71.  How many undirected graphs (not necessarily connected) can be constructed out of a given set V = {v1, v2, ... vn} of n vertices? 
a.  n(n1)/2 
b.  2^n 
c.  n! 
d.  2^n(n1)/2 
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Answer: (d).2^n(n1)/2

72.  The rank of the matrix is : 
a.  4 
b.  2 
c.  1 
d.  0 
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Answer: (c).1

73.  The trapezoidal rule for integration give exact result when the integrand is a polynomial of degree: 
a.  0 but not 1 
b.  1 but not 0 
c.  0 or 1 
d.  2 
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Answer: (c).0 or 1

74.  The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is 
a.  2 
b.  3 
c.  4 
d.  n  2⌊n/2⌋ + 2 
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Answer: (d).n  2⌊n/2⌋ + 2

75.  If X, then Y unless Z" is represented by which of the following formulae in propositional logic? ("¬" is negation "^" is conjunction, and "→" is implication) 
a.  (X ^ ¬ Z) → Y 
b.  (X ^ Y) → ¬ Z 
c.  (X → (Y ^ ¬ Z) 
d.  (X → Y(^ ¬ Z) 
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Answer: (a).(X ^ ¬ Z) → Y

76.  The decimal value 0.25 
a.  is equivalent to the binary value 0.1 
b.  is equivalent to the binary value 0.01 
c.  is equivalent to the binary value 0.00111.... 
d.  cannot be represented precisely in binary 
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Answer: (b).is equivalent to the binary value 0.01

77.  Maximum number of edges in a n  node undirected graph without self loops is 
a.  n^2 
b.  n(n  1)/2 
c.  n  1 
d.  (n + 1) (n)/2 
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Answer: (b).n(n  1)/2

78.  The NewtonRaphson iteration Xn + 1 = (Xn/2) + 3/(2Xn) can be used to solve the equation 
a.  X^2 = 3 
b.  X^3 = 3 
c.  X^2 = 2 
d.  X^3 = 2 
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Answer: (a).X^2 = 3

79.  Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is : 
a.  1/16 
b.  1/8 
c.  7/8 
d.  15/16 
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Answer: (c).7/8

80.  A B+ tree index is to be built on the Name attribute of the relation STUDENT. Assume that all student names are of length 8 bytes, disk block are size 512 bytes, and index pointers are of size 4 bytes. Given this scenario, what would be the best choice of the degree (i.e. the number of pointers per node) of the B+ tree? 
a.  16 
b.  42 
c.  43 
d.  44 
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Answer: (c).43
