(SEM II) THEORY EXAMINATION 2023-24 ENGINEERING MATHEMATICS-II

This document contains the complete B.Tech (Semester II) Engineering Mathematics–II Question Paper for the academic year 2023–24, Subject Code BAS203, as used in the official university theory examination. The paper is designed to test a student’s mastery of advanced mathematical techniques essential for engineering, including differential equations, Laplace transforms, Fourier series, complex analysis, and analytic functions.

The question paper is divided into three structured sections—Section A, Section B, and Section C—each evaluating a different depth of mathematical understanding.

Section A contains short conceptual questions (2 marks each), covering basic yet critical topics such as particular integrals, complementary functions, Laplace transforms of exponential–polynomial functions, Fourier series constants, residue evaluation at poles, contour integration, and definitions in complex analysis. These questions aim to test conceptual clarity and quick mathematical reasoning.

Section B includes medium-length questions (7 marks each) requiring application of methods such as variation of parameters, convolution theorem, radius of convergence tests, harmonic function verification, and evaluation of complex integrals using Cauchy’s formula. Numerical and theoretical understanding is tested together in this section.

Section C contains long, analytical questions involving differential equation solving, Laplace transform applications to initial value problems, Fourier sine series expansions, convergence testing of advanced series, analytic function formulation, Laurent series expansion, and complex contour integration. These questions demand strong problem-solving skills and deep conceptual understanding.

To give an idea of the level and type of questions included, here are a couple of sample questions from the paper:

Sample Questions

“Find the particular integral of d²y/dx² + 4y = sin(2x).”
— Tests understanding of solving second-order differential equations using operator methods.

“Using the Laplace transformation, solve the differential equation y″ + 4y′ + 4y = 6e⁻ᵗ, given y(0) = –2 and y′(0) = 8.”
— Evaluates skill in Laplace transforms and initial value problems.

These represent the nature and difficulty of the entire question paper.

In addition to these sample problems, the examination includes many other similar and related questions covering:

Operator methods for solving advanced differential equations

Laplace transforms of complex functions and their inverses

Harmonic function identification and analytic function formulation

Laurent series expansions in specified annular regions

Convergence analysis of special series

Complex integration along contours

Fourier series (half-range sine/cosine expansions)

The paper provides a comprehensive academic overview of the Engineering Mathematics–II syllabus, helping students understand the exam pattern, logical structure, and topic weightage. It serves as an excellent tool for exam preparation, revision, and identifying important mathematical techniques crucial for engineering applications.

Furthermore, additional questions of similar type and difficulty level are available in the accompanying notes, helping students strengthen their practice and conceptual understanding for university examinations.