Madurai Kamraj University (MKU) 2006-2nd Year M.C.A Computer Aplications All subject s - Question Paper

simplex method to solve the LPP. Minimize z= -4x1 + X2 + 2X3Subject to 2x1 - 3X2 + 2X3 <=12
-5x1 + 2X2+3X3 >=4 3x1-2x3=-1 and X1, X2, X3 >=0.


10. (a) Use penalty method to solve the subsequent LPP. Minimize Z=4X1+X2 Subject
to3X1+X2=3 4X1 + 3X2 >= six x1 + 2X2 <=3 and X1,X2 >=0.Or (b) Solve by the dual simplex
method the subsequent LPP Minimize z = 5x1 + 6X2Subject to X +X2 2:24xj + X2 2: four X2 2:0.
(b) A fair die is tossed repeatedly. If Xn denotes the maximum of the numbers occurring in the
first n tosses, obtain the transition probability matrix p of the Markov chain {XnJ. obtain also p2
and P(X2 = 6).


11. (a) A supermarket has 2 girls ringing up sales at the counters. If the service time for every
customer is exponential with mean four minutes and if the people arrive in a Poisson fashion at
the rate of 10 per hour (i) What is the probability of having to wait for service?(ii) What is
the expected percentage of idle time for every girl?(iii) If a customer has to wait, what is the
expected length of his waiting time. Or (b) Discus the fields of application for queuing.
discuss queue discipline and its different form.


12. (a) A travelling salesman has to visit five cities. He wishes to begin from a particular city visit
every city once and then return to his starting point cost of going from 1 city to a different is
shown beneath. You are needed to obtain the lowest cost route.
To city
A B C D E
A 00 four 10 14 2
B 12 00 six 10 4
From City C 16 14 00 eight 14
D 24 eight 12 00 10
E two six four 16 00
Or (b) obtain the optimum integer solution to the subsequent linear programming issue
Maximize Z =XI + 2X2 Subject to 2X257 xI + X2 572x] 51 and xI' X2 2: 0 and are integers.


13. (a) describe the Markov -'property for a discrete space continuous time process. Prove that a
process having independent and stationary increments is Markov.


M.C.A 2nd Year May 2006


PAPER-II COMPUTER GRAPHICS


Time: 3 hours maximum: 100marks

PART A ans all ques. (8x5=40 marks)

1. (a) Write short notes on Graphical User Interface. Or (b). Write an algorithm for line
drawing and line commands.

2. (a) Write a note on bundled attributes. Or (b). elaborate the transformation commands?

Earning:   Approval pending.