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Devi Ahilya University 2009 B.Sc Computer Science Part II(3 Y.D.C.) - Question Paper

Sunday, 20 January 2013 02:55Web

2009
B.Sc. Part II(3 Y.D.C.) exam
COMPUTER SCIENCE
PAPER II
CPN - 22 : Computer Oriented Numerical Methods
Time : 3 Hours
Max. Marks : 50

Note : ans all 5 ques.. All ques. carry equal marks. ans must be to the point.
The blind candidates will be provided 60 minutes extra time.

1. Derive the formula for Newton-Raphson method giving Geometrical Interpretation. obtain a root
and accurate it to 4 decimal places of the subsequent formula x^x = 1000 using Newton-
Raphson method.
Or
(a) Write a program for Secant Method.
(b) Write a program for Bisection method.

2. Solve the subsequent system of equations by Gauss-Seidal method :
27x+6y-z = 85
6x+15y+2z = 72
x+y+54z = 110
Or
(a) Write a program for Gauss Elimination method.
(b) obtain the inverse of subsequent matrix by Triangularization method :
50 107 36
25 54 20
31 66 21

3. Using Rnge-Kutta 4th order method to solve :
dy/dx = 1+y^2 where y(0) = 0 at x= 0.2.
Or
(a) Write a program for Trapezoidal Rule.
(b) Write an Algorithm for the Euler's Method.

4. From the subsequent table obtain the number of learner who found (a) less than 45 marks(b)
more than 45 marks :
Marks found : 30-40 40-50 50-60 60-70 70-80
No. of Students 31 48 56 35 31
Or
(a) e^x = (?^2/E)e^x.Ee^x/?^2e^x
(b) Write an algorithm for Lagrange's Interpolation.

5. Fit a 2nd degree parabola with the use of subsequent table :
x : one two three four 5
y : 1090 1220 1390 1625 1916
Or
(a) Write a program to fit a linear curve.
(b) Write an algorithm to fit the curve of the form y = ax^b.