(SEM II) THEORY EXAMINATION 2017-18 ENGINEERING MATHEMATICS-II

This PDF is the official Engineering Mathematics–II (RAS203) question paper for B.Tech Semester-II (2017–18). It represents a complete university-level exam conducted for first-year engineering students across Uttar Pradesh Technical University–affiliated colleges. The paper carries 70 marks and is designed to be attempted in 3 hours, making it a crucial reference for exam preparation, revision, or understanding the academic structure of Engineering Mathematics-II.

The paper is divided into three structured sections to test different levels of mathematical understanding:

SECTION A – Short Conceptual Questions

This section contains 7 short questions, each worth 2 marks. They cover quick, direct concepts from a wide range of topics. These questions test a student’s basic command over differential equations, Laplace transforms, Legendre polynomials, and PDE classification.

For example, one question asks students to:

Form a differential equation from the set of solutions {eˣ, x eˣ, x² eˣ} 

Find the inverse Laplace transform of a rational function involving s² + 8 in the numerator 

Such questions check whether the student understands fundamental formulas and can apply them quickly.

SECTION B – Medium-Length Analytical Problems

This section requires students to attempt any three out of five questions, each carrying 7 marks. Here, the problems demand analytical ability, derivations, and step-by-step solutions.

Topics include:

Solving second-order differential equations

Proving identities involving Bessel functions

Drawing graphs and finding Laplace transforms of periodic functions

Calculating Fourier series for piecewise-defined functions

Solving heat equations using separation of variables

These questions are moderately lengthy and test a student’s problem-solving skills.

SECTION C – Long, High-Weightage Problems

This section contains three parts, and students must attempt one question from each part. Each question carries 7 marks and involves deep understanding and longer solutions.

Typical questions include:

Solving simultaneous differential equations with higher-order derivatives

Using variation of parameters to solve complex ODEs

Proving Rodrigues’ formula for Legendre polynomials

Solving differential equations using series methods

Applying Laplace transform techniques to solve ODEs

Deriving Fourier series to prove classic mathematical results

Solving partial differential equations, heat flow, and wave equation problems

These problems are designed to evaluate complete mastery over Engineering Mathematics-II.

2–3 Sample Questions from the Paper (as required)

Below are selected examples from the PDF to highlight the exam style:

1. Short Question (Differential Equation Formation)

Determine the differential equation whose set of independent solutions is {eˣ, x eˣ, x² eˣ}.
 

2. Laplace Transform Question

Find the inverse Laplace transform of

s2+8s2+5s+4.\frac{s^2 + 8}{s^2 + 5s + 4}.s2+5s+4s2+8​.

3. Long Question (Legendre Polynomial Theory)

State and prove Rodrigues’ formula for Legendre’s polynomial.