Tribhuvan University · BCA Semester IV
BCA 4th Semester Numerical Methods Past Questions
Tribhuvan University BCA Semester IV Numerical Methods past questions from 2020 and 2023, including numerical methods for root finding, interpolation, integration, linear equations, differential equations, PDEs and curve fitting.
Exam pattern: Group B contains six questions to attempt for 30 marks, while Group C contains two questions for 20 marks. The supplied 2020 and 2023 text contains some missing mathematical expressions, so unclear equations are marked instead of being guessed.
Numerical Methods Past Questions 2020
BCA Semester IV · CACS25260 Marks · Pass 24 · 3 Hours
Group B
Attempt any SIX · 6 × 5 = 302. Compute the root of an equation in the vicinity of x = 5 using the Newton-Raphson method.
3. Estimate the value of ln(2.5) using the Newton-Gregory forward difference formula from the following data:
| x | 1.0 | 2.0 | 3.0 | 4.0 |
|---|---|---|---|---|
| ln(x) | 0.0 | 0.6931 | 1.0986 | 1.3863 |
4. Write an algorithm to compute integration using Simpson’s 1/3 rule. Evaluate the given integration using Simpson’s 1/3 rule. [2.5+2.5]
The integral expression was missing from the supplied transcription.
The integral expression was missing from the supplied transcription.
5. What is meant by an ill-conditioned system? Find the Cholesky decomposition of the given matrix. [5]
The matrix was missing from the supplied transcription.
The matrix was missing from the supplied transcription.
6. Use the classical Runge-Kutta method to estimate y(0.4) for the given differential equation with y(0)=0, assuming h=0.2.
The differential equation was missing from the supplied transcription.
The differential equation was missing from the supplied transcription.
7. Solve the Poisson equation over the square domain 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3 with f = 0 on the boundary and h = 1.
8. Write short notes on any TWO:
- Types of Errors
- Convergent Methods
- PDE
Group C
Attempt any TWO · 2 × 10 = 209. Write an algorithm and program to compute the root of a nonlinear equation using the bisection method. [4+6]
10. Given the data points, estimate the function value using cubic splines.
The supplied transcription is corrupted and does not preserve the complete table/function or target value. Verify the original paper before solving.
The supplied transcription is corrupted and does not preserve the complete table/function or target value. Verify the original paper before solving.
11.
- a) Solve the given system of equations by the Gauss-Seidel method.
- b) Write an expansion of Taylor’s Theorem and solve the equation for x = 0.5 using Taylor’s method.
Numerical Methods Past Questions 2023
BCA Semester IV · CACS252 · Batch 202060 Marks · Pass 24 · 3 Hours
Group B
Attempt any SIX · 6 × 5 = 302. Explain the concept of error. Explain the taxonomy/classification of errors.
3. Estimate the value of sin θ at the specified value using an appropriate interpolation/difference formula from the given set of data.
The complete data table and target value were missing in the supplied transcription.
The complete data table and target value were missing in the supplied transcription.
4. Write an algorithm and program to calculate integration using the Trapezoidal rule. [2+3]
5. What is the form of the resultant matrix using the Gauss-Jordan method? Solve the following system using Gauss-Jordan:
[1+4]
| x + 2y − 3z = 4 |
| 2x + 4y − 5z = 8 |
| −x − y + 2z = −1 |
6. Find the value of the specified function using Newton’s backward difference formula from the given data.
The complete data and target value were missing from the supplied transcription.
The complete data and target value were missing from the supplied transcription.
7. Solve the ordinary differential equation using the fourth-order Runge-Kutta method to estimate y(0.4) for the equation dy/dx = x² + y² with y(0)=0, assuming h=0.2.
8. Solve for the steady-state temperatures in a rectangular plate of 8 cm × 10 cm. One 10 cm side is held at 50°C, another 10 cm side at 30°C, and the other two sides at 10°C. Assume grid size 2 cm × 2 cm.
Short notes: Interpretation; Boundary value problems; Partial Differential Equations.
Group C
Attempt any TWO · 2 × 10 = 209.
- a) Compute the root of a nonlinear equation using the Newton-Raphson method. [5]
- b) Fit a set of data using Least Square Regression. [5]
10.
- a) Write and implement an algorithm to solve a system of linear equations using the Gauss-Seidel method with a suitable numerical example. [2.5+2.5]
- b) Write a program to solve ordinary differential equations using Heun’s method. [5]
11.
- a) Apply a factorization method to solve the given system of equations. [5]
- b) Solve the supplied numerical-analysis problem using the specified method. [5]
BCA 4th Semester Numerical Methods Exam Preparation
Important recurring areas include Newton-Raphson, bisection, interpolation, numerical integration, Gauss-Jordan, Gauss-Seidel, Cholesky decomposition, Runge-Kutta, Heun’s method, Poisson equations, boundary value problems, PDEs, errors and least-square regression.
More BCA resources: BCA 4th Semester Study Materials · BCA Study Materials · Tribhuvan University Resources.