(SEM-III) THEORY EXAMINATION 2019-20 MATHEMATICS-IV

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.