This question paper is designed for a 3-hour examination carrying a total of 100 marks.
It includes three structured sections – A, B, and C, covering both conceptual understanding and application-based numerical/analytical problems from:
Core Areas Covered
Partial Differential Equations (PDEs)
Solution Methods (Separation of Variables, Charpit's Method, Laplace Method)
Wave, Heat and Laplace Equations
Curve Fitting & Statistics
Correlation & Regression
Probability & Random Variables
Discrete Probability Distributions
Moments and Hypothesis Testing
Boolean Algebra, Relations & Groups (Discrete Structures concepts)
SECTION A – Short Answer Questions (20 Marks)
This section contains 10 brief questions (2 marks each) testing the student’s understanding of:
Basic PDE formation and classification
Standard PDEs (wave, heat equations)
Mean, correlation, probability basics
Binomial distribution
Null hypothesis and control charts
Hasse diagrams and partial orders
This part checks fundamentals, definitions, formulas, and conceptual clarity.
SECTION B – Descriptive/Analytical Questions (30 Marks)
Students must attempt any 3 out of 5 questions (10 marks each).
This section includes:
Solving PDEs using operator methods
Wave equation solution using separation of variables
Curve fitting (parabolic regression)
Probability problems (drawing balls, conditional probability)
Hypothesis testing using student data (t-test)
These questions require step-by-step derivation, analytical thinking, and mathematical explanation.
SECTION C – Long Answer / Advanced Problems (50 Marks)
This section contains 5 questions, each with two alternative parts, and students must attempt one from each:
Topics include:
Complete solution of first-order PDEs (Lagrange, Charpit methods)
Heat and Laplace equation solving by separation of variables
Correlation coefficient, central moments, skewness & kurtosis
Probability distributions (PMF problems, continuous distributions)
Hypothesis testing, ANOVA
Boolean algebra, truth tables, switching circuits
Group theory, distributive lattices
This section evaluates deep understanding, mathematical rigor, and application of advanced concepts.
Overall Description
This question paper thoroughly assesses the student’s:
Conceptual understanding
Problem-solving skills
Ability to apply mathematical tools
Statistical reasoning
Logical and structured approach to PDEs & Discrete Mathematics
It ensures comprehensive evaluation through definitions, derivations, numerical problems, proofs, and logical reasoning questions.
