(SEM III) THEORY EXAMINATION 2020-21 MATHEMATICS

This document is the B.Tech Semester III Theory Examination 2020–21 Question Paper for the subject MATHEMATICS-IV (KAS302) under Dr. A.P.J. Abdul Kalam Technical University (AKTU). The exam carries 100 marks, and the duration is 3 hours.

The uploaded paper consists of three main sections:
SECTION A (Short Answer Questions), SECTION B (Long Questions), SECTION C (Very Long/Advanced Problems).

The printed pages (Page 1 and Page 2) clearly show all questions, marks distribution, and course outcome (CO) mapping.

 SECTION A — 10 Brief Questions (10 × 2 = 20 Marks)

As seen on Page 1, Section A contains ten 2-mark questions testing fundamental concepts of:

Charpit Method

Solving first-order PDEs

Classification of PDEs

Radio equations

Moments, mean & variance

Regression & correlation

Probability density functions

Binomial distribution

When F-test is applied

t-test for small samples

Each question is short and conceptual, designed to test basic mathematical clarity.
 

SECTION B — Any 3 Long Questions (3 × 10 = 30 Marks)

Section B contains five descriptive questions, from which students must attempt any three.
These questions require full derivations, formula application, data handling, and theorem usage.

Topics include:

Solving second-order PDE with variables x, y

Vibrating string displacement function using Fourier sine series

Least-square fitting of curve y=abxy = ab^xy=abx with given data table

Bayes' Theorem with urn problem (white & red balls)

Chi-square test of association using contingency table (father–son eye color)

SECTION C — Advanced/Long Problems (Multiple 10-Mark Choices)

Section C appears across Page 1 and Page 2, with sub-sections numbered 3, 4, 5, 6, and 7, each offering two choices, from which students must attempt any one per number.

These include:

PDEs & Mathematical Physics (Q3, Q4)

Solving operator-based PDEs using D & D'

Heat conduction in insulated rod

Laplace equation with boundary conditions

Statistics, Probability & Regression (Q5, Q6)

Moment generating function of Binomial distribution

Regression equation for given maintenance-cost data

Poisson distribution as limit of Binomial

Normal distribution life-expectancy problem (battery cell life)

Statistical Inference & Quality Control (Q7)

ANOVA for comparing deaths across three hospitals

Construction of np-chart using defectives in 10 samples

Each question is worth 10 marks, requiring full working steps, derivations, and interpretation of statistical results.

Overall Summary of the Document

The uploaded Mathematics-IV question paper thoroughly examines:

Partial Differential Equations

Heat & wave equations

Curve fitting & regression

Probability & Bayes’ theorem

Moments, mean, variance, correlation

Binomial, Poisson, and Normal distributions

Hypothesis testing (t-test, F-test, chi-square test, ANOVA)

Quality control charts (np-chart)

The paper structure consists of:

Section A: Conceptual basics

Section B: Core descriptive mathematics

Section C: Advanced mixed-topics with analytical evaluation

The two-page document is neatly formatted, with a clear table layout, topic variety, and balanced distribution of mathematical methods and applied statistics.