(SEM III) THEORY EXAMINATION 2024-25 MATHEMATICS-IV

This is a 3-hour Theory Examination for B.Tech (Semester III) subject BAS303 – Mathematics-IV, carrying a total of 70 marks.
The paper is divided into three sections – A, B, and C, and students must answer the questions as per instructions.
The exam covers key areas of partial differential equations, probability theory, statistics, regression, curve fitting, SQC, Laplace/heat equations, normal distribution, and hypothesis testing.

SECTION A – Short Answer Questions (14 Marks)

Section A contains 7 questions, each of 2 marks, and all must be attempted.
This section focuses on basic concepts and definitions, such as:

solving a simple first-order PDE

arbitrary constants in the 1D wave equation

moment coefficient of skewness

parameters of a binomial distribution

probability density function

statistical quality control

null hypothesis

This section tests quick recall and fundamental understanding of mathematical definitions.

SECTION B – Descriptive Questions (21 Marks)

Students must attempt any three out of the given questions (each 7 marks).
These questions require steps, calculations, and reasoning.
Topics include:

solving second-order PDEs using operator and characteristic methods

solving PDE by separation of variables

solving regression equations and finding correlation + variance

normal distribution probability calculations

SQC techniques, objectives, and advantages

This section checks a student’s ability to apply formulas, calculate results, and interpret mathematical meaning.

SECTION C – Long/Applied Questions (35 Marks)

Section C contains five sets of questions, each with two choices.
Students must answer one question from each set, each worth 7 marks.
These questions require deeper conceptual application:

Set 1

solving nonlinear first-order PDE

solving PDE using differential operators

Set 2

solving Laplace equation with boundary conditions

finding displacement of a vibrating string using wave equation

Set 3

curve fitting by exponential form 𝑦 = 𝑎𝑒^{bx}

calculation of moments, skewness, kurtosis from grouped data

Set 4

binomial/Poisson probability approximations

mean and variance of successes in multiple dice throws

Set 5

testing difference of means of two independent samples (t-test)

testing association between income and school type (chi-square test)

This section tests higher-level mathematical understanding, PDE modeling, real-life data analysis, hypothesis testing, and advanced probability concepts.

Overall Summary

The Mathematics-IV paper evaluates a student’s ability in:

partial differential equations

wave and heat equations

regression and correlation

curve fitting

normal distribution

binomial/Poisson probability

moments, skewness & kurtosis

statistical quality control (SQC)

t-test and chi-square test

Section A checks basics,
Section B checks problem solving,
Section C checks deep application and statistical reasoning.