51.  Which of the following is FALSE ? 
a.  The grammar S→aSaSbSÎ, where S is the only nonterminal symbol, and Î is the null string, is ambiguous. 
b.  An unambiguous grammar has same left most and right most derivation. 
c.  An ambiguous grammar can never be LR(k) for any k. 
d.  Recursive descent parser is a topdown parser. 
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Answer: (b).An unambiguous grammar has same left most and right most derivation.

52.  The regular grammar for the language L = {a^nb^m  n + m is even} is given by
(A) S → S1  S2 S1 → a S1  A1 A1 → b A1  λ S2 → aaS2  A2 A2 → b A2  λ (B) S → S1  S2 S1 → a S1  a A1 S2 → aa S2  A2 A1 → bA1  λ A2 → bA2  λ (C) S → S1  S2 S1 → aaa S1  aA1 S2 → aaS2  A2 A1 → bA1  λ A2 → bA2  λ (D) S → S1  S2 S1 → aa S1  A1 S2 → aaS2  aA2 A1 → bbA1  λ A2 → bbA2  b 
a.  A 
b.  B 
c.  C 
d.  D 
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Answer: (d).D

53.  Let Σ = {a, b} and language L = {aa, bb}. Then, the complement of L is 
a.  {λ, a, b, ab, ba} U {w ϵ {a, b}*  w > 3} 
b.  {a, b, ab, ba} U {w ϵ {a, b}*  w ≥ 3} 
c.  {w ϵ { a, b}*  w > 3} U {a, b, ab, ba} 
d.  {λ, a, b, ab, ba} U {w ϵ {a, b}*  w ≥ 3} 
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Answer: (d).{λ, a, b, ab, ba} U {w ϵ {a, b}*  w ≥ 3}

54.  Consider the following identities for regular expressions :
(a) (r + s)* = (s + r)* (b) (r*)* = r* (c) (r* s*)* = (r + s)* Which of the above identities are true ? 
a.  (a) and (b) only 
b.  (b) and (c) only 
c.  (c) and (a) only 
d.  (a), (b) and (c) 
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Answer: (d).(a), (b) and (c)

55.  Given the following two languages:
L1 = {uww^Rn  u, v, w ϵ {a, b}+} L2 = {uwwR^n  u, v, w ϵ {a, b}+, u ≥ v} Which of the following is correct ? 
a.  L1 is regular language and L2 is not regular language 
b.  L1 is not regular language and L2 is regular language 
c.  Both L1 and L2 are regular languages 
d.  Both L1 and L2 are not regular languages 
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Answer: (a).L1 is regular language and L2 is not regular language

56.  Given a Turing Machine:
M = ({q0, q1}, {0, 1}, {0, 1, B}, δ, B, {q1}) Where δ is a transition function defined as δ (q0, 0) = (q0, 0, R) δ (q0, B) = (q1, B, R) The language L(M) accepted by Turing machine is given as : 
a.  0* 1* 
b.  00* 
c.  10* 
d.  1*0* 
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Answer: (b).00*

57.  Let G = (V, T, S, P) be a contextfree grammar such that every one of its productions is of the form A → n, with v = k > 1. The derivation tree for any string W ϵ L (G) has a height such that 
a.  A 
b.  B 
c.  C 
d.  D 
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Answer: (d).D

58.  Consider the following linear programming problem:
Max. z = 0.50x2 – 0.10x1 Subject to the constraints 2x1 + 5x2 ≤ 80 x1 + x2 ≤ 20 and x1, x2 ≥ 0 The total maximum profit (z) for the above problem is: 
a.  6 
b.  8 
c.  10 
d.  12 
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Answer: (b).8

59.  The regular expression for the complement of the language L = {anbmn≥4, m≤3} is: 
a.  (λ + a + aa + aaa)b* + a*bbbb* + (a + b)*ba(a + b)* 
b.  (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ab(a + b)* 
c.  (λ + a + aa + aaa) + a*bbbbb* + (a + b)*ab(a + b)* 
d.  (λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ba(a + b)* 
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Answer: (d).(λ + a + aa + aaa)b* + a*bbbbb* + (a + b)*ba(a + b)*

60.  Consider the following two languages:
L1 = {0i1j  gcd(i,j)=1} L2 is any subset of 0*. Which of the following is correct? 
a.  L1 is regular and L2* is not regular 
b.  L1 is not regular and L2* is regular 
c.  Both L1 and L2* are regular languages 
d.  Both L1 and L2* are not regular languages 
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Answer: (b).L1 is not regular and L2* is regular
