(SEM II) THEORY EXAMINATION 2022-23 ENGINEERING MATHEMATICS-II

The Engineering Mathematics–II (BAS203) question paper is a 3-hour, 70-mark examination designed to assess a student's understanding of advanced mathematical concepts used in engineering. The paper is structured into three major sections—A, B, and C—each addressing different levels of difficulty and types of mathematical problems.

SECTION A – Very Short Answer Questions (14 Marks)

This section contains seven questions, each carrying 2 marks, meant to test the student’s basic conceptual clarity. These questions are short and direct, requiring brief explanations, statements, definitions, or quick computations.

Topics include:

Solving simple differential equations

Properties of Laplace transforms

Convergence of sequences

Analyticity of complex functions

Classification of singularities

Finding inverse Laplace transforms

Determining invariant points in complex transformations

This section checks fundamental knowledge and ensures that the student understands basic tools and principles needed for more advanced problems.

SECTION B – Short Descriptive / Medium-Level Problems (21 Marks)

This section consists of five questions, out of which any three must be answered.
Each question carries 7 marks, requiring step-by-step reasoning, derivations, proofs, numerical computation, or diagram-based explanation.

The problems involve:

Solving higher-order differential equations

Computing Laplace transforms and proving integral results

Testing convergence of infinite series

Checking analyticity using Cauchy–Riemann equations

Evaluating integrals using Cauchy Integral Formula

These questions measure a student’s ability to apply mathematical techniques, show proper steps, and derive results accurately.

 SECTION C – Long, Advanced, Analytical Questions (35 Marks)

This section has five questions, each with two choices (a or b). Students must attempt one option from each question.
Each carries 7 marks and requires a full-length solution with clear steps.

These are high-level mathematical problems, reflecting real engineering applications and deeper theoretical understanding. The questions cover:

Advanced Differential Equation Methods

Variation of parameters

Changing independent variables

Solving non-homogeneous differential equations

Laplace Transform Applications

Convolution theorem

Solving initial value problems using Laplace transforms

Fourier Series

Expanding functions into Fourier or half-range series

Using expansions to prove standard mathematical identities

Complex Analysis

Constructing analytic functions

Deriving bilinear transformations and mapping regions

Expanding complex functions in different regions

Evaluating definite integrals using contour integration

Section C evaluates a student’s ability to handle complex, multi-step problems, demonstrate logical reasoning, and apply mathematics to engineering scenarios.

OVERALL SUMMARY OF THE QUESTION PAPER (LONG FORM)

This question paper is designed to comprehensively assess a B.Tech second-semester student's understanding of Engineering Mathematics–II. It contains a balanced mixture of short conceptual checks, medium-length problem-solving questions, and long analytical problems involving advanced mathematics. Topics span across differential equations, Laplace transforms, sequences and series, Fourier analysis, complex variables, and contour integration, ensuring both theoretical understanding and practical application. The structured format from Section A to Section C guides students from basic recall-type questions to highly analytical ones, reflecting increasing levels of difficulty and depth of knowledge.