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
Set Theory & Algebra    UGC NET CS 2016 July – II    
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Question 2
The number of different spanning trees in complete graph, K4 and bipartite graph, K2,2 have ______ and _______ respectively.
A
14, 14
B
16, 14
C
16, 4
D
14, 4
Graph Theory    UGC NET CS 2016 July – II    
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Question 2 Explanation: 
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 Km,n is equal to m(n-1) * n(m-1). So, spanning trees in K2,2 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.
Set Theory & Algebra    UGC NET CS 2016 July – II    
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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
Probability    UGC NET CS 2016 July – II    
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Question 4 Explanation: 
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? 5 (2)
A
2
B
4
C
5
D
6
UGC NET CS 2016 July – II    
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Question 5 Explanation: 
555 (3) 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
Digital Logic & Number representation    UGC NET CS 2016 July – II    Logic functions and Minimization    
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Question 6 Explanation: 
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
  5. 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
Digital Logic & Number representation    Number Representation    UGC NET CS 2016 July – II    
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Question 7 Explanation: 
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: 8 (2)
A
F = yz` + y`z
B
F = xy` + x`y
C
F = x`z + xz`
D
F = x`z + xz` + xyz
Set Theory & Algebra    UGC NET CS 2016 July – II    
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Question 8 Explanation: 
8 (4) 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
UGC NET CS 2016 July – II    
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Question 9 Explanation: 
(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
Digital Logic & Number representation    UGC NET CS 2016 July – II    Sequential circuits    
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There are 50 questions to complete.


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