# UGC NET Solved Computer Science Paper III June 2014 - Part 7

61.       Given the following equalities :
E1 : nK+Î + nK lg n = q(nK+Î) for all fixed K and Î, K > 0 and Î > 0.
E2 : n32n + 6n23n = O(n32n)
Which of the following is true?
(A) E1 is correct and E2 is correct.
(B) E1 is correct and E2 is not correct.
(C) E1 is not correct and E2 is correct.
(D) E1 is not correct and E2 is not correct.
62.       Consider the fractional knapsack instance n = 4, (p1, p2, p3, p4) = (10, 10, 12, 18), (w1, w2, w3, w4) = (2, 4, 6, 9) and M = 15. The maximum profit is given by
(Assume p and w denotes profit and weight of objects respectively)
(A) 40
(B) 38
(C) 32
(D) 30
63.       The solution of the recurrence relation of
(A) O(n2)
(B) O(nlg n)
(C) O(n)
(D) O(l g n)
64.       If h is chosen from a universal collection of hash functions and is used to hash n keys into a table of size m, where n ≤ m, the expected number of collisions involving a particular key K is
(A) less than 1
(B) less than lg n
(C) greater than 1
(D) greater than lg n
65.       Given the following statements :
S1 : The subgraph-isomorphism problem takes two graphs G1 and G2 and asks whether G1 is a subgraph of G2.
S2 : The set-partition problem takes as input a set S of numbers and asks whether the numbers can be partitioned into two sets A
Which of the following is true?
(A) S1 is NP problem and S2 is P problem.
(B) S1 is NP problem and S2 is NP problem.
(C) S1 is P problem and S2 is P problem.
(D) S1 is P problem and S2 is NP problem.
66.       Suppose that the splits at every level of quicksort are in the proportion (1 – a) to a, where 0 < a ≤ ½ is a constant. The minimum depth of a leaf in the recursion tree is approximately given by
67.       Ten signals, each requiring 3000 Hz, are multiplexed on to a single channel using FDM. How much minimum bandwidth is required for the multiplexed channel? Assume that the guard bands are 300 Hz wide.
(A) 30,000
(B) 32,700
(C) 33,000
(D) None of the above
68.       A terminal multiplexer has six 1200 bps terminals and ‘n’ 300 bps terminals connected to it. If the outgoing line is 9600 bps, what is the value of n?
(A) 4
(B) 8
(C) 16
(D) 28
69.       Which of the following is used in the options field of IPv4?
(A) Strict source routing
(B) Loose source routing
(C) time stamp
(D) All of the above
70.    Which layers of the OSI reference model are host-to-host layers?
(A) Transport, Session, Presentation, Application
(B) Network, Transport, Session, Presentation
1. 