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.
