61.  A recursive function h, is defined as follows:
h(m) = k, if m=0 = 1, if m=1 = 2h(m1) + 4h(m2), if m≥2 If the value of h(4) is 88 then the value of k is: 
a.  0 
b.  1 
c.  2 
d.  1 
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Answer: (c).2

62.  The asymptotic upper bound solution of the recurrence relation given by
T(n)= 2T(n/2)+n/log n is: 
a.  O(n^2) 
b.  O(n log n) 
c.  O(n log log n) 
d.  O(log log n) 
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Answer: (c).O(n log log n)

63.  The minimum number of scalar multiplication required, for parenthesization of a matrixchain product whose sequence of dimensions for four matrices is <5,10,3,12,5> is 
a.  630 
b.  580 
c.  480 
d.  405 
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Answer: (d).405

64.  What is the probability that a randomly selected bit string of length 10 is a palindrome? 
a.  1/64 
b.  1/32 
c.  1/8 
d.  1/4 
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Answer: (b).1/32

65.  Given the following graphs. Which of the following is correct? 
a.  G1 contains Euler circuit and G2 does not contain Euler circuit 
b.  G1 does not contain Euler circuit and G2 contains Euler circuit 
c.  Both G1 and G2 do not contain Euler circuit 
d.  Both G1 and G2 contain Euler circuit 
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Answer: (c).Both G1 and G2 do not contain Euler circuit

66.  Consider a weighted complete graph G on the vertex set {v1, v2, …. vn} such that the weight of the edge (vi, vj) is 4 i – j. The weight of minimum cost spanning tree of G is: 
a.  4n^2 
b.  n 
c.  4n – 4 
d.  2n – 2 
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Answer: (c).4n – 4

67.  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 
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Answer: (c).5

68.  The symmetric difference of two sets S1 and S2 is defined as
S1ΘS2 = {xxϵS1 or xϵS2, but x is not in both S1 and S2} The nor of two languages is defined as nor (L1,L2) = {ww ∉ L1 and ww ∉ L2} Which of the following is correct? 
a.  The family of regular languages is closed under symmetric difference but not closed under nor 
b.  The family of regular languages is closed under nor but not closed under symmetric difference 
c.  The family of regular languages are closed under both symmetric difference and nor 
d.  The family of regular languages are not closed under both symmetric difference and nor 
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Answer: (c).The family of regular languages are closed under both symmetric difference and nor

69.  Consider a source with symbols A, B, C, D with probabilities 1/2, 1/4, 1/8, 1/8 respectively. What is the average number of bits per symbol for the Huffman code generated from above information? 
a.  2 bits per symbol 
b.  1.75 bits per symbol 
c.  1.50 bits per symbol 
d.  1.25 bits per symbol 
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Answer: (b).1.75 bits per symbol

70.  How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women? 
a.  75240 
b.  52492 
c.  41800 
d.  9900 
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Answer: (b).52492
