U.G.C. NET Exam. 24 June, 2019 Paper–II (COMPUTER SCIENCE & APPLICATIONS)

Total Questions: 100

1. Which of the following is correct for the given poset?

Correct Answer: (d) There does not exist a greatest element and a least element
Solution:

A relation R on set A is called partial ordering or partial order if it is reflexive, anti-symmetric and transitive. A set together with a partial ordering R is called a partial ordered set or poset. The poset is denoted as (S,R).
Relations can be used to order some or all the elements of a set. For instance, the set of natural number is ordered by the relation ≤ such that for every ordered pair (x, y) in the relation, natural number x comes before the natural number y unless both are equal. So option fourth is correct.

2. How many ways are there to place 8 indistinguishable balls into four distinguishable bins?

Correct Answer: (b)
Solution:

3. How many bit strings of length ten either start with a 1 bit or end with two bits 00?

Correct Answer: (c) 640
Solution:

4. Suppose that a connected planar graph has six vertices, each of degree four. Into how many regions is the plane divided by a planar representation of this graph?

Correct Answer: (b) 8
Solution:

We apply Euler's formula where r = e – v + 2 since each vertex has degree 4, the sum of the degree is 24.
By handshaking theorem, 2e = 24
So e = 12
r = 12 – 6 + 2
r = 8
So we have 8 regions in this graph

5. For which values of m and n does the complete bipartite graph km.n have a Hamilton circuit?

Correct Answer: (c) m = n, m, n ≥ 2
Solution:

6. Which of the following is principal conjunctive normal form for [(p ∨ q) ^ ¬ p → ¬ q]?

Correct Answer: (a) p ∨ ¬ q
Solution:

Given (p ∨ q) ^ ¬ p → ¬ q
The precedence of the used operators are :-
^ > ∨ →
Therefore, [(p ∨ q) ^ ¬ p → ¬ q]
⇔ [((p ∨ q) ^ ¬ p) → ¬ q]
⇔ [((p ^ ¬ q) ∨ (q ^ ¬ p)) → ¬ q] – using distributive
law
⇔ [(F ∨ (q ^ ¬ p)) → ¬ q]
⇔ [(q ^ ¬ p) → ¬ q]
⇔ [ ¬ (q^ ¬ p) ∨ ¬ q] – using demorgan's law
⇔ [ ¬ q ∨ p ∨ ¬ q] ⇔ [p ∨ ¬ q]

7. How many cards must be selected from a standard deck of 52 cards to guarantee that at least three hearts are present among them?

Correct Answer: (d) 42
Solution:

In this the worst case will happen as follows
:-
1st 13 * 3 = 39 cards that we pick up turns out to be any one of diamonds or spades or clubs but not hearts. Now when we pick the next 3 cards they are guaranteed to be hearts (Qwe have already picked cards from all other suits)
∴ We need to pick 13 + 13 + 13 + 3 = 42 cards in order to guarantee that there are atleast 3 cards of hearts in the selected cards.

8. Match List-I with List-II :

Correct Answer: (d) (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)
Solution:

9. Find the zero-one matrix of the transitive closure of the relation given by the matrix A :

Correct Answer: (a)
Solution:

Let the elements be a, b, c on which the relation is defined. Then from the matrix we can say that the relation given is
{(a, a), (a, c), (b, b), (c, a), (c, b)}
Now, what are the minimum number of ordered pairs that we should add to the given relation that it becomes transitive relation ?
Using Warshall's Algorithm we can see that (c, c) and
(a, b) are missing.
After adding them to the relation and making the matrix again the matrix will become

10. Answer the following question

Correct Answer: (b)
Solution:

Here in Cj, we have two numbers which are highest (ie. 2 in column 1st and 2 in column 3rd) So we can choose any column to begin with : So lets start with column 3rd for convenience. Hence column 3rd become key column. Now, we find Theta = b/corresponding key column element.