To guarantee correction of upto t errors, the minimum Hamming distance dmin in a block code must be

Consider the following statements :

(a) False╞ True
(b) If α╞ (β ∧ γ) then α╞ β and α╞ γ.

Which of the following is correct with respect to the above statements ?

Consider the following English sentence :

“Agra and Gwalior are both in India”.

A student has written a logical sentence for the above English sentence in First-Order Logic using predicate In(x, y), which means x is in y, as follows :

 In(Agra, India) ⋁ In(Gwalior, India) 

Which one of the following is correct with respect to the above logical sentence ?

Consider the following two sentences :

(a) The planning graph data structure can be used to give a better heuristic for a planning problem.
(b) Dropping negative effects from every action schema in a planning problem results in a relaxed problem.

Which of the following is correct with respect to the above sentences ?

A knowledge base contains just one sentence, ∃x AsHighAs (x, Everest). Consider the following two sentences obtained after applying existential instantiation.

(a) AsHighAs (Everest, Everest)
(b) AsHighAs (Kilimanjaro, Everest)

Which of the following is correct with respect to the above sentences ?

Consider the set of all possible five-card poker hands dealt fairly from a standard deck of fifty-two cards. How many atomic events are there in the joint probability distribution ?

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

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 

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).

The equivalence of ¬∃ x Q(x) is :

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

       List-I                   List-II
(a) ∀x∀y(f(x)=f(y)⟶x=y)      (i) Constant
(b) ∀y∃x(f(x)=y)             (ii) Injective
(c) ∀xf(x)=k                (iii) Surjective 

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

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

Which of the following statements is true ?

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

The number of substrings that can be formed from string given by

“a d e f b g h n m p” is

Match the List 1 and List 2 and choose the correct answer from the code given below

 LIST 1			 LIST 2
(a) Equivalence		 (i) p ⇒ q
(b) Contrapositive     	(ii) p ⇒ q : q ⇒ p
(c) Converse	       (iii) p ⇒ q : ∼q ⇒ ∼p
(d) Implication		(iv) p ⇔ q

The K-coloring of an undirected graph G = (V, E) is a function

C: V ➝ {0, 1, ......, K-1} such that c(u)≠c(v) for every edge (u,v) ∈ E

Which of the following is not correct?

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

Choose the correct answer for the code given below:

A survey has been conducted on methods of commuter travel. Each respondent was asked to check Bus, Train or Automobile as a major methods 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 complete the survey form ?

A full joint distribution for the Toothache, Cavity and Catch is given in the table below:

Which is the probability of Cavity, given evidence of Toothache ?

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.

Choose the correct answer from the code given below :

Consider the statements below :

“There is a country that borders both India and Nepal.“

Which of the following represents the above sentence correctly ?

Use Dual Simplex Method to solve the following problem :

Maximize z = -2x₁ - 3x₂
subject to:
x₁ + x₂ ≥ 2
2x₁ + x₂ ≤ 10
x₁ + x₂ ≤ 8
x₁, x₂ ≥ 0

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 ?