91.  Find the number of ways to paint 12 offices so that 3 of them will be green, 2 of them pink, 2 of them yellow and the rest ones white. 
a.  55,440 
b.  1,66,320 
c.  4.790E+08 
d.  39,91,680 
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Answer: (b).1,66,320

92.  How many people must there be in a room before there is a 50% chance that two of them were born on the same day of the year ? 
a.  At least 23 
b.  At least 183 
c.  At least 366 
d.  At least 730 
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Answer: (a).At least 23

93.  The number of possible parenthesizations of a sequence of n matrices is 
a.  O(n) 
b.  θ(n Ig n) 
c.  Ω(2^n) 
d.  None of the above 
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Answer: (c).Ω(2^n)

94.  The relation "divides" on a set of positive integers is .................. 
a.  Symmetric and transitive 
b.  Anti symmetric and transitive 
c.  Symmetric only 
d.  Transitive only 
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Answer: (b).Anti symmetric and transitive

95.  A test contains 100 true/false questions. How many different ways can a student answer the questions on the test, if the answer may be left blank also. 
a.  100P2 
b.  100C2 
c.  2^100 
d.  3^100 
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Answer: (d).3^100

96.  Which of the following connected simple graph has exactly one spanning tree? 
a.  Complete graph 
b.  Hamiltonian graph 
c.  Euler graph 
d.  None of the above 
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Answer: (d).None of the above

97.  How many edges must be removed to produce the spanning forest of a graph with N vertices, M edges and C connected components? 
a.  M+NC 
b.  MNC 
c.  MN+C 
d.  M+N+C 
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Answer: (c).MN+C

98.  The solution of recurrence relation, T(n) = 2T(floor (√n)) + logn is 
a.  O(n log log logn) 
b.  O(n log logn) 
c.  O(log logn) 
d.  O(logn log logn) 
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Answer: (d).O(logn log logn)

99.  The upper bound of computing time of m coloring decision problem is 
a.  O(nm) 
b.  O(n^m) 
c.  O(nm^n) 
d.  O(n^mm6n) 
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Answer: (c).O(nm^n)

100.  Which one of the following statements is incorrect ? 
a.  The number of regions corresponds to the cyclomatic complexity. 
b.  Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph. 
c.  Cyclometric complexity for a flow graph G is V(G) = E–N+2, where E is the number of edges & N is the number of nodes in the flow graph. 
d.  Cyclometric complexity for a flow graph G is V(G) = P + 1, where P is the number of predicate nodes contained in the flow graph G. 
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Answer: (b).Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph.
