A directory of Objective Type Questions covering all the Computer Science subjects. Here you can access and discuss Multiple choice questions and answers for various compitative exams and interviews.

21. How many edges are there in a forest of t-trees containing a total of n vertices?
a. n + t
b. n -t
c. n * t
d. n^t
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Answer: (b).n -t

22. 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
a. 6x+7,  6x+11
b. 6x + 11, 6x + 7
c. 5x + 5, 5x + 5
d. None of the above
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Answer: (a).6x+7,  6x+11

23. A graph is non-planar if and only if it contains a subgraph homomorphic to
a. K3, 2 or K5
b. K3,3 and K6
c. K3,3 or K5
d. k2,3 and K5
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Answer: (c).K3,3 or K5

24. If the primal Linear Programming problem has unbounded  solution, then it's dual problem will  have
a. feasible solution
b. alternative solution
c. no feasible solution at all
d. no bounded solution at all
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Answer: (c).no feasible solution at all

25. 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  ?
a. ∂L(X ' , λ' , S') / ∂xj = 0 , j= 1,2.....m
b. λ[gi(X') -bi]= 0, i =1,2,3...m
c. gi (X ') ≤ bi , i = 1,2....m
d. All of these
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Answer: (b).λ[gi(X') -bi]= 0, i =1,2,3...m

26. The following Linear Programming problem has :
Max                                   Z =x1 +x2
Subject to                         = x1-x2 ≥ 0                                  
                                             3x1 -x2 ≤ -3                                
      and                              xI , x2  ≥ 0
a. Feasible solution
b. No feasible solution
c. Unbounded solution
d. Single point as solution
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Answer: (c).Unbounded solution

27. 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
a. 4, 5
b. 5, 4
c. 3, 1
d. 13, 8
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Answer: (b).5, 4

28. 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
a. h* is equal to h
b. h* overestimates h
c. h* underestimates h
d. none of these
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Answer: (c).h* underestimates h

29. The recurrence relation T(n) = m T(n/2) tan2 is satisfied by
a. O(n^2)
b. O(n^logm)
c. O(n^2 log n)
d. O(n log n)
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Answer: (b).O(n^logm)

30. A ___________ complete subgraph and a __________ subset of vertices of a graph G = (V, E) are a clique and a vertex cover respectively.
a. minimal, maximal
b. minimal, minimal
c. maximal, maximal
d. maximal, minimal
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Answer: (d).maximal, minimal

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