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?

• A. 10
• B. 15
• C. 25
• D. 30

Answer: (C)

UGC NET CS 2016 July – II Set Theory & Algebra
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Question 2

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

• A. 14, 14
• B. 16, 14
• C. 16, 4
• D. 14, 4

Answer: (C)

UGC NET CS 2016 July – II Graph Theory
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Spanning trees in complete graph is equal to n^(n-2)(where n is no of sides or regularity in complete graph). So, spanning trees in complete graph K₄ will be 4^{(4 - 2)}. i.e. 4² = 16. Spanning trees in a bipartite graph K_m,n is equal to m^(n-1) * n^(m-1). So, spanning trees in K_2,2 will be 2^(2-1) * 2^(2-1). i.e. 2¹ * 2¹.= 4. So, option (C) is correct.

Question 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.

Answer: (C)

UGC NET CS 2016 July – II Set Theory & Algebra
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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?

• A. 3/4
• B. 2/3
• C. 1/2
• D. 1/3

Answer: (B)

UGC NET CS 2016 July – II Probability
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There are BB RR and BR, total outcome is 3, probability that the opposite side is the same color as the one side we observed: It is clear that BB and RR will show the same color on opposite side, so favorable outcome will be 2. Probability will be favorable outcome / total outcome i.e. 2 / 3. So, option (B) is correct.

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?

• A. 2
• B. 4
• C. 5
• D. 6

Answer: (C)

UGC NET CS 2016 July – II
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Total 5 clique will be there. So, option (C) is correct.

Question 6

Which of the following logic expressions is incorrect?

• A. 1 ⊕ 0 = 1
• B. 1 ⊕ 1 ⊕ 1 = 1
• C. 1 ⊕ 1 ⊕ 0 = 1
• D. 1 ⊕ 1 = 0

Answer: (C)

UGC NET CS 2016 July – II Digital Logic & Number representation Logic functions and Minimization
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We know that x ⊕ y = x`y + xy` So,

1. 1 ⊕ 0 = 1`0 + 10` = 0 * 0 + 1 * 1 = 0 + 1 = 1
2. 1 ⊕ 1 ⊕ 1 = (1 ⊕ 1) ⊕ 1 = (1`1 + 11`) ⊕ 1 = (0) ⊕ 1 = 1`0 + 10` = 0 * 0 + 1 * 1 = 0 + 1 = 1
3. 1 ⊕ 1 ⊕ 0 = 1 ⊕ (1 ⊕ 0 ) = 1 ⊕ ( 1`0 + 10` = 0 * 0 + 1 * 1 = 0 + 1 ) = 1 ⊕ 1 = 1`1 + 11` = 0
4. 1 ⊕ 1 = 1`1 + 11` = 0
So, option (C) is correct.

Question 7

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

• A. 16
• B. 32
• C. 48
• D. 64

Answer: (D)

UGC NET CS 2016 July – II Digital Logic & Number representation Number Representation
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The IEEE-754 double-precision format to represent floating point numbers, has a length of 64 bits. 1 bit for sign, 11 bit for exponent and rest 52 is for fraction. So, option (D) is correct.

Question 8

Simplified Boolean equation for the following truth table is:

• A. F = yz` + y`z
• B. F = xy` + x`y
• C. F = x`z + xz`
• D. F = x`z + xz` + xyz

Answer: (C)

UGC NET CS 2016 July – II Set Theory & Algebra
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So, option (C) is correct.

Question 9

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

• A. AB`
• B. AB`C
• C. A`B
• D. ABC

Answer: (A)

UGC NET CS 2016 July – II
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(AB` + AB`C + AC) (A`C` + B`) = AB` +AB`C +AB`C = AB` +AB`C = AB`(1 + C) = AB` So, option (A) is correct.

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.

• A. No change
• B. Set
• C. Reset
• D. Toggle

Answer: (D)

UGC NET CS 2016 July – II Digital Logic & Number representation Sequential circuits
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