This document is the B.Tech Semester–III Theory Examination 2019–20 question paper for MATHEMATICS–IV (Sub Code: KAS302) under Dr. A.P.J. Abdul Kalam Technical University (AKTU).
The uploaded file contains three pages and is divided into three sections — SECTION A, SECTION B, and SECTION C.
The exam is of 3 hours duration, and the total marks are 100.
The paper evaluates students on Partial Differential Equations (PDEs), Statistics, Probability Distributions, Curve Fitting, Regression, Poisson Distribution, Bayes’ Theorem, and Normal Distribution, as clearly shown in the images across pages.
SECTION A — Short Questions (10 × 2 = 20 Marks)
(Visible on Page 1)
Section A contains ten brief questions, each carrying 2 marks, testing foundational concepts of PDEs and basic probability/statistics.
Questions include:
Solving a first–order partial differential equation yq−xp=zyq - xp = zyq−xp=z
Cauchy’s problem ux−uy=0u_x - u_y = 0ux−uy=0 with given condition
Classification of PDEs: elliptic, parabolic, hyperbolic
Solving PDE ∂2u∂x2+∂u∂y+u=0\frac{\partial^2 u}{\partial x^2} + \frac{\partial u}{\partial y} + u = 0∂x2∂2u+∂y∂u+u=0
Finding mean of a number set (e.g., 6, 8, 9, 10, 12, 11)
Calculating the first moment of a distribution
Rewriting PDEs in standard form (as shown on Page 1 table)
All questions appear clearly in the table format on Page 1.
SECTION B — Long Descriptive Questions (Any 3 × 10 = 30 Marks)
(Shown on Page 2)
Section B contains five 10-mark questions, from which students must attempt any three.
Topics include:
Exponential curve fitting PVy=kPV^y = kPVy=k (table on Page 2 shows P and V values)
Poisson distribution fitting to yeast cell count data (table given on Page 2)
Statistical testing with chi-square, mean/variance explanations
Moments and related definitions
Regression and correlation introduction
A detailed table for Poisson distribution calculations (frequency of yeast cells 0–10) is provided on Page 2.
SECTION C — Applied / Advanced Problems (Q3–Q6 × 10 Marks)
(Visible on Page 3)
Section C contains four questions (Q3–Q6), each having two alternatives (a or b).
Students attempt one from each question number.
Q3 — Regression / Probability
Find the multiple regression equation for X1X_1X1 on X2,X3X_2, X_3X2,X3 using the table given (Page 3).
OR apply a probability method from alternate part.
Q4 — Bayes’ Theorem / Binomial Distribution
Bayes’ theorem problem: civilian and army officer shooting probability scenario.
OR normal/binomial distribution–based question.
Q5 — Normal Distribution
Mean and standard deviation problem using normal distribution.
OR alternative statistical measure question.
Q6 — Student’s t-test / F-test
Student’s t–distribution explanation or numerical.
OR F–test / variance comparison problem.
(Page 3 contains clear regression data table with variables X1,X2,X3X_1, X_2, X_3X1,X2,X3.)
OVERALL SUMMARY OF THE DOCUMENT
The uploaded Mathematics–IV (KAS302) question paper evaluates:
Formation, classification & solution of PDEs
Cauchy’s problems and order/degree identification
Curve fitting (exponential form)
Moments, mean, variance, correlation
Poisson distribution fitting using observed frequency table
Regression equations using real data
Bayes’ theorem and conditional probability
Normal distribution for real-world measurements
Student’s t-test, F-test, chi-square ideas
The paper follows a strict AKTU pattern:
SECTION A: Basic conceptual recall
SECTION B: Statistics & distribution-based long questions
SECTION C: Advanced applied probability & regression
The 3-page document is neatly formatted with data tables and clearly printed PDE/statistics questions.
