Q. How many solutions do the following equation have x1 + x2 + x3 = 11
where x1 ≥ 1, x2 ≥2, x3 ≥ 3

View solution

Q. The number of distinct bracelets of five beads made up of red, blue, and green beads (two bracelets are indistinguishable if the rotation of one yield another) is,

View solution

Q. 58 lamps are to be connected to a single electric outlet by using an extension board each of which has four outlets. The number of extension boards needed to connect all the light is

View solution

Q. The power set of AUB, where A = {2, 3, 5, 7} and B = {2, 5, 8, 9} is

View solution

Q. Which is not the correct statement ?

View solution

Q. Given the following statements :

(i) Recursive enumerable sets are closed under complementation.
(ii) Recursive sets are closed under complementation.

Which is/are the correct statements ?

View solution

Q. Let θ(x, y, z) be the statement “x + y = z” and let there be two quantifications given as

(i) ∀x ∀y  Z ∃ θ(x, y, z)
(ii) ∃Z ∀x ∀y θ(x, y, z)
 
Where x, y, z are real numbers. Then which one of the following is correct ?

View solution

Q. Let P(rn, n) be the statement if "m divides n" where the universe of discourse for both the variables is the set of positive integers. Determine the truth values of each of the-following propositions:

I. ∀m ∀n P(m,n)
II. ∃m  ∀n P(m,n)

View solution

Q. Big O estimate for
( f(x) = (x + 1) log(x2 + 1) +3x2 is given as

View solution

Q. How many edges are there in a forest of t-trees containing a total of n vertices?

View solution

Q. Let f and g be the functions from the set of integers to the set integers defined by

f(x) = 2x + 3 and g(x) = 3x + 2

Then the composition  of f and g and g and f is given as

View solution

Q. A graph is non-planar if and only if it contains a subgraph homomorphic to

View solution

Q. If the primal Linear Programming problem has unbounded  solution, then it's dual problem will  have

View solution

Q. Given the problem to maximize
            f(x), X =(x1, x2 ,..... .xn)
subject to m number of inequality constraints
  gi(x) ≤ bi  , i = 1, 2 ...... m
including the non-negativity constraints x ≥ 0
Which of the following conditions is a Kuhn-Tucker necessary condition for a local maxima at x  ?

View solution

Q. The following Linear Programming problem has :
Max                                   Z =x1 +x2
Subject to                         = x1-x2 ≥ 0                                  
                                             3x1 -x2 ≤ -3                                
      and                              xI , x2  ≥ 0

View solution

Q. Given a flow graph with 10 nodes,13 edges and one connected components, the number of regions and the number  of predicate (decision) nodes in the flow graph will be

View solution

Q. If h* represents an estimate of the cost of getting from the current node N to the goal node and h represents actual cost of getting from the current node to the goal node, then A*algorithm gives an optimal solution if

View solution

Q. The recurrence relation T(n) = m T(n/2) tan2 is satisfied by

View solution

Q. A ___________ complete subgraph and a __________ subset of vertices of a graph G = (V, E) are a clique and a vertex cover respectively.

View solution

Q. A certain tree has two vertices of degree 4, one vertex of degree 3 and one vertex of degree 2. If the other vertices have degree 1, how many vertices are there in the graph?

View solution