(SEM III) THEORY EXAMINATION 2022-23 MATHEMATICS-V

This question paper evaluates a student’s understanding of Fourier Transforms, Z-Transforms, Probability Theory, Statistics, Numerical Methods, and Design of Experiments. It is divided into three sections — A, B, and C — and carries a total of 100 marks to be completed in 3 hours.

Section A

This section contains 10 short-answer questions, each testing fundamental concepts. Topics include:

Convolution theorem (Fourier Transform)

Fourier sine/cosine transform formulas

Probability distributions and normalization

Normal probability density function

Finite differences and calculus of finite increments

Lagrange interpolation

Hypothesis testing and level of significance

F-distribution mean and variance

Principles and advantages of experimental design
Students must answer all questions briefly and precisely.

Section B

Students must attempt any three questions. This section includes long-answer, problem-solving, and analytical questions, covering:

Fourier Transform of piecewise functions

Poisson probability problems (errors, occurrences)

Numerical solution of nonlinear equations (Regula-Falsi method)

Hypothesis testing using sample means (t-test)

Construction and evaluation of control charts (np-charts)
These questions test understanding, computation skills, and interpretation.

Section C

This section contains one question from each pair, requiring deeper analytical skills. It includes:

Solving difference equations using Z-Transform

Deriving Fourier integral representation and evaluating integrals

Binomial distribution mean/variance; solving mixed PDFs using integration

Newton–Raphson method; forward difference table and interpolation

ANOVA one-way classification model, assumptions, hypothesis

Goodness-of-fit test for Poisson distribution (Chi-square test)

RBD analysis; control charts for fraction defective

Purpose and Learning Outcomes

The question paper is designed to assess the student's ability to:

Apply Fourier and Z-transform techniques to solve differential/difference equations
Use probability and statistics in engineering situations
Perform numerical approximation using classical methods
Conduct hypothesis testing and interpret statistical results
Work with control charts and quality control data
Demonstrate conceptual clarity in transforms, distributions, numerical methods & design of experiments