Annamalai University 2007 B.C.A Computer Application
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5. (a) Show that every equivalence relation
defined on a set decomposes the set into disjoint equivalent classes. (10)
(b) Find all the partition of
X = { a, b, c, d }. (10)
6. Write an algorithm for multiplying two polynomials P and Q.
7. Suppose G is a finite cycle for graph with at least one edge, show that G has at least two vertices of degree 1.
8. Show that language L is recognizable by a Turing machine M if L is a type O language.
Name of the Candidate :
7 2 5 6
B.C.A. DEGREE EXAMINATION, 2007
(FIRST YEAR)
(PART - III)
(PAPER - I)
( New Regulations )
May ] [ Time : 3 Hours
Maximum : 100 Marks
Answer any FIVE questions.
All questions carry equal marks.
(5 x 20 = 100)
1. (a) A manufacturer of furniture makes two products chairs and tables. Processing of these products in done on machines - A and B. A chair requires 2 hours on machine - A and 6 hours on machine-B. A table requires 5 hours on machine - A and no time on machine - B. There are 16 hours of time per day available on
machine - A and 30 hours of time on machine - B. Profit gained by the manufacturer from the chair and table is Rs. 2 and Rs. 10 respectively. What should be the daily production of each of the two products? (10)
(b) Use simplex method to solve the LPP maximize z = 5Xj + 3x2 subject to constraints xi + x2 < 2 5Xj + 2x2 < 10 3Xj + 8x2 < 12
(a) Solve the following LPP by using its dual: maximize z = 2x + x2 subject to constraints
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E F G H | ||||||||||||||||||||
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3. Use revised simplex method to solve LPP
Maximize z = 2x + x2 subject to constraints 3Xj + 4x2 < 6 6Xj + x2 < 3 xp x2 -
4. Find the optimal sequences for processing the jobs on 4 machines whose processing times are given as
|
Mi |
m2 |
m3 |
M4 | |
|
25 |
15 |
14 |
24 | |
|
J2 |
22 |
12 |
20 |
22 |
|
J3 |
23 |
13 |
16 |
25 |
|
J4 |
26 |
10 |
13 |
29 |
Turn over
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Attachment: |
| Earning: Approval pending. |
