Engineering Mathematics-II PYQ 2023-24 AKTU Question Paper

AKTU · BTECH · Semester 2 · Engineering Mathematics-II · Session 2023-24 · PYQ

AKTU Engineering Mathematics-II previous year question paper 2023-24 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 2023-24

  1. Q1a. Find the Particular Integral of (D² − 4D + 4)y = e^(2x) (2 marks, 2023-24)
  2. Q1b. Find the Complementary Function of (D³ + 2D² − 3D)y = 0 (2 marks, 2023-24)
  3. Q1c. Find the Laplace Transform of t⁴e^(2t) (2 marks, 2023-24)
  4. Q1d. What is the constant term (a₀) in the Fourier series expansion of f(x) = x² in (−π, π)? (2 marks, 2023-24)
  5. Q1e. Find the residue of f(z) = cos z / [z(z+5)] at z = 0 (2 marks, 2023-24)
  6. Q1f. Evaluate ∫_C (z² + 1) / (z² − 1) dz using Cauchy Integral Formula where C: |z − 1| = 1 (2 marks, 2023-24)
  7. Q1g. Define Laurent's series. (2 marks, 2023-24)
  8. Q2a. Solve using method of variation of parameters: y'' + y = cosec x (7 marks, 2023-24)
  9. Q2b. Using convolution theorem, find the Inverse Laplace Transform of 1 / [(s²+a²)(s²+b²)] (7 marks, 2023-24)
  10. Q2c. Test the convergence of the series: ∑ [1 / (n log n)²] (7 marks, 2023-24)
  11. Q2d. Find the harmonic conjugate of u = x³ − 3xy² + 3x² − 3y² and hence find the analytic function f(z) = u + iv. (7 marks, 2023-24)
  12. Q2e. Evaluate ∮_C e^(2z) / [(z−1)(z−2)] dz where C: |z| = 3 using Cauchy Integral Formula. (7 marks, 2023-24)
  13. Q3a. Solve: (D² − 4D + 4)y = 8x²e^(2x) sin 2x (7 marks, 2023-24)
  14. Q3b. Solve the simultaneous differential equations: dx/dt + 2x − 3y = 0; dy/dt − 3x + 2y = 0 (7 marks, 2023-24)
  15. Q4a. Find L{ (1 − cos t) / t² } using properties of Laplace Transform. (7 marks, 2023-24)
  16. Q4b. Using Laplace Transform, solve: y'' + 3y' + 2y = e^(−t), y(0) = 0, y'(0) = 1 (7 marks, 2023-24)
  17. Q5a. Find half range Fourier sine series of f(x) = x(π − x) in (0, π). (7 marks, 2023-24)
  18. Q5b. Test convergence of the series: ∑ (n!)² / (2n)! using Raabe's test. (7 marks, 2023-24)
  19. Q6a. Find the analytic function f(z) = u + iv given u + v = (x − y)(x² + 4xy + y²) using Milne's Thomson method. (7 marks, 2023-24)
  20. Q6b. Define analytic function. Show that f(z) = |z|² is not analytic anywhere except at origin. (7 marks, 2023-24)
  21. Q7a. Expand f(z) = (z² − 1) / [(z + 2)(z + 3)] in Laurent's series valid for |z| > 3. (7 marks, 2023-24)
  22. Q7b. Evaluate ∮_C (z + 4) / (z² + 2z + 5) dz where C: |z + 1 − i| = 2 using Cauchy Integral Formula. (7 marks, 2023-24)

AKTU paper codes: BAS203, KAS203

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