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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Q. Consider the sentence below:

“There is a country that borders both India and Nepal”
Which of the following represents the above sentence correctly?

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Q. A full joint distribution for the Toothache, Cavity and Catch is given in the table below. What is the probability of Cavity, given evidence of Toothache?

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Q. E is the number of edges in the graph and f is maximum flow in the graph. When the capacities are integers, the runtime of Ford-Fulberson algorithm is bounded by:

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Q. Which of the following statements is false about convex minimization problem?

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Q. The following LPP
Maximize z = 100x1+2x2+5x3
Subject to

14x1+x2−6x3+3x4 = 7
32x1+x2−12x3 ≤ 10
3x1−x2−x3 ≤ 0
x1, x2, x3, x4 ≥ 0

has

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Q. Digital data received from a sensor can fill up 0 to 32 buffers. Let the sample space be S={0, 1, 2, .........., 32} where the sample j denote that j of the buffers are full and
p(i) =1/561 (33 - i). Let A denote the event that the even number of buffers are full. Then p(A) is:

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Q. The equivalence of

¬ ∃x Q(x) is:

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Q. Match the following in List - I and List - II, for a function f:

List - I
(a) ∀x ∀y (f (x)=f (y) → x=y)
(b) ∀y ∃ x (f (x)=y)
(c) ∀x f (x)=k

List - II
(i) Constant
(ii) Injective
(iii) Surjective

Code:
(a) (b) (c)

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Q. Which of the relations on {0, 1, 2, 3} is an equivalence relation?

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Q. Which of the following is an equivalence relation on the set of all functions from Z to Z?

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Q. Which of the following statements is true?

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