Engineering Mathematics-II (BAS203) AKTU previous year questions 2019–2025
Every Engineering Mathematics-II question from 5 AKTU papers, tagged by unit, topic and marks. A few recent questions from each unit are listed below; open the page to filter by unit, topic or mark type.
Unit 1: Ordinary Differential Equation of Higher Order – AKTU PYQs
- Find the general solution of the following differential equation: d³y/dx³ + dy/dx = 0 (2 marks, 2025, Linear ODE Constant Coefficients)
- Find the Particular Integral for the following differential equation: y'' − 8y' + 16y = e^(4x) (2 marks, 2025, Linear ODE Constant Coefficients)
- Find the general solution of the differential equation y'' − 2y' + 2y = x + e^x cos x (7 marks, 2025, Linear ODE Constant Coefficients)
- Find the general solution of the differential equation: x² d²y/dx² − x dy/dx + 4y = x sin(log x). (7 marks, 2025, Cauchy-Euler Equation)
- Solve the following set of simultaneous linear differential equations: dx/dt = 3x + 8y; dy/dt = −x − 3y (7 marks, 2025, Linear ODE Constant Coefficients)
Unit 2: Laplace Transform – AKTU PYQs
- Find Laplace Transform of f(t) = sin 2t cos 3t. (2 marks, 2025, Laplace Transform Fundamentals)
- Find inverse Laplace Transform of F(s) = (s−1)/(s²+3s+2). (2 marks, 2025, Inverse Laplace Transform)
- Solve the following differential equations using Laplace Transform: d³y/dt³ + 2d²y/dt² − dy/dt − 2y = 0; y(0) = 1, y'(0) = y''(0) = 2 (7 marks, 2025, Applications of Laplace Transform)
- Find the Laplace Transform of the following function: ∫₀ᵗ (eᵗ sin t / t) dt. (7 marks, 2025, Laplace Transform Fundamentals)
- Use convolution theorem to evaluate L⁻¹[ p² / (p²+4)(p²+9) ] (7 marks, 2025, Inverse Laplace Transform)
Unit 3: Sequence and Series – AKTU PYQs
- 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)
Unit 4: Complex Variable – Differentiation – AKTU PYQs
- 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)
Unit 5: Complex Variable – Integration – AKTU PYQs
- 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)