STUPIDSID
Solve any one question fromQ.1(a,b) and Q.2(a,b)
1(a)
Explain various errors with respect to numerical computation.
6 M
1(b)
Explain with suitable example Descartes' Rule of Signs.
6 M
2(a)
Explain various errors with respect to numerical computation.
6 M
2(b)
Using Birge Vieta method, find the real root of the equation: \( x^4-3x^2+2x-7=0\)/ Perform two interations. Take P0=1.3.
6 M
Solve any one question fromQ3(a,b) and Q.4(a,b)
3(a)
Using N-R method, obtain the real root of the equation: \( \cos x-xe^x=0. \)/ Take x0=1. Perform 4 interations.
6 M
3(b)
Using Newton Backward Difference interpolation, find y at x=12, given that:
| x | y |
| 2 | 94.8 |
| 5 | 87.9 |
| 8 | 81.3 |
| 11 | 75.1 |
| 14 | 82.5 |
7 M
4(a)
Explain Regula Falsi method with suitable diagram.
6 M
4(b)
Fit a curve of type
y = mx + c, for the following data using Least Square approximation method.
y = mx + c, for the following data using Least Square approximation method.
| x | y |
| 0.2 | 0.447 |
| 0.4 | 0.632 |
| 0.6 | 0.775 |
| 0.8 | 0.894 |
| 1 | 1 |
7 M
Solve any one question fromQ5(a,b) and Q.6(a,b)
5(a)
Using Gauss Jacobi interactive method, obtain solution of system of linear simultaneous equations given below. Perform 5 interations.
4x +y-z=4
2x+3y+z =4
x+ y +5z = 16.
Take x0=y0=z0=0.
4x +y-z=4
2x+3y+z =4
x+ y +5z = 16.
Take x0=y0=z0=0.
6 M
5(b)
Using Gauss elimination method solve the following system of linear simultaneous equations:
3x-y+2z=12
x+2y+3z=11
2x-2y-z=2.
3x-y+2z=12
x+2y+3z=11
2x-2y-z=2.
6 M
6(a)
Explain Gauss-Seidel method of solution of system of linear simulataneous equations.
6 M
6(b)
Using power method, find the largest eigenvalue for the following matrix:
\[A=\begin{bmatrix} 4 &1 \\ 1& 3 \end{bmatrix}\]
Take [0 1] T. Perform 5 interations.
\[A=\begin{bmatrix} 4 &1 \\ 1& 3 \end{bmatrix}\]
Take [0 1] T. Perform 5 interations.
6 M
Solve any one question fromQ.7(a,b) and Q.8(a,b)
7(a)
Evaluate:
\[\int_{0.2}^{1}\left ( 1+x^3 \right )dx\]
using Simpson's (3/8) th rule with step size 0.1.
\[\int_{0.2}^{1}\left ( 1+x^3 \right )dx\]
using Simpson's (3/8) th rule with step size 0.1.
6 M
7(b)
Using 4th order R-K method find y(0.1) given that:
y(0) = 1 and y'(0)=0 and \(\frac{d^2y}{dx^2}-x\frac{dy}{dx}-y. \)/
Take h = 0.1.
y(0) = 1 and y'(0)=0 and \(\frac{d^2y}{dx^2}-x\frac{dy}{dx}-y. \)/
Take h = 0.1.
7 M
8(a)
Find the first derivative of f(x) at x= 1.5 from the following data:
| x | y |
| 1.5 | 3.375 |
| 2.0 | 7.0 |
| 2.5 | 13.625 |
| 3.0 | 24 |
| 3.5 | 38.875 |
| 4.0 | 59 |
6 M
8(b)
Evaluate the given integral using Trapezoidal rule. Take h = 0.2, k = 0.2 \[\int_{1}^{1.4}\int_{2}^{2.4}\frac{1}{xy} dx dy.\]
7 M
More question papers from Numerical Method and Computer Programming