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

The 2022 Engineering Mathematics-II previous year question paper (Government College of Engineering and Technology, Jammu), with every question and its marks.

University: Government College of Engineering and Technology, Jammu
Subject: Engineering Mathematics-II
Course: Engineering Mathematics - II
Branch: Civil/Mech/Elec/E&C/Comp/IT Engg.
Year: 2022
Paper: end-term
Duration: 180 minutes
Total marks: 100

Instructions

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

Questions

Section - A

Attempt at least two questions from this Section.

Q1. (a) Show that the series $1 + \frac{1}{1 \cdot 4} + \frac{1}{2 \cdot 5} + \frac{1}{3 \cdot 6} + \frac{1}{4 \cdot 7} + \ldots$ is convergent. (b) Test for convergence or divergence of the series $\frac{1}{(\log 2)^p} + \frac{1}{(\log 3)^p} + \frac{1}{(\log 4)^p} + \ldots$ [20 marks]
Q2. (a) Discuss the convergence or divergence of the series $\sum \left(\frac{1+n}{n}\right)^n$ (b) Find the interval of convergence of the series: $1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \ldots$ [20 marks]
Q3. (a) Draw the graph of $f(x) = |\cos x|$ in $(-\pi, \pi)$. Is it odd or even function? Also expand it as a Fourier series in $(-\pi, \pi)$. (b) Using Fourier Cosine series of $f(x) = (x - 1)^2$ for $x \in (0, 1)$, show that $\frac{\pi^2}{6} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \ldots$ [20 marks]
Q4. (a) Expand $f(x) = x^2 - x$ as a Fourier Sine series in $(0, 1)$. (b) Using Parseval's identity for Fourier series of $f(x) = |x|$ in $(-\pi, \pi)$, show that $\sum_{n=1}^{\infty} \frac{1}{(2n - 1)^4} = \frac{\pi^4}{96}$ [20 marks]

Section - B