M.C.A. (Semester (CBCS) Examination Nov/Dec-2018
Science
DISCRETE MATHEMATICAL STRUCTURES
iI
Time 2½ Hours Max. Marks: 70
Instructions: All questions are compulsory
Figures to the right indicate full marks
Q.1 Multiple choice questions (each questions of 1 marks) 14
A Relation R on set A is equivalence Relation if
Reflexive Transitive
Symmetric All of above
In how many ways committee of 6 can be choose from 12 people


In a group closure property is given by
b ∈ G a ∗ b ∈ G a ∗ b b ∗ a
a ∗ e e ∗ a a a ∗ b ∗ c a ∗ b ∗ c
An arrangement of set of n objects is called
Partition Combination
Permutation Group
A single vertex with single loop is cycle of length
Zero One
Two Three
Inverse of any matrix A is
One Unique
Different It self
A graph with neither loop nor multiple edges between any pair of vertices is
called
Multi graph Regular graph
Simple graph Connected graph
In set theory
U
U None of above
Matrix is nonsingular if
A 0 A 0
A 1 A
10) In group G existence of identity is given by
a ∗ b b ∗ a a ∗ e e e ∗ a 8
a ∗ a−1 a−1 ∗ a e none of these
11) Let L be lattice then a ∈ iff
0
1
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12) If p is true, q is false then p
True False
1 Both a c
13) For only set A where U is universal set A U
A U
None of above
14) The function f R → R such that ∈ is called
Constant function Identity function
One-one function Onto function
Q.2 Answer the following (any four) 08
Define graph give an example.
Find
Define Group
Write formula for nCr nPr
Define Lattice
Write short notes on (any two) 06
Boolean matrix
Function
Permutation combination
Q.3 Answer the following (any two) 08
Show that nP(n − r −
Draw Hasse diagram for poset P S C
is power set of S

Find determinant of A
5 3 2
7 3 4
8 5
Answer the following (Any one) 06
Types of Matrices
Explain properties
Reflexive
ii) Symmetric
Q.4 Answer the following (any two) 10



Find degree of all vertices in above graph
Dn denotes set of all positive divisors of n
D30 10, 15, 30} draw Hasse diagram for D30
Find determinant of A
1 −2 1
0 −1 1
2 0 −3

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Answer the following (Any one) 04
Define
symmetric Matrix
ii) Skew symmetric matrix with example
Define
walk
ii) path with example
Q.5 Answer the following (any two) 14
Show that
p q
ii) p q
Find eigen values and eigen vectors of
A
3 4
4 −3
Let L1, L2 be two Lattices
L1 L2=
• 6
• 4
• 2
• 7
• 5
• 3
• 1
Find Lattice L1 × L2 and draw a L1 × L2