About this previous year paper
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