Engineering Mathematics-II PYQ 2018-19 AKTU Question Paper

AKTU · BTECH · Semester 2 · Engineering Mathematics-II · Session 2018-19 · PYQ

AKTU Engineering Mathematics-II previous year question paper 2018-19 for B.Tech Semester 2. Covers Ordinary Differential Equation of Higher Order, Laplace…

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Engineering Mathematics-II AKTU syllabus

  1. Unit 1: Ordinary Differential Equation of Higher Order
  2. Unit 2: Laplace Transform
  3. Unit 3: Sequence and Series
  4. Unit 4: Complex Variable – Differentiation
  5. Unit 5: Complex Variable – Integration

Questions in Engineering Mathematics-II AKTU PYQ 2018-19

  1. Q1a. Find the P.I of d²y/dx² + 4y = sin 2x (2 marks, 2018-19)
  2. Q1b. Solve simultaneous equations dx/dt = 3y, dy/dt = 3x (2 marks, 2018-19)
  3. Q1c. Find the volume of solid generated by revolving the circle x² + y² = 25 about y-axis. (2 marks, 2018-19)
  4. Q1d. Evaluate Γ(−5/2) where Γ is gamma function (2 marks, 2018-19)
  5. Q1e. Find the Fourier constant a₁ of f(x) = x², −π ≤ x ≤ π (2 marks, 2018-19)
  6. Q1f. Discuss the convergence of sequence aₙ = 2n / (n² + 1). (2 marks, 2018-19)
  7. Q1g. Show that complex function f(z) = z³ is analytic. (2 marks, 2018-19)
  8. Q1h. Define Conformal mapping. (2 marks, 2018-19)
  9. Q1i. Evaluate ∫₀^(1+i) (x² − iy) dz along the path y = x. (2 marks, 2018-19)
  10. Q1j. Find residue of f(z) = cos z / z(z + 5) at z = 0 (2 marks, 2018-19)
  11. Q2a. Use Frobenius method to solve 9x(1 − x) d²y/dx² − 12 dy/dx + 4y = 0 (10 marks, 2018-19)
  12. Q2b. Apply Dirichlet integral to find the volume of an octant of the sphere x² + y² + z² = 25. (10 marks, 2018-19)
  13. Q2c. Find half range sine series of f(x) = { x, 0 < x < 2; 4 − x, 2 < x < 4 } (10 marks, 2018-19)
  14. Q2d. Show that u = x⁴ − 6x²y² + y⁴ is harmonic function. Find complex function f(z) whose u is a real part. (10 marks, 2018-19)
  15. Q2e. Expand f(z) = 1 / ((z − 1)(z − 2)) in regions (i) 1 < |z| < 2 (ii) 2 < |z| (10 marks, 2018-19)
  16. Q3a. Solve d²y/dx² + y = tan x by method of variation of parameter. (10 marks, 2018-19)
  17. Q3b. Solve x² d²y/dx² − 2(x² + x) dy/dx + (x² + 2x + 2)y = 0 by Normal Form. (10 marks, 2018-19)
  18. Q4a. Prove that β(m, n) = Γm Γn / Γ(m + n) where Γ is gamma function (10 marks, 2018-19)
  19. Q4b. Use Beta and Gamma function to solve ∫₀^∞ 1/(1 + x⁴) dx ∫₀^(π/2) √(cot θ) dθ (10 marks, 2018-19)
  20. Q5a. Find the Fourier series of f(x) = x sin x, −π ≤ x ≤ π (10 marks, 2018-19)
  21. Q5b. State D'Alembert's test. Test the series 1 + x/2 + x²/5 + x³/10 + … + xⁿ/(n² + 1) + ……… (10 marks, 2018-19)
  22. Q6a. Let f(z) = x²y⁵(x + iy) / (x⁴ + y¹⁰) when z ≠ 0, f(z) = 0 when z = 0. Prove that Cauchy Riemann satisfies at z = 0 but function is not differentiable at z = 0. (10 marks, 2018-19)
  23. Q6b. Find Mobius transformation that maps points z = 0, −i, 2i into the points w = 5i, ∞, −i/3 respectively. (10 marks, 2018-19)
  24. Q7a. Using Cauchy Integral formula evaluate ∫_c sin z / (z² + 25) dz where c is circle |z| = 8 (10 marks, 2018-19)
  25. Q7b. Apply residue theorem to evaluate ∫₋∞^∞ x² dx / [(x² + 1)(x² + 4)] (10 marks, 2018-19)

AKTU paper codes: BAS203, KAS203

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