π/2) = (3−i)/2. (7 marks, 2025, Analytic Functions)
- If f(z) = { x³y⁵(x+iy) / (x⁶+y¹⁰) ; z ≠ 0 and 0 ; z = 0 }, show that f(z) is not analytic at z = 0 even if Cauchy-Riemann equations are satisfied at origin. (7 marks, 2025, Analytic Functions)
- Show that f(z) = z|z| is nowhere analytic. (7 marks, 2025, Analytic Functions)
- Find the harmonic conjugate of u = x³ − 3xy² + 3x² − 3y² and hence find the analytic function f(z) = u + iv. (7 marks, 2024, Analytic Functions)
- Find the analytic function f(z) = u + iv given u + v = (x − y)(x² + 4xy + y²) using Milne's Thomson method. (7 marks, 2024, Analytic Functions)
- Define analytic function. Show that f(z) = |z|² is not analytic anywhere except at origin. (7 marks, 2024, Analytic Functions)
- Show that the function f(z) = |z|² is not analytic at origin. (2 marks, 2023, Analytic Functions)
- Find the invariant points of the transformation w = (2z + 6) / (z + 7). (2 marks, 2023, Conformal Mapping)
- Show that the function f(z) defined by f(z) = x³y⁵(x + iy) / (x⁶ + y¹⁰), z ≠ 0, f(0) = 0 is not analytic at the origin even though it satisfies Cauchy-Riemann equations at the origin. (7 marks, 2023, Analytic Functions)
- Determine an analytic function f(z) = u + iv in terms of z whose real part u(x, y) is eˣ(x cos y − y sin y) and f(1) = e. (7 marks, 2023, Analytic Functions)
- Find the bilinear transformation which maps the points z = 0, −1, i onto w = i, 0, ∞. Also, find the image of the unit circle |z| = 1. (7 marks, 2023, Conformal Mapping)
Most asked Unit 4 topics
- Analytic Functions – asked 15 times
- Conformal Mapping – asked 7 times
- Complex Variable Functions
Unit 4 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 4 in every paper
- 15 questions were asked again in a later year
Unit 4 questions year by year
- 2025: 4 Unit 4 questions asked (23 marks across that year's papers)
- 2024: 3 Unit 4 questions asked (21 marks across that year's papers)
- 2023: 5 Unit 4 questions asked (25 marks across that year's papers)
- 2022: 5 Unit 4 questions asked (34 marks across that year's papers)
- 2019: 5 Unit 4 questions asked (34 marks across that year's papers)