July 2016 - Paper 2

1:  

How many different equivalence relations with exactly three different equivalence classes
are there on a set with five elements ?

A.

10

B.

15

C.

25

D.

30

 
 

Option: C

Explanation :

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2:  

The number of different spanning trees in complete graph, K4 and bipartite graph, K2, 2have ______ and _______ respectively.

A.

14, 14

B.

16, 14

C.

16, 4

D.

14, 4

 
 

Option: C

Explanation :

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3:  
Suppose that R1 and R2 are reflexive relations on a set A. Which of the following statements is correct ?
A.

R1 ∩ R2 is reflexive and R1 ∪ R2 is irreflexive.

B.

R1 ∩ R2 is irreflexive and R1 ∪ R2 is reflexive.

C.

Both R1 ∩ R2 and R1 ∪ R2 are reflexive.

D.

Both R1 ∩ R2 and R1 ∪ R2 are irreflexive.

 
 

Option: C

Explanation :

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4:   There are three cards in a box. Both sides of one card are black, both sides of one card are
red, and the third card has one black side and one red side. We pick a card at random and
observe only one side.What is the probability that the opposite side is the same colour
as the one side we observed ?
A.

3/4

B.

2/3

C.

1/2

D.

1/3

 
 

Option: B

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5:  

A clique in a simple undirected graph is a complete subgraph that is not contained in any larger complete subgraph. How many cliques are there in the graph shown below ?


21177
A.

2

B.

4

C.

5

D.

6

 
 

Option: C

Explanation :

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