Calicut University 2006 M.C.A , - 2K 301 - NUMERICAL ANALYSIS
Third Semester M.C.A Degree Examination, August 2006
MCA 2K 301 - NUMERICAL ANALYSIS & OPTIMIZATION TECHNIQUES
(New Scheme)
M0630I
Reg: .. Name:
THIRD SEMESTER MCA DEGREE EXAMINATION -JUNE 2006 MCA 2K 301 - NUMERICAL ANLYSIS & OPTIMIZATION TECHNIQUES
I'inic : 3 I lotus
Marks: 100
Answer any five Qitesiions
a. Using Regula-Falsi method, find the positive root of the equation x*2x2i 10x-2CM3. correct to three places of decimals
b. Solve by Grout** trtangularisation meihod. the system of equations:
xry+2r-7. 3x+2y4/. = 13, 4x+3y+2z-8
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a. Find the values of y at x--21 and x28 from the following table | ||||||||||
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from the following data
at x=0. from the following data
I
8
4
15
b Using Lagranges interpolation formula find y <6J
,..x 1 ) " 2 ~~ : 7 1 8 " i 1-1_4 | 5 :___I
a. Find dv/dx and d2ydx
U-! 0
l_v.i.4
I 2
b. Evaluate o J e dx. using Simpsons rule and by dividing the range of integration in to 4 equal parts
a. Using Taylors series method, solve the equation dy/dx=x2-ry2, given y 1, when x-0 and get y (0.1).
b. Use Rulers method to solve the equation dy/dx=xy given y (0) - I and find y (0.4)
Using Runge-Kutta method, solve the equations dy/dxy-x, given y (0) -
2 and taking h~ 0.1 and get the value of y (0 2) in two steps
Using Simplex method, solve the LPP Maximize 2=5x1 3xj subject to the constraints Xj+Xj<-2, 5x:+2x2<=10, 3xi*-8xj<=12 xi.x; >=0
i
OR
Use dual simplex method 10 solve the LPP Minimi/e Z" Xi +2x:'*-3x?
STC 2xi-x;-x> >* -4 xi+\j+2xj<* 8 XrXj>-2 >-*0
7
Solve the following iraosporlation problem whose cost matrix is
|
Dl |
D2 |
D3 |
D4 |
Supply | |
|
Ol |
21 |
16 |
25 |
13 |
11 |
|
02 |
17 |
18 |
14 |
23 |
13 |
|
03 |
32 |
27 |
18 |
41 |
19 |
|
Demand |
6 |
10 |
12 |
15 |
OR
Solve the following assignment problem, so that the total cost is a minimum
MHN
A B C I)
|
1 |
15 |
13 |
14 |
17 |
|
11 |
11 |
12 |
15 |
13 |
|
III |
18 |
12 |
10 |
11 |
|
IV |
15 |
17 |
14 |
16 |
2
|
Attachment: |
| Earning: Approval pending. |
