This document contains the full B.Tech Numerical Methods & Applied Mathematics semester examination question paper, designed for 70 marks with a duration of 3 hours. The exam tests a student’s understanding of numerical computation, error analysis, interpolation, curve fitting, iteration methods, numerical solutions of differential equations, and regression analysis. The paper is divided into three structured sections—A, B, and C, covering theory, numerical problem-solving, and algorithm-based applications.
SECTION – A (Short Conceptual Questions – 7 × 2 = 14 Marks)
Students must answer all seven short questions. These questions are theory-oriented and test basic understanding of numerical and statistical concepts. The topics include:
Pitfalls and limitations of floating-point representation
Proof of the identity involving forward difference operator Δ
Computing absolute and relative error for approximations
Writing Gauss’s forward interpolation formula
The identity involving Chebyshev polynomials (T₀, T₂, T₄)
Meaning and use of histograms in data visualization
Concept and purpose of null hypothesis in statistics
These questions measure fundamental clarity required for solving numerical computation problems.
SECTION – B (Numerical / Analytical Questions – 5 × 7 = 35 Marks)
Students must attempt any five of eight numerical problems. This section tests the ability to apply algorithms and formulas to real numerical situations.
Key topics and types of problems include:
Root-Finding Methods
Solving non-linear equations using the Regula Falsi method to four-decimal accuracy
Interpolation Techniques
Finding missing table entries using interpolation
Applying Bessel’s interpolation formula using central differences
Constructing cubic Lagrange interpolation polynomial
Numerical Solution of Differential Equations
Using Runge–Kutta method (RK-2 or RK-4) to compute y(0.1), y(0.2)
Curve Fitting
Fitting a curve of the form y = ax + bx² using the least squares method
Iterative Linear System Solvers
Solving a system of equations using Gauss–Seidel method (three iterations)
Regression Analysis
Calculating two regression lines using given summarized data
(price vs supply)
These problems require careful computation, use of numerical formulas, and understanding of algorithmic steps.
SECTION – C (Long Numerical Problems – 2 × 10.5 = 21 Marks)
This section contains three long, advanced numerical questions, and students must attempt any two. These questions involve higher-level numerical methods and deeper algorithmic understanding.
Q3 – Milne’s Method
Using given values of y(x), apply Milne’s Predictor–Corrector method to find y(2)
Tests knowledge of multi-step numerical ODE solutions
Q4 – Euler’s Modified (Improved Euler) Method
Solving dy/dx = log₁₀(x + y) with initial value y(0) = 1
Computing y(0.2) and y(0.5)
Tests predictor-corrector and refinement logic
Q5 – Newton’s Divided Difference Formula
Derivation of Newton divided difference interpolation formula
Using the given table to compute f(6)
Checks theoretical understanding + practical application
This section evaluates deep numerical analysis skills, multi-step algorithm implementation, and ability to solve computational problems requiring precision.
