Engineering Mathematics-II 2022 Question Paper — Government College o…

Instructions

• Attempt five questions in all selecting at least two questions from each Section.
• Each question carries 20 marks.

Questions

Section A

• Q1. (a) Show that the series $\frac{1}{\sqrt{3}\cdot 4} + \frac{1}{\sqrt{4}\cdot 5} + \frac{1}{\sqrt{5}\cdot 6} + \dots$ is divergent. (b) Test whether the given series converges conditionally or not $\frac{1}{2} - \frac{2}{5} + \frac{3}{10} - \frac{4}{17} + \dots$ [20 marks]
• Q2. (a) Show that the series $\sum \left[\sqrt{(n^3+1)} - \sqrt{n^3}\right]$ is convergent. (b) Discuss the convergence or divergence of the series $\sum \left(\frac{n}{n+1}\right)^{n^2}$ [20 marks]
• Q3. (a) Expand the periodic function $f(x) = x \cos x$ in $(-\pi, \pi)$ as a Fourier series. (b) Derive the complex form of Fourier series of a periodic function $f(x)$ in $(-l, l)$ [20 marks]
• Q4. (a) Expand the function $f(x) = c - x$ in $(0, c)$ as a Fourier Cosine series. (b) Using Parseval's identity for Fourier sine series of $f(x) = x(\pi - x)$ in $(0, \pi)$, show that $\sum_{n=1}^{\infty} \frac{1}{(2n-1)^6} = \frac{\pi^6}{960}$ [20 marks]

Section B

• Q5. Solve the following differential equations: (a) $\left(1 + e^{x/y}\right)dx + e^{x/y}\left(1 - \frac{x}{y}\right)dy = 0$. (b) $(D^3 - D^2 - 6D)y = x^2$ [20 marks]
• Q6. Solve the following ordinary differential equations: (a) $xydy - y^2dx = (x^2 + y^2)dy$ (b) $(D^2 - 2D + 1)y = x\sin x$ [20 marks]
• Q7. Solve (a) $\frac{dx}{x^2+y^2} = \frac{dy}{2x} = \frac{dz}{(x+y)z}$. (b) $z^2(p^2 + q^2 + 1) = c^2$ [20 marks]
• Q8. Solve the following partial differential equations: (a) $(D^3 - 7DD'^2 - 6D'^3)z = x^2y$. (b) $(D^2 + DD' + D' - 1)z = e^{-x}$. [20 marks]

Related pages

• Engineering Mathematics-II syllabus
• All Engineering Mathematics-II papers from 2022

Other years

• Engineering Mathematics-II 2022 question paper — end-term
• Engineering Mathematics-II 2018 question paper — end-term
• Engineering Mathematics-II 2018 question paper — end-term