About this previous year paper
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.