11.  Let Nf and Np denote the classes of languages accepted by nondeterministic finite automata and nondeterministic pushdown automata, respectively. Let Df and Dp denote the classes of languages accepted by deterministic finite automata and deterministic pushdown automata, respectively. Which one of the following is TRUE? 
a.  Df ⊂ Nf and Dp ⊂ Np 
b.  Df ⊂ Nf and Dp = Np 
c.  Df = Nf and Dp = Np 
d.  Df = Nf and Dp ⊂ Np 
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Answer: (d).Df = Nf and Dp ⊂ Np

12.  The regular expression 0*(10*)* denotes the same set as 
a.  (1*0)*1* 
b.  0 + (0 + 10)* 
c.  (0 + 1)* 10(0 + 1)* 
d.  none of these 
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Answer: (d).none of these

13.  The smallest finite automation which accepts the language {x  length of x is divisible by 3} has : 
a.  2 states 
b.  3 states 
c.  4 states 
d.  5 states 
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Answer: (b).3 states

14.  Given an arbitary nondeterministic finite automaton (NFA) with N states, the maximum number of states in an equivalent minimized DFA is at least 
a.  N^2 
b.  2^N 
c.  2N 
d.  N! 
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Answer: (b).2^N

15.  Consider a DFA over ∑ = {a, b} accepting all strings which have number of a’s divisible by 6 and number of b’s divisible by 8. What is the minimum number of states that the DFA will have? 
a.  8 
b.  14 
c.  15 
d.  48 
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Answer: (d).48

16.  Let S and T be language over Σ = {a,b} represented by the regular expressions (a+b*)* and (a+b)*, respectively. Which of the following is true? 
a.  S ⊂ T 
b.  T ⊂ S 
c.  S = T 
d.  S ∩ T = φ 
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Answer: (c).S = T

17.  Let L denotes the language generated by the grammar S > 0S0/00. Which of the following is true? 
a.  L = 0+ 
b.  L is regular but not 0+ 
c.  L is context free but not regular 
d.  L is not context free 
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Answer: (b).L is regular but not 0+

18.  What can be said about a regular language L over {a} whose minimal finite state automaton has two states? 
a.  L must be {a^n n is odd} 
b.  L must be {a^n n is even} 
c.  L must be {a^n ³ O} 
d.  Either L must be {a^n  n is odd}, or L must be {a^n  n is even} 
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Answer: (d).Either L must be {a^n  n is odd}, or L must be {a^n  n is even}

19.  How many minimum states are required in a DFA to find whether a given binary string has odd number of 0's or not, there can be any number of 1's. 
a.  1 
b.  2 
c.  3 
d.  4 
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Answer: (b).2

20.  Consider alphabet ∑ = {0, 1}, the null/empty string λ and the sets of strings X0, X1 and X2 generated by the corresponding nonterminals of a regular grammar. X0, X1 and X2 are related as follows: X0 = 1 X1 X1 = 0 X1 + 1 X2 X2 = 0 X1 + {λ} Which one of the following choices precisely represents the strings in X0? 
a.  10 (0* + (10)*)1 
b.  10 (0* + (10)*)*1 
c.  1(0* + 10)*1 
d.  10 (0 + 10)*1 + 110 (0 + 10)*1 
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Answer: (c).1(0* + 10)*1
