61.  Let L be the language generated by regular expression 0*10* and accepted by the deterministic finite automata M. Consider the relation RM defined by M. As all states are reachable from the start state, RM has ................ equivalence classes. 
a.  2 
b.  4 
c.  5 
d.  6 
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Answer: (d).6

62.  Let L = {0^n1^n  n≥0} be a context free language.
Which of the following is correct? 
a.  L’ is context free and L^k is not context free for any k≥1 
b.  L’ is not context free and L^k is context free for any k≥1 
c.  Both L’ and L^k is for any k≥1 are context free 
d.  Both L’ and L^k is for any k≥1 are not context free 
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Answer: (c).Both L’ and L^k is for any k≥1 are context free

63.  Given a Turing Machine
M = ({q0,q1,q2,q3}, {a,b}, {a,b,B}, δ, B, {q3}) Where δ is a transition function defined as δ(q0,a) = (q1,a,R) δ(q1,b) = (q2,b,R) δ(q2,a) = (q2,a,R) δ(q2,b) = (q3,b,R) The language L(M) accepted by the Turing Machine is given as: 
a.  aa*b 
b.  abab 
c.  aba*b 
d.  aba* 
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Answer: (c).aba*b

64.  Match the following :
List  I List  II (a) {a^n b^nn > 0} is a deterministic (i) but not recursive language context free language (b) The complement of {a^n b^n a^nn > 0} (ii) but not context free language is a context free language (c) {a^n b^n a^n} is context sensitive language (iii) but can not be accepted by a deterministic pushdown automation (d) L is a recursive language (iv) but not regular Codes : (a) (b) (c) (d) 
a.  (i) (ii) (iii) (iv) 
b.  (i) (ii) (iv) (iii) 
c.  (iv) (iii) (ii) (i) 
d.  None of the above is correct match 
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Answer: (d).None of the above is correct match

65.  The language of all nonnull strings of a’s can be defined by a context free grammar as
follow : S→a SS a a The word a^3 can be generated by ................ different trees. 
a.  Two 
b.  Three 
c.  Four 
d.  Five 
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Answer: (c).Four

66.  The context free grammar given by
S→XYX X→aXbXλ Y→bbb generates the language which is defined by regular expression: 
a.  (a+b)*bbb 
b.  abbb(a+b)* 
c.  (a+b)*(bbb)(a+b)* 
d.  (a+b)(bbb)(a+b)* 
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Answer: (c).(a+b)*(bbb)(a+b)*

67.  There are exactly ................ different finite automata with three states x, y and z over the alphabet {a, b} where x is always the start state. 
a.  64 
b.  256 
c.  1024 
d.  5832 
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Answer: (d).5832

68.  Given the following two languages :
L1={a^n b a^nn>0} L2={a^n b a^n b^n+1n>0} Which of the following is correct? 
a.  L1 is context free language and L2 is not context free language 
b.  L1 is not context free language and L2 is context free language 
c.  Both L1 and L2 are context free languages 
d.  Both L1 and L2 are not context free languages 
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Answer: (a).L1 is context free language and L2 is not context free language

69.  Consider a language A defined over the alphabet ∑={0, 1} as A = {0^[n/2] 1^n: n >= 0} .
The expression [n/2] means the floor of n/2, or what you get by rounding n/2 down to the nearest integer. Which of the following is not an example of a string in A ? 
a.  011 
b.  0111 
c.  0011 
d.  001111 
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Answer: (c).0011

70.  A grammar G is LL(1) if and only if the following conditions hold for two distinct productions A → α  β
I. First (α) ∩ First (β) ≠ {a} where a is some terminal symbol of the grammar. II. First (α) ∩ First (β) ≠ λ III. First (α) ∩ Follow(A) = φ if λ є First (β) 
a.  I and II 
b.  I and III 
c.  II and III 
d.  I, II and III 
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Answer: (d).I, II and III
