Mathematics-IV Unit 1 – Partial Differential Equations: AKTU previous year questions
46 AKTU questions from Unit 1 (Partial Differential Equations) asked in 2021–2026, tagged by marks, year and topic. In short: about 28 marks of every paper come from this unit; the most asked topic is Higher Order Linear PDE (17 times); 26 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 1 previous year questions
- What is a linear partial differential equation of first order? Write its general form. (2 marks, 2026, Origin of PDE)
- State Charpit's method and mention when it is used. (2 marks, 2026, Charpit's Non-Linear PDE Method)
- Solve the linear partial differential equation (y + z) ∂z/∂x + (x + z) ∂z/∂y = x + y using Lagrange's method. (7 marks, 2026, Lagrange's Linear PDE Method)
- Solve the non-linear partial differential equation p² + q² = z where p = ∂z/∂x, q = ∂z/∂y using Charpit's method. (7 marks, 2026, Charpit's Non-Linear PDE Method)
- Solve the partial differential equation (D² - 4DD' + 4D'²)z = e^(2x+y). (7 marks, 2026, Higher Order Linear PDE)
- Solve the PDE yzp - xzq = xy. (2 marks, 2025, Lagrange's Linear PDE Method)
- Form the partial differential equation by eliminating arbitrary function from the following: z = f(x + it) + g(x - it). (2 marks, 2025, Origin of PDE)
- Use the method of characteristics to solve the first order PDE u_x - yu = 0; u(0, y) = 1. (2 marks, 2025, Lagrange's Linear PDE Method)
- Solve the following differential equation using Lagrange's equation: (x² - yz)p + (y² - zx)q = z² - xy. (7 marks, 2025, Lagrange's Linear PDE Method)
- Solve: r - 4s + 4t + p - 2q = e^(x+y) cos(2x + 3y). (7 marks, 2025, Higher Order Linear PDE)
- Solve the partial differential equation: ∂²z/∂x² - ∂²z/∂y² = tan³x·tany − tanx·tan³y. (7 marks, 2025, Higher Order Linear PDE)
- Solve: (x² – y² – yz)p + (x² – y² – zx)q = z(x – y). (7 marks, 2025, Lagrange's Linear PDE Method)
Most asked Unit 1 topics
- Higher Order Linear PDE – asked 17 times
- Lagrange's Linear PDE Method – asked 13 times
- Charpit's Non-Linear PDE Method – asked 10 times
Unit 1 question pattern
- 2-mark questions: 17 asked in 2021–2026
- 7-mark questions: 14 asked in 2021–2026
- 10-mark questions: 15 asked in 2021–2026
- About 28 marks from Unit 1 in every paper
- 26 questions were asked again in a later year
Unit 1 questions year by year
- 2026: 5 Unit 1 questions asked (25 marks across that year's papers)
- 2025: 9 Unit 1 questions asked (48 marks across that year's papers)
- 2024: 7 Unit 1 questions asked (39 marks across that year's papers)
- 2023: 10 Unit 1 questions asked (68 marks across that year's papers)
- 2022: 10 Unit 1 questions asked (68 marks across that year's papers)
- 2021: 5 Unit 1 questions asked (34 marks across that year's papers)