THEORY EXAMINATION (SEM–II) 2016-17 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES

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.