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TAMIL NADU OPEN UNIVERSITY
Chennai-15.
B.Sc Maths with Computer Applications – Third Year
SPOT ASSIGNMENT
COURSE
Real and Complex Analysis
COURSE CODE
BMC- 31
Time: 1 Hour
ADMISSION YEAR
AY – 2013 - 14
Total Marks: 25
Answer all questions.
1.
Define continuous function, uniformly continuous function and give
8 Marks
the relationship between them with justification.
2.
State and prove First Mean Value theorem for integrals.
9 Marks
3.
Define an analytic function and prove that if f is analytic in a
8 Marks
region , then the real and imaginary parts are harmonic.
TAMIL NADU OPEN UNIVERSITY
Chennai-15.
B.Sc Maths with Computer Applications – Third Year
SPOT ASSIGNMENT
COURSE
Linear Algebra and
Boolean Algebra
COURSE CODE
BMC- 32
Time: 1 Hour
ADMISSION YEAR
AY – 2013 - 14
Total Marks: 25
Answer all questions.
1.
State and prove equivalent conditions for a set of vectors to be a
8 Marks
basis for a vector space.
2.
Define an inner product space and prove that if W is a subspace of a
9 Marks
finite dimensional inner product space then V = W  W.
3.
Define a Boolean algebra and list some properties.
8 Marks
TAMIL NADU OPEN UNIVERSITY
Chennai-15.
B.Sc Maths with Computer Applications – Third Year
SPOT ASSIGNMENT
COURSE
Linear Programming and
Operations Research
COURSE CODE
ADMISSION YEAR
BMC- 33
AY – 2013 - 14
Time: 1 Hour
Total Marks: 25
Answer all questions.
1. Find the optimal assignment for the following cost matrix:
I
8 Marks
II III IV
A 11 17 8 16
B  9 7 12 10
C 13 16 15 12


D 14 10 12 11
2.
Use dual simplex method to solve the L.P.P.
Minimize
10 Marks
Z = x1 + 2x2 + 3x3
subject to the constraints:
x1 – x2 + x3  4
x1 – x2 + 2x3 ≤ 8
x2 – x3  2
x1, x2, x3  0
3.
A TV Repairman finds that the time spent on his jobs has an 7 Marks
exponential distribution with mean 30 minutes. If he repairs sets in
the order in which they came in and if the arrival of sets is
approximately poisson with an average rate of 10 per 8 hours day,
what is repairman’s expected idle time each day? How many jobs
are ahead of the average set just brought in?
TAMIL NADU OPEN UNIVERSITY
Chennai-15.
B.Sc Maths with Computer Applications - Third Year
SPOT ASSIGNMENT
COURSE
Graph Theory
COURSE CODE
ADMISSION YEAR
BMC – 34
AY 2013 - 14
Time: 1 Hour
Total Marks: 25
Answer all questions.
1
Develop and Algorithm to check whether a given sequence is graphic
9 Marks
or not and illustrate.
2
Define a tree and prove that if G is a tree, then q = p – 1.
8 Marks
3
Define a critical graph and prove that if G is k – critical then  ≥ k – 1.
8 Marks
TAMIL NADU OPEN UNIVERSITY
Chennai-15.
B.Sc Maths with Computer Applications - Third Year
SPOT ASSIGNMENT
COURSE
COURSE CODE
Introduction to
Internet Programming (Java)
Time: 1 Hour
BMC – 35
ADMISSION YEAR
AY 2013 – 14
Total Marks: 25
Answer all questions.
1
What is inheritance ? explain.
8 Marks
2
Write a program to check whether a given number is a palindrome or
9 Marks
not.
3
Write a note on “Applet”.
8 Marks