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.
