This document contains the complete B.Tech (Semester IV) Theory Examination 2024–25 question paper for MATHEMATICS–IV (BAS403). The paper spans four printed pages, carries 70 marks, and evaluates a student’s competency in Partial Differential Equations (PDEs), Fourier transforms, curve fitting, correlation & regression, probability distributions, numerical methods, hypothesis testing, and statistical decision-making.
Section A – Short Conceptual Questions (14 Marks)
Section A includes seven 2-mark questions designed to test fundamental mathematical understanding. Topics include:
Forming a partial differential equation by eliminating arbitrary functions
Solving a first-order PDE using the method of characteristics
Classifying a PDE operator
Finding mean & variance using given moments
Calculating regression coefficient
Finding probabilities from a joint density function
Writing the formula for Chi-square test
These questions test the foundational concepts of PDEs, statistics, and probability.
Section B – Intermediate Level Problems (21 Marks)
Students must attempt any three out of five questions. This section includes:
Solving a PDE using Lagrange’s equation
Solving the wave equation for a stretched string with fixed ends using given initial conditions
Computing absolute moments, β₁ and β₂ to comment on skewness and kurtosis
Finding the 99th percentile of a normal distribution using given mean, SD, and Z-values
Performing a Chi-square goodness-of-fit test for distribution of digits in a telephone directory
These questions assess analytical skills in PDEs, wave motion, descriptive statistics, and hypothesis testing.
Section C – Advanced PDEs, Fourier Transforms & Regression (35 Marks)
Section C contains five long questions, each with two subparts, covering:
1. Advanced PDE Solutions
Solving nonlinear PDEs using transformations
Solving operator-based PDEs such as (D−D′−1)(D−D′−2)z(D - D' -1)(D - D' - 2)z(D−D′−1)(D−D′−2)z
2. Heat Equation & Fourier Cosine Transform
Solving heat conduction problems for an insulated bar
Finding Fourier Cosine Transform of f(x)=11+x2f(x)=\frac{1}{1+x^2}f(x)=1+x21
3. Curve Fitting & Regression
Fitting an exponential curve of the form y=abxy = ab^xy=abx
Finding lines of regression and estimating supply for a given price
4. Probability & Z-Distribution
Using binomial/Poisson approximation to calculate probabilities
Calculating number of students within score intervals using standard normal distribution
5. Hypothesis Testing & Control Charts
Performing a t-test to compare sample mean with assumed mean
Constructing an np-control chart to check if a manufacturing process is under control
These problems test mastery in higher mathematics, statistical inference, signal methods, and engineering-oriented PDE solutions.
Summary
This Mathematics–IV (BAS403) exam paper covers a comprehensive range of applied mathematics topics:
Formation & solution of PDEs
Method of characteristics & operator method
Wave & heat equations
Fourier transforms
Curve fitting, correlation & regression
Moments, skewness & kurtosis
Probability distributions & normal curve applications
Chi-square & t-tests
Control charts in quality control
It serves as a complete academic resource for engineering students studying advanced applied mathematics in their 4th semester.
