Q. Consider a complete bipartite graph km,n. For which values of m and n does this, complete graph have a Hamilton circuit ?

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Q. How many cards must be chosen from a deck to guarantee that atleast

i. two aces of two kinds are chosen.
ii. two aces are chosen.
iii. two cards of the same kind are chosen.
iv. two cards of two different kinds are chosen

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Q. A text is made up of the characters α, β, γ, δ and σ with the probability 0.12, 0.40, 0.15, 0.08 and 0.25 respectively. The optimal coding technique will have the average length of

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Q. Consider an undirected graph G with 100 nodes. The maximum number of edges to be included in G so that the graph is not connected is

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Q. The amortized time complexity to perform ............. operation(s) in Splay trees is O(Ig n).

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Q. The number of eight-bit strings beginning with either 111 or 101 is ...............

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Q. Find the number of ways to paint 12 offices so that 3 of them will be green, 2 of them pink, 2 of them yellow and the rest ones white.

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Q. How many people must there be in a room before there is a 50% chance that two of them were born on the same day of the year ?

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Q. The number of possible parenthesizations of a sequence of n matrices is

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Q. The relation "divides" on a set of positive integers is ..................

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Q. A test contains 100 true/false questions. How many different ways can a student answer the questions on the test, if the answer may be left blank also.

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Q. Which of the following connected simple graph has exactly one spanning tree?

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Q. How many edges must be removed to produce the spanning forest of a graph with N vertices, M edges and C connected components?

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Q. The solution of recurrence relation, T(n) = 2T(floor (√n)) + logn is

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Q. The upper bound of computing time of m coloring decision problem is

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Q. Which one of the following statements is incorrect ?

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Q. Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex s to u has weight 53 and shortest path from s to v has weight 65. Which statement is always true ?

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Q. In any simplex table, if corresponding to any negative Dj, all elements of the column are negative or zero, the solution under the test is

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Q. Let a * H and b * H be two co-sets of H.

(i) Either a * H and b * H are disjoint
(ii) a * H and b * H are identical

Then,

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Q. Domain and Range of the function
Y = –√(–2x + 3) is

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