Q. Consider an experiment of tossing two fair dice, one black and one red. What is the probability that the number on the black die divides the number on red die ?

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Q. In how many ways can 15 indistinguishable fishes be placed into 5 different ponds, so that each pond contains atleast one fish ?

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Q. Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ?
(a) deg (v) >= n / 2 for each vertex of G
(b)  | E(G) | >= 1 / 2 (n-1) (n-2) + 2 edges
(c) deg (v) + deg (w) >= n for every v and w not connected by an edge

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Q. An all-pairs shortest-paths problem is efficiently solved using :

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Q. The travelling salesman problem can be solved in :

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Q. Let f (n) and g(n) be asymptotically non-negative functions. Which of the following is correct?

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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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