The Computer Application is one of the thrust areas in Science and technology. The Department offers Masters' programme in Computer Applications (M.C.A), MSc Computer Science with specialization in soft computing and research programme leading to Ph.D.

In appreciation of its growing importance in business and the industrial scenario, the University established a Department of Computer Applications to facilitate research and human resources development in the subject.

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Question paper for Department of computer application from Cochin University of Science And Technology





Question paper for Department of computer application from Cochin University of Science And Technology:

CAS 2101 COMBINATORICS AND GRAPH THEORY

(a) Show that for each integer n > 0
nCo +nC1 +nC2 + nCn = 2
n

Solve the recurrence relation an - 3an_1 = n, n ~ 1, ao = 1.
A committee of eight is to be formed from 16 men and 10 women. In how many
ways can the committee be formed if
(i) there is no restrictions?
(ii) at least six men in the committee?

Prove that an mxm matrix whose elements belong to (-1, 1) is a Hadamad matrix if and only if its columns are orthogonal.
Why is a square block design called symmetric?
What is an error correcting code? ExpllJin by giving an example.

Define subgraph and path in a graph with example.
Explain traveling salesman problem.

Define a fundamental cycle and fundamental cut-set in a graph with an example.
(a)Show that a complete graph on four vertices is self dual.
(b) Draw the undirected graph whose incidence matrix is the following
(c) Prove that ,1.4 -3,1.3 +3,1.2 +4 cannot be a chromatic polynomial of any graph.

(a) Let A = {1,2,3,4} and the relation R on A is given by
R = {(I,I), (1,2), (2,1), (2,2), (2,4), (3,4), (4,1)}. Draw the digraph of'R,

Define a tournament. Illustrate with an example that a tournament has a directed Hamiltonian path.

Give one application ofa rooted tree in the study of Computer Science.