Q. How many strings of 5 digits have the property that the sum of their digits is 7 ?

View solution

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 ?

View solution

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

View solution

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

View solution

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

View solution

Q. The travelling salesman problem can be solved in :

View solution

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

View solution

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 ?

View solution

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

View solution

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

View solution

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 ?

View solution

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)

View solution

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

View solution

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?

View solution

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.

View solution

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

View solution

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

View solution

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)

View solution

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

0 and 100   and     -6 and 34

View solution

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:

View solution