Numerical Method (CACS252) TU Board 2025 Question Paper – BCA Semester 4

Tribhuvan University

Bachelor of Computer Application

Semester 4 · TU Board 2025

Course Title: Numerical Method (CACS252)

Full Marks: 60Pass Marks: 24Time: 3 hours

Candidates are required to answer the question in their own words as far as possible.

Group A

Attempt any SIX question.(6 × 5 = 30)

2.
What do you mean by true error? Find a positive root of equation $x^{2} = 1$ , which lies between 0 and 1 using bisection method.

Answer comingAlso asked in 2020
5
3.
What is interpolation? Given the following set of data points, obtained the table of divided difference. Use the table to estimate the value of $f (1.5)$ . $i$ 01234 $x_{i}$ 12345 $f (x_{i})$ 072663124

Answer coming
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4.
Solve the following system of equations by Gauss elimination method. $2 x + y + 4 z = 12$ $8 x - 3 y + 2 z = 23$ $4 x + 11 y - z = 33$

Answer comingAlso asked in 2026, 2024, 2023, 2020
5
5.
The distance of motorbike at interval 2 minutes are given below: Time(minutes)0246Distance(Km)01.53.86.7 Evaluate the velocity and acceleration of motorbike at time 2.37 and 4.57 minutes.

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6.
Write a program to compute value of $y$ when $x = 2$ such that $\frac{d y}{d x} = 3 x^{2} + 1$ with $y (1) = 2$ and $h = 0.25$ using Euler's method.

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7.
Find the largest Eigen value and corresponding Eigen vector of the following matrix using power method. $120210 00 - 1$

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8.
Solve the Poisson equation $\nabla^{2} f = 2 x^{2} y^{2}$ over the square domain $0 \leq x \leq 3$ and $0 \leq y \leq 3$ with $f = 0$ on the boundary and $h = 1$ .

Answer comingAlso asked in 2022, 2021, 2020
5

Attempt any TWO questions(2 × 10 = 20)

9.
What do you mean by ill condition? Solve the following system using Jacobi iteration method. $2 a + b + c = 5$ $3 a + 5 b + 2 c = 15$ $2 a + b + 4 c = 8$

Answer coming
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10.
How interpolation is differ from regression? Write down algorithm and program for Lagrange interpolation polynomial.

Answer coming
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11.
What is fixed point iteration method? How it converge the root of non-linear equation? Find the root of equation $f (x) = x^{2} - 3 x + 2$ using N-R method.

Answer coming
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