Q. Given the following equalities :

E1 : nK+∈ + nK lg n = Ф(nK+∈) for all fixed K and ∈, K ≥ 0 and ∈ > 0.

E2 : n32n + 6n23n = O(n32n)

Which of the following is true ?

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Q. How many different equivalence relations with exactly three different equivalence classes are there on a set with five elements

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Q. Suppose that R1 and R2 are reflexive relations on a set A.
Which of the following statements is correct ?

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Q. There are three cards in a box. Both sides of one card are black, both sides of one card are red, and the third card has one black side and one red side. we pick a card at random and observe only one side. What is the probability that the opposite side is the same colour as the one side we observed ?

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Q. The cyclomatic complexity of a flow graph V(G), in terms of predicate nodes is:
(Where P is number of predicate nodes in flow graph V(G)

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Q. How many multiples of 6 are there between the following pairs of numbers?
0 and 100 and -6 and 34

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Q. Consider a Hamiltonian Graph G with no loops or parallel edges and with |V(G)|=n≥3. Then which of the following is true?

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Q. Which of the following statements is false?
(A) Optimal binary search tree construction can be performed efficiently using dynamic programming.
(B) Breadth-first search cannot be used to find connected components of a graph.
(C) Given the prefix and postfix walks of a binary tree, the tree cannot be re-constructed uniquely.
(D) Depth-first-search can be used to find the components of a graph.

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Q. Which of the following strings would match the regular expression: p+[3-5]*[xyz] ?

I. p443y
Il. p6y
III. 3xyz
IV. p35z
V. p353535x
Vl. ppp5

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Q. Match the following:
List-I                  List-II
a. Absurd          i. Clearly impossible being
contrary to some evident truth.
b. Ambiguous   ii. Capable of more than one
interpretation or meaning.
c. Axiom            iii. An assertion that is accepted
and used without a proof.
d. Conjecture    iv. An opinion Preferably based
on some experience or wisdom.

Code:
     a   b   c    d

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Q. The functions mapping R into R are defined as:

f(x) = x^3-4x, g(x)=1/(x^2+1) and h(x)=x^4

Then find the value of the following composite functions:
hog(x) and hogof(x)

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Q. How many multiples of 6 are there between the following pairs of numbers?

0 and 100   and     -6 and 34

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Q. A recursive function h, is defined as follows:

h(m) = k, if m=0
= 1, if m=1
= 2h(m-1) + 4h(m-2), if m≥2

If the value of h(4) is 88 then the value of k is:

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Q. The asymptotic upper bound solution of the recurrence relation given by

T(n)= 2T(n/2)+n/log n is:

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Q. The minimum number of scalar multiplication required, for parenthesization of a matrix-chain product whose sequence of dimensions for four matrices is <5,10,3,12,5> is

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Q. What is the probability that a randomly selected bit string of length 10 is a palindrome?

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Q. 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:

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Q. The symmetric difference of two sets S1 and S2 is defined as

S1ΘS2 = {x|xϵS1 or xϵS2, but x is not in both S1 and S2}

The nor of two languages is defined as
nor (L1,L2) = {w|w ∉ L1 and w|w ∉ L2}

Which of the following is correct?

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Q. 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?

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Q. How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women?

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