101.  Identify the correct translation into logical notation of the following assertion. "Some boys in the class are taller than all the girls" Note : taller(x,y) is true if x is taller than y. 
a.  (∃x) (boy(x) → (∀y) (girl(y) ∧ taller(x,y))) 
b.  (∃x) (boy(x) ∧ (∀y) (girl(y) ∧ taller(x,y))) 
c.  (∃x) (boy(x) → (∀y) (girl(y) → taller(x,y))) 
d.  (∃x) (boy(x) ∧ (∀y) (girl(y) → taller(x,y))) 
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Answer: (d).(∃x) (boy(x) ∧ (∀y) (girl(y) → taller(x,y)))

102.  If a fair coin is tossed four times. What is the probability that two heads and two tails will result? 
a.  3/8 
b.  1/2 
c.  5/8 
d.  2/4 
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Answer: (a).3/8

103.  The number of different n × n symmetric matrices with each element being either 0 or 1 is: (Note: power(2, x) is same as 2x) 
a.  power(2, n) 
b.  power(2, n^2) 
c.  power(2, (n^2 + n)/2) 
d.  power(2, (n^2  n)/2) 
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Answer: (c).power(2, (n^2 + n)/2)

104.  Let A, B, C, D be n × n matrices, each with nonzero determinant. If ABCD = 1, then B1 is 
a.  D^1C^1A^1 
b.  CDA 
c.  ADC 
d.  Does not necessarily exist 
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Answer: (b).CDA

105.  What is the result of evaluating the following two expressions using threedigit floating point arithmetic with rounding? (113. + 111.) + 7.51 113. + (111. + 7.51) 
a.  9.51 and 10.0 respectively 
b.  10.0 and 9.51 respectively 
c.  9.51 and 9.51 respectively 
d.  10.0 and 10.0 respectively 
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Answer: (a).9.51 and 10.0 respectively

106.  The tightest lower bound on the number of comparisons, in the worst case, for comparisonbased sorting is of the order of 
a.  n 
b.  n^2 
c.  n log n 
d.  n log2 n 
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Answer: (c).n log n

107.  The problems 3SAT and 2SAT are 
a.  both in P 
b.  both NPcomplete 
c.  NPcomplete and in P respectively 
d.  undecidable and NPcomplete respectively 
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Answer: (c).NPcomplete and in P respectively

108.  The following propositional statement is (P → (Q v R)) → ((P ^ Q) → R) 
a.  satisfiable but not valid 
b.  valid 
c.  a contradiction 
d.  none of the above 
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Answer: (a).satisfiable but not valid

109.  How many solutions does the following system of linear equations have ? x + 5y = 1 x  y = 2 x + 3y = 3 
a.  infinitely many 
b.  two distinct solutions 
c.  unique 
d.  none of these 
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Answer: (c).unique

110.  An examination paper has 150 multiplechoice questions of one mark each, with each question having four choices. Each incorrect answer fetches 0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is: 
a.  0 
b.  2550 
c.  7525 
d.  9375 
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Answer: (d).9375
