(SEM III) THEORY EXAMINATION 2022-23 MATHEMATICS IV

This question paper is designed for a 3-hour examination carrying a total of 100 marks.
It includes three structured sections – A, B, and C, covering both conceptual understanding and application-based numerical/analytical problems from:

Core Areas Covered

Partial Differential Equations (PDEs)

Solution Methods (Separation of Variables, Charpit's Method, Laplace Method)

Wave, Heat and Laplace Equations

Curve Fitting & Statistics

Correlation & Regression

Probability & Random Variables

Discrete Probability Distributions

Moments and Hypothesis Testing

Boolean Algebra, Relations & Groups (Discrete Structures concepts)

SECTION A – Short Answer Questions (20 Marks)

This section contains 10 brief questions (2 marks each) testing the student’s understanding of:

Basic PDE formation and classification

Standard PDEs (wave, heat equations)

Mean, correlation, probability basics

Binomial distribution

Null hypothesis and control charts

Hasse diagrams and partial orders

This part checks fundamentals, definitions, formulas, and conceptual clarity.

SECTION B – Descriptive/Analytical Questions (30 Marks)

Students must attempt any 3 out of 5 questions (10 marks each).
This section includes:

Solving PDEs using operator methods

Wave equation solution using separation of variables

Curve fitting (parabolic regression)

Probability problems (drawing balls, conditional probability)

Hypothesis testing using student data (t-test)

These questions require step-by-step derivation, analytical thinking, and mathematical explanation.

SECTION C – Long Answer / Advanced Problems (50 Marks)

This section contains 5 questions, each with two alternative parts, and students must attempt one from each:

Topics include:

Complete solution of first-order PDEs (Lagrange, Charpit methods)

Heat and Laplace equation solving by separation of variables

Correlation coefficient, central moments, skewness & kurtosis

Probability distributions (PMF problems, continuous distributions)

Hypothesis testing, ANOVA

Boolean algebra, truth tables, switching circuits

Group theory, distributive lattices

This section evaluates deep understanding, mathematical rigor, and application of advanced concepts.

Overall Description

This question paper thoroughly assesses the student’s:

Conceptual understanding

Problem-solving skills

Ability to apply mathematical tools

Statistical reasoning

Logical and structured approach to PDEs & Discrete Mathematics

It ensures comprehensive evaluation through definitions, derivations, numerical problems, proofs, and logical reasoning questions.