# RTU Previous Year Question Papers BE

# Computer Application in Civil Engineering Feb 2011

**Unit-I**

1.a) Find the roots of equation x^{3} – x – 4 = 0 correct to three decimal places using Newton-Rap son Method.

b) Write the algorithm for finding, roots of a non linear equation using Bisection Method.

**OR**

a) F ind the truncation error for e ^{x} at x — and x = – when we use

i) First three terms

ii) First four terms.

b) Find the real root of / (jc) = x^{3} – 2x – 5 = 0

by Bisection Method.

**Unit -II**

2. a) Solve the following system of equations by Gauss-Seidal Method

27 x + 6y – z = 85 6jc+ 15y + 2z = 12 x +y + 54z =110

b) Write the algorithms for solving the Linear simultaneous equations using triangularizing method.

**OR**

(a)What do you mean by Linear independent simultaneous equations?

(b) Solve the following equations:

x + 2y + 3z = 1 2x + 3y + 2z = 2 3x + 3y + 4z = 1 by Gauss Elimination Method.

**Unit-III**

(a)Write a short note on “Regression Analysis”.

(b)Fit a second degree parabola to the following data taking x as the independent variable.

a; : | l | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

y‘ | 2 | 6 | 7 | 8 | 10 | 11 | 11 | 10 | 9 |

**OR**

(a)Write a short note on “Numerical Analysis.

(b)The ordinates of the normal curve are given by the following table.

x: | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 |

v: j • | .3989 | .3910 | .3683 | .3332 | .2897 |

Evaluate

(i) y (0-25) (ii) y (0.62)

**Unit-IV**

4 (a)Compute the values of by the

i) Trapezoidal rule

ii) Simpson’s ~ rule and compare your result with the true value.

(b)What is the use of “Numerical Integration” to find area of a curve.

**OR**

a) Evaluate by Simpson’s rule with six intervals.

b) A curve is drawn to pass through the points given by the following table

x: | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 |

y’ | 2 | 2.4 | 2.7 | 2.8 | 3 | 2.6 | 2.1 |

Estimate the area bounded by the curve, x – axis and the lines x = 1 and x = 4.

**Unit-V**

5. a) Use Euler’s modified method with one step to obtain the value ofy at x = 0.1 when ^j-=x^{2} +y with x = 0, y = 0.94.

b) Explain any one method used for numerical solution of partial differential equation.

**OR**

Use Runge-Kutta fourth order method to solve £^{:}=-2V with x_{0} = 0_{0}= 1