MCA-09
December Examination 2016
MCA IInd Year Examination
Discrete Mathematics
Paper MCA-09
Time 3 Hours Max. Marks 80
Note: The question paper is divided into three sections B and C. Use of non-programmable scientific calculator is allowed in this paper.
Section A 8 × 2 16
Note: Section contain 08 Very Short Answer Type Questions. Examinees have to attempt all questions. Each question is of 02 marks and maximum word limit may be thirty words.
Write the set of even natural numbers less than 9.
Define an injective function.
Define negation of a statement.
Explain logical equivalence.
Write associative law for Boolean algebra.
State principle of inclusion-exclusion.
Define cyclc group.
(viii) Define complete graph.
515
MCA-09 200 3 (P.T.O.)
MCA-09 200 3 (Contd.)
515
Section B 4 × 8 32
Note: Section contain 08 Short Answer Type Questions.
Examinees will have to answer any four questions.
Each question is of 08 marks. Examinees have to delimit
each answer in maximum 200 words.
Prove that for set B and C
A
A B
Prove that relation R defined on set of integers by
R y ∈ z and x y is even is an equivalence relation.
Explain conditional and bi-conditional statements by using truth
table.
If a is any element in a Boolean algebra B then prove that:
a x 1 and ax 0 ⇒ x
A person throw a dice and tosses a coin. The combined out comes of
the dice and the coin are recorded. How many possible outcomes are
there? Write all such possible outcomes.
Prove that any two right cosets of a subgroup are either disjoint or
identical.
Prove that every field is an integral domain but converse is not true.
Draw the following graph:
3-regular but not complete
A complete bipartite graph having 2 vertices in one partite set
and 4 vertices in other partite set.
MCA-09 200 3
515
Section C 2 × 16 32
Note: Section contain 04 Long Answer Type Questions.
Examinees will have to answer any two questions.
Each question is of 16 marks. Examinees have to delimit
each answer in maximum 500 words.
10) Find the adjacency matrix and incidence matrix of the multi
graph shown in figure.
Prove that every tree has either one or two centres.
11) Prove that a group of order 5 is abelian
A polygon has 44 diagonals, find the number of sides.
12) If f NXN → NXN defined by f 3a × 4b, ∈ NXN
then examine f for bijection.
Using Pigeon-hole principle prove that among any group of 367
people, there must be at least two with same birth day.
13) Verify the validity of the following argument.
Every living thing is a planet or animal. John's gold fish is alive and
it is not a planet. All animals have hearts. Therefore John's gold fish
has a heart.