- Which one of the following can causes a blunders in system?

- Human imperfection
- Numerical Methods
- Computing Methods
- Measuring Methods

- Which one of the following be possible solution of system of linear equation with equations 2x-y = 5 and 3x-3/2y=4 ?

- Unique Solution
- No solution
- Infinite Solution
- Iii-condition

- In which method improved rood x1 is calculated as x0-f(x0)/f’(x0)?

- Bisection Method
- Secant Method
- Newton-Raphson Method
- False Point Method

- Which one of the following is not an open end method (extrapolation method) of solving non linear equattions?

- Bisection Method
- Newton -Raphson Method
- Secant Method
- Fixed Point Method

- Which one of the following is an iteration method of solving the system of linear equations?

- Gauss-jardon Method
- Matrix inverse Method
- Trangular Factorization Method
- Gauss-seidel Method

- Which of the following is a cubic splines with zero second derivatives at the end points?

- Quadratic Splines
- Natural cubic Splines
- Semi-cubic Splines
- No Splines

- Which one of the following is correct value of Romberg estimate R(0,0) for 1∫2 1/x dx ?

- 70
- 85
- 75
- 80

- Which one of the following is an Elliptic Equation?

- Laplace Equation
- Crank Nicolson Method
- Bender-Schmid Equation
- Newton-Gregory Method

- Which one of the following method is similar to two stage Runge Kutta Method?

- Tayler Series Method
- Euler’s Method
- Picard’s Method
- Heun’s Method

- Which one of the following is the correct value off eigen values for 8×1 – 4×2 = ʵx1 and 2×1 – 2×2 = ʵx2?

- 4,5
- 6,4
- 8,2
- 4,2

Group B

- why is the study of errors important to a computational scientist ? Differentiate between inherent and numerical errors.
- Find the root of equation x
^{2 – }4x – 10 = 0 using bisection method where root lies between 5 and 6. - Find the square root of 3.5 using second order Larange interpolation polynomial using the following data table.

X | 1 | 2 | 3 | 4 | 5 |

F(x) | 1 | 1.4142 | 1.7321 | 2 | 2.2361 |

- Write a program to calculate the integral using Trapezoidal Rules?
- solve the following set of equation using Gauss-Jardon Method

3x-5y+ 2z = 15

4x – y + z = 2

X – 3y + 7z = 22

- Use classical Runge -Kutta Method to estimate (0.2) when y’(x) = x
^{2}+ y^{2 }with y(0) = 0 and h = 0.2 - solve the poisson equation over the square domain 0 ≤ x≤ 3 and 0≤ y≤ 3 with f = 0

GROUP C

- a) Factroize the matrix

1 2 3

2 8 22 Using Cholesky’s Method

22 8 2

(b) Locate the root of equation x^{2} + x – 2 = 0 using the fixed point method?

10 (a) Fit a straight line to the following set of data points.

X | 1 | 3 | 4 | 6 | 8 | 9 |

y | 1 | 3 | 4 | 4 | 5 | 7 |

(b)Differentiate between ordinary and partial differential equations with their applications

- Given the data points:

I | 0 | 1 | 2 |

Xi | 2 | 3 | 4 |

fi | 4 | 9 | 16 |

Estimate the function value f at x = 2-5 using cubic splines.