**Attempt any Six Questions**

2. Why is the study of error important to a computation scientist? Differentiate between inherent and numerical methods

3. Find the root of equation x^{2} - 4x - 10 = 0 using bisection method where root lies between 3 and 6

4. Find the square root of 3.5 using second-order Lagrange interpolation polynomial using the following table.

x | 1 | 2 | 3 | 4 | 5 |

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

5. Write a program to calculate the internal using Trapezoidal Rule

6. Solve the following set of equation using Gauss-Jordan Method

3x - 5y + 2z = 15

4x - y + z = 2

x - 3y + 7z = 22

7. Use Classical Runge-Kutta method to estimate y(0.2) when y'(x) = x^{2} + y^{2} with y(0) = 0 and h = 0.2

8. Solve the Poisson equation ∇^{2}ƒ = 2x^{2}y^{2} over the square domain 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3 with ƒ = 0 on the boundary and h = 1

**Attempt any two question**

9 (a) Factorize the matrix

[123282232282] using Cholesky's method.

(b) Locate the root 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 | 2 | 3 | 4 | 5 | 6 |

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

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

11. Given the data points.

1 | 0 | 1 | 2 |

x_{i} |
2 | 3 | 4 |

f_{i} |
4 | 9 | 16 |

Estimate the function value f at x = 2.5 using cubic splines.