Q. In a set of 8 positive integers, there always exists a pair of numbers having the same remainder when divided by:

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Q. A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls are red and two are green?

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Q. The number of edges in a complete graph with ‘n’ vertices is equal to:

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Q. Depth ion travels of the following directed graph is:

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Q. If (a^2−b^2) is a prime number where a and bϵN, then:

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Q. For a complete graph with N vertices, the total number of spanning trees is given by:

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Q. Let A and B be two arbitrary events, then:

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Q. Consider the relation on the set of non-negative integers defined by x≡y if and only if:

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Q. Minimum number of individual shoes to be picked up from a dark room (containing 10 pair of shoes) if we have to get atleast one proper pair:

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Q. If f(x) =x+1 and g(x)=x+3 then fofofof is:

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Q. If Im denotes the set of integers modulo m, then the following are fields with respect to the operations of addition modulo m and multiplication modulo m:
(i) Z23      (ii) Z29
(iii) Z31    (iv) Z33

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Q. In mathematical logic, which of the following are statements?

(i) There will be snow in January.
(ii) What is the time now?
(iii) Today is Sunday.
(iv) You must study Discrete mathematics

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Q. Match the List-I with List-II and choose the correct answer from the code given below:

List I List II

(a) Equivalence (i) p⇒q
(b) Contrapositive (ii) p⇒q : q⇒p
(c) Converse (iii) p⇒q : ∼q⇒∼p
(d) Implication (iv) p⇔q

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Q. A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls will be red and two will be green?

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Q. A survey has been conducted on methods of commuter travel. Each respondent was asked to check Bus, Train and Automobile as a major method of travelling to work. More than one answer was permitted. The results reported were as follows:

Bus 30 people; Train 35 people; Automobile 100 people; Bus and Train 15 people; Bus and Automobile 15 people; Train and Automobile 20 people; and all the three methods 5 people. How many people completed the survey form?

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Q. If a graph (G) has no loops or parallel edges, and if the number of vertices (n) in the graph is n≥3, then graph G is Hamiltonian if

(i) deg(v) ≥ n/3 for each vertex v
(ii) deg(v) + deg(w) ≥ n whenever v and w are not connected by an edge
(iii) E(G) ≥ 1/3(n−1)(n−2)+2

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Q. Consider two sequences X and Y:

X = <0,1,2,1,3,0,1>
Y = <1,3,2,0,1,0>

The length of longest common subsequence between X and Y is

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Q. Consider the following terminology and match List I with List II and choose the correct answer from the code given below.

b = branching factor
d = depth of the shallowest solution
m = maximum depth of the search tree
l = depth limit

List I List II
(Algorithms) (Space Complexity)
(a) BFS search (i) O(bd)
(b) DFS search (ii) O(b^d)
(c) Depth-limited search (iii) O(bm)
(d) Iterative deepening search (iv) O(bl)

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Q. Consider the following statements:

S1: A heuristic is admissible if it never overestimates the cost to reach the goal.
S2: A heuristic is monotonous if it follows triangle inequality property.

Which of the following is true referencing the above statements?

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Q. Consider a vocabulary with only four propositions A, B, C and D. How many models are there for the following sentence?

¬A ∨ ¬B ∨ ¬C ∨ ¬D

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