Engineering Mathematics-II PYQ 2021-22 AKTU Question Paper

AKTU · BTECH · Semester 2 · Engineering Mathematics-II · Session 2021-22 · PYQ

AKTU Engineering Mathematics-II previous year question paper 2021-22 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 2021-22

  1. Q1a. Find the differential equation which represents the family of straight lines passing through the origins? (2 marks, 2021-22)
  2. Q1b. State the criterion for linearly independent solutions of the homogeneous linear nth order differential equation. (2 marks, 2021-22)
  3. Q1c. Evaluate: ∫₀¹ dx/√(−log x). (2 marks, 2021-22)
  4. Q1d. Find the volume of the solid obtained by rotating the ellipse x² + 9y² = 9 about the x-axis. (2 marks, 2021-22)
  5. Q1e. Test the series ∑_{n=1}^{∞} (1/n) sin(1/n). (2 marks, 2021-22)
  6. Q1f. Find the constant term when f(x) = 1 + |x| is expanded in Fourier series in the interval (−3, 3). (2 marks, 2021-22)
  7. Q1g. Show that f(z) = z + 2z̄ is not analytic anywhere in the complex plane. (2 marks, 2021-22)
  8. Q1h. Find the image of |z − 2i| = 2 under the mapping w = 1/z. (2 marks, 2021-22)
  9. Q1i. Expand f(z) = eᶻ / (z − 2) in a Laurent series about the point z = 2. (2 marks, 2021-22)
  10. Q1j. Discuss the nature of singularity of cot(πz) / (z − a)² at z = a and z = ∞. (2 marks, 2021-22)
  11. Q2a. Solve: (d²x/dt²) + (dy/dt) + 3x = e⁻ᵗ , (d²y/dt²) − 4(dx/dt) + 3y = sin 2t. (10 marks, 2021-22)
  12. Q2b. Assuming Γn Γ(1−n) = π cosec nπ, 0 < n < 1, show that ∫₀^∞ x^(p−1) / (1 + x) dx = π / sin nπ ; 0 < p < 1. (10 marks, 2021-22)
  13. Q2c. Test the series x/(1.2) + x²/(3.4) + x³/(5.6) + x⁴/(7.8) + ........ (10 marks, 2021-22)
  14. Q2d. If f(z) = u + iv is an analytic function, find f(z) in term of z if u − v = (eʸ − cos x + sin x) / (cosh y − cos x) when f(π/2) = (3 − i)/2. (10 marks, 2021-22)
  15. Q2e. Evaluate by contour integration: ∫₀²π (1 − cos θ) cos(nθ + sin θ) dθ ; n ∈ I. (10 marks, 2021-22)
  16. Q3a. Use the variation of parameter method to solve the differential equation (D² − 1)y = 2(1 − e^(−2x))^(−1/2). (10 marks, 2021-22)
  17. Q3b. Solve: (1 + x)² d²y/dx² + (1 + x) dy/dx + y = 4 cos log(1 + x). (10 marks, 2021-22)
  18. Q4a. The arc of the cardioid r = a(1 + cos θ) included between −π/2 ≤ θ ≤ π/2 is rotated about the line θ = π/2. Find the area of surface generated. (10 marks, 2021-22)
  19. Q4b. Evaluate ∭ xyz sin(x + y + z) dx dy dz, the integral being extended to all positive values of the variables subject to the condition x + y + z ≤ π/2. (10 marks, 2021-22)
  20. Q5a. Test for convergence of the series (a + x)/1! + (a + 2x)²/2! + (a + 3x)³/3! + …… (10 marks, 2021-22)
  21. Q5b. Obtain Fourier series for the function f(x) = { 1 + 2x/π, −π < x < 0 ; 1 − 2x/π, 0 < x < π }. Hence deduce that 1/1² + 1/3² + 1/5² + …… = π²/8. (10 marks, 2021-22)
  22. Q6a. Prove that w = z / (1 − z) maps the upper half of the z-plane onto upper half of the w-plane. What is the image of the circle |z| = 1 under this transformation? (10 marks, 2021-22)
  23. Q6b. Find a bilinear transformation which maps the points i, −i, 1 of the z-plane into 0, 1, ∞ of the w-plane respectively. (10 marks, 2021-22)
  24. Q7a. Evaluate ∮_c eᶻ / [z(1 − z)³] dz, where c is (i) |z| = 1/2 (ii) |z − 1| = 1/2 (iii) |z| = 2. (10 marks, 2021-22)
  25. Q7b. Find the Taylor's and Laurent's series which represent the function (z² − 1) / [(z + 2)(z + 3)] when (i) |z| < 2 (ii) 2 < |z| < 3 (iii) |z| > 3. (10 marks, 2021-22)

AKTU paper codes: BAS203, KAS203

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