(SEM IV) THEORY EXAMINATION 2022-23 MATHEMATICS V

SECTION A — What This Section Contains

Section A includes 10 short 2-mark questions focusing on the basic concepts of Z-transform, Fourier integrals, probability distributions, interpolation, numerical methods, statistical tests, and quality control charts.

The questions check understanding of:

Z-transform of sequences

Fourier integral representation

Normal distribution applications

Validity of probability density functions

Lagrange’s inverse interpolation formula

Newton–Raphson convergence rate

F-test with expression & application

Null hypothesis

Statistical Quality Control (SQC)

R-chart definition and one application

This section tests fundamental formulas, definitions, reasoning, and direct applications used in transforms, statistics, and numerical methods.

SECTION B — What This Section Contains

Section B requires answering any three 10-mark questions.
These questions involve transform computations, probability, interpolation polynomials, and hypothesis testing.

The topics include:

Fourier cosine transform and derivation of Fourier sine transform

Finding mean & standard deviation from given percentile information

Constructing interpolation polynomial from data and estimating values

Student’s t-test on annual rainfall data

Principles of experimental design and completely randomized design

This section checks the ability to apply transforms, solve probabilistic problems, build interpolation models, and perform statistical hypothesis testing.

SECTION C — What This Section Contains

Section C contains long descriptive or numerical problems, one part to be solved from each question pair.

The topics include:

Solving PDE using Fourier transform

Solving difference equations using Z-transform

Problems on Poisson distribution, continuous distributions, mean & probability

Continuous frequency estimation from grouped data

Root finding by Regula-Falsi method to 4 decimal accuracy

Chi-square test for observed vs. expected frequencies (pea breeding example)

F-test for comparison of variances of two samples

Construction of p-chart from defectives data

Construction of mean chart & range chart using given sample means and ranges