# UGC NET CS 2016 July – II

• Last Updated : 07 Apr, 2021

 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? A 2 B 4 C 5 D 6
UGC NET CS 2016 July – II
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Question 5 Explanation: 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` = 0So, 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: 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: 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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