61.  Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the edge with minimum weight. Which of the following statements is false? 
a.  Every minimum spanning tree of G must contain emin 
b.  If emax is in a minimum spanning tree, then its removal must disconnect G 
c.  No minimum spanning tree contains emax 
d.  G has a unique minimum spanning tree 
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Answer: (c).No minimum spanning tree contains emax

62.  Let G be an undirected graph. Consider a depthfirst traversal of G, and let T be the resulting depthfirst search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true? 
a.  {u,v} must be an edge in G, and u is a descendant of v in T 
b.  {u,v} must be an edge in G, and v is a descendant of u in T 
c.  If {u,v} is not an edge in G then u is a leaf in T 
d.  If {u,v} is not an edge in G then u and v must have the same parent in T 
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Answer: (c).If {u,v} is not an edge in G then u is a leaf in T

63.  Consider the following statements: S1: The sum of two singular n × n matrices may be nonsingular S2: The sum of two n × n nonsingular matrices may be singular. Which of the following statements is correct? 
a.  S1 and S2 are both true 
b.  S1 is true, S2 is false 
c.  S1 is false, S2 is trueS1 and S2 are both fals 
d.  S1 and S2 are both false 
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Answer: (a).S1 and S2 are both true

64.  Consider two wellformed formulas in prepositional logic. Which of the following statements is correct? 
a.  F1 is satisfiable, F2 is valid 
b.  F1 unsatisfiable, F2 is satisfiable 
c.  F1 is unsatisfiable, F2 is valid 
d.  F1 and F2 are both satisfiable 
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Answer: (a).F1 is satisfiable, F2 is valid

65.  Let f(n) = n^2Logn and g(n) = n (logn)^10 be two positive functions of n. Which of the following statements is correct? 
a.  f(n) = O(g(n)) and g(n) != O(f(n)) 
b.  f(n) != O(g(n)) and g(n) = O(f(n)) 
c.  f(n) = O(g(n)) but g(n) = O(f(n)) 
d.  f(n) != O(g(n)) but g(n) != O(f(n)) 
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Answer: (b).f(n) != O(g(n)) and g(n) = O(f(n))

66.  Let r and s be two relations over the relation schemes R and S respectively, and let A be an attribute in R. then the following relational algebra expression is always equal to 
a.  A 
b.  B 
c.  C 
d.  D 
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Answer: (c).C

67.  How many 4digit even numbers have all 4 digits distinct? 
a.  2240 
b.  2296 
c.  2620 
d.  4536 
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Answer: (b).2296

68.  Let f: A→B be a function, and let E and F be subsets of A. Consider the following statements about images. S1: f (E ∪ F) = f (E) ∪ f (F) S1: f (E ∩ F) = f (E) ∩ f (F) Which of the following is true about S1 and S2? 
a.  Only S1 is correct 
b.  Only S2 is correct 
c.  Both S1 and S2 are correct 
d.  None of S1 and S2 is correct 
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Answer: (a).Only S1 is correct

69.  Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day? 
a.  1/7^7 
b.  1/7^6 
c.  1/2^7 
d.  7/2^7 
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Answer: (b).1/7^6

70.  Consider an undirected unweighted graph G. Let a breadthfirst traversal of G be done starting from a node r. Let d(r,u) and d(r,v) be the lengths of the shortest paths from r to u and v respectively in G. If u is visited before v during the breadthfirst traversal, which of the following statements is correct? 
a.  d(r, u) < d(r, v) 
b.  d(r,u) > d(r,v) 
c.  d(r,u) <= (r,v) 
d.  None of the above 
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Answer: (c).d(r,u) <= (r,v)
