Engineering Mathematics-II PYQ 2025-26 AKTU Question Paper

AKTU · BTECH · Semester 2 · Engineering Mathematics-II · Session 2025-26 · PYQ

AKTU Engineering Mathematics-II previous year question paper 2025-26 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 2025-26

  1. Q1a. Solve the following differential equation, g being constant: \frac{d^2\theta}{dt^2}+g\theta=0. (2 marks, 2025-26)
  2. Q1b. Determine the Laplace transform of f(t)=\begin{cases}e^{-t},&0<t<3,\\0,&t>3.\end{cases} (2 marks, 2025-26)
  3. Q1c. Determine the value of b_n if f(x)=1, 0\le x\le2, is expanded as f(x)=\sum_{n=1}^{\infty}b_n\sin\frac{n\pi x}{2}. (2 marks, 2025-26)
  4. Q1d. Determine the value of n\;(\ne0) for which u=(x^2+y^2)^{n/2} is harmonic. (2 marks, 2025-26)
  5. Q1e. Determine the pole of the function f(z)=\frac{z^2}{(z-1)^2(z+2)}. (2 marks, 2025-26)
  6. Q1f. Determine the particular integral of \frac{d^2y}{dx^2}-\frac{dy}{dx}=e^x+e^{-x}. (2 marks, 2025-26)
  7. Q1g. Determine the function whose Laplace transform is F(s)=\frac{1}{s^2-4s+8}. (2 marks, 2025-26)
  8. Q2a. Apply method of variation of parameters to determine the general solution of x^2\frac{d^2y}{dx^2}-2x\frac{dy}{dx}+2y=x^3+x. (7 marks, 2025-26)
  9. Q2b. Apply Laplace transform method to solve \frac{d^2y}{dt^2}-3\frac{dy}{dt}+2y=4t+e^{3t},\qquad y(0)=1,\quad y'(0)=-1. (7 marks, 2025-26)
  10. Q2c. Determine the Fourier series expansion of the following function: f(x)=1+x,\quad-1<x<1,\qquad f(x+2)=f(x). Hence compute the sum of the series 1-\frac13+\frac15-\frac17+\cdots. (7 marks, 2025-26)
  11. Q2d. Prove that for the function f(z)=\frac{\bar z^2}{z}, z\ne0; f(0)=0, Cauchy-Riemann equations are satisfied at the origin. Does f'(z) exist there? (7 marks, 2025-26)
  12. Q2e. Use Cauchy integral formula to evaluate \oint_C\frac{\sin\pi z^2+\cos\pi z^2}{(z-1)(z-2)}\,dz, where C is the circle |z|=3. (7 marks, 2025-26)
  13. Q3a. Solve (D^2-2D+4)y=\sin2x, given that y=1/8, y'=4, when x=0. Find the value of y when x=\pi/4. (7 marks, 2025-26)
  14. Q3b. Solve the following differential equation by changing the independent variable: \frac{d^2y}{dx^2}-\frac1x\frac{dy}{dx}+4x^2y=x^4. (7 marks, 2025-26)
  15. Q4a. Apply convolution theorem to evaluate: L^{-1}\!\left\{\frac{s}{(s^2+4)^2}\right\}. (7 marks, 2025-26)
  16. Q4b. Determine the Laplace transform of the following functions: f(t)=\begin{cases}0,&0<t<a,\\1,&a<t<2a,\\2,&2a<t<3a,\end{cases}\qquad f(t+3a)=f(t). (7 marks, 2025-26)
  17. Q5a. Test for convergence the series \frac{x}{1\cdot2}+\frac{x^2}{2\cdot3}+\frac{x^3}{3\cdot4}+\frac{x^4}{4\cdot5}+\cdots. (7 marks, 2025-26)
  18. Q5b. (i) Given the function f(x)=\begin{cases}x,&0<x<1,\\2-x,&1<x<2.\end{cases} Expand f(x) as a series of cosines. \text{(ii) Test the convergence of the series }1+\frac{1^2}{2^2}+\frac{2^2}{3^3}+\frac{3^3}{4^4}+\cdots. (7 marks, 2025-26)
  19. Q6a. If u+v=(x+y)(2-4xy+x^2+y^2), find f(z)=u+iv in terms of z. (7 marks, 2025-26)
  20. Q6b. Find the Bilinear transformation which maps the points z=0,-1,i into w=i,0,\infty. Also find the image of the unit circle |z|=1. (7 marks, 2025-26)
  21. Q7a. Apply the method contour integration to evaluate the integral \int_0^{2\pi}\frac{1}{3-2\cos\theta+\sin\theta}\,d\theta. (7 marks, 2025-26)
  22. Q7b. Expand f(z)=\frac{1}{(z+1)(z+3)} in Laurent series valid for (i) 1<|z|<3, (ii) |z|>3, (iii) 0<|z+1|<2, (iv) |z|<1. (7 marks, 2025-26)

AKTU paper codes: BAS203, KAS203

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