UGC NET CS 2016 July – II

Question 1

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

• 10
• 15
• 25
• 30

Question 2

The number of different spanning trees in complete graph, K₄ and bipartite graph, K_2,2 have ______ and _______ respectively.

• 14, 14
• 16, 14
• 16, 4
• 14, 4

Question 3

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

• R₁ ∩ R₂ is reflexive and R₁ ∪ R₂ is irreflexive.
• R₁ ∩ R₂ is irreflexive and R₁ ∪ R₂ is reflexive.
• Both R₁ ∩ R₂ and R₁ ∪ R₂ are reflexive.
• Both R₁ ∩ R₂ and R₁ ∪ R₂ are irreflexive.

Question 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?

• 3/4
• 2/3
• 1/2
• 1/3

Question 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?

• 2
• 4
• 5
• 6

Question 6

Which of the following logic expressions is incorrect?

• 1 ⊕ 0 = 1
• 1 ⊕ 1 ⊕ 1 = 1
• 1 ⊕ 1 ⊕ 0 = 1
• 1 ⊕ 1 = 0

Question 7

The IEEE-754 double-precision format to represent floating point numbers, has a length of _____ bits.

• 16
• 32
• 48
• 64

Question 8

Simplified Boolean equation for the following truth table is:

• F = yz` + y`z
• F = xy` + x`y
• F = x`z + xz`
• F = x`z + xz` + xyz

Question 9

The simplified form of a Boolean equation (AB` + AB`C + AC) (A`C` + B`) is :

• AB`
• AB`C
• A`B
• ABC

Question 10

In a positive-edge-triggered JK flip-flop, if J and K both are high then the output will be _____ on the rising edge of the clock.

• No change

• Set

• Reset

• Toggle