Q. Which of the following is FALSE ?

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Q. Consider the languages L1 = ϕ, and L2 = {1}. Which one of the following represents
L1* U L2* L1* ?

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Q. Given the following statements :
(A) A class of languages that is closed under union and complementation has to be closed under intersection.
(B) A class of languages that is closed under union and intersection has to be closed under complementation.
Which of the following options is correct?

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Q. Given the following two languages:

L1 = {a^nb^n|n≥0, n≠100}
L2 = {w ϵ {a,b,c}*| na(w) = nb(w) = nc(w)}

Which of the following options is correct?

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Q. Given the following two statements:

A. L = {w|na(w) = nb(w)} is deterministic context free language, but not linear.
B. L = {an bn} U {an b2n} is linear, but not deterministic context free language.

Which of the following options is correct?

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Q. Which of the following pairs have different expressive power?

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Q. Which of the following statements is false?

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Q. Let C be a binary linear code with minimum distance 2t + 1 then it can correct upto ............bits of error.

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Q. From the given data below:

a b b a a b b a a b

which one of the following is not a word in the dictionary created by LZ-coding (the initial words are a, b)?

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Q. The number of strings of length 4 that are generated by the regular expression (0+1+|2+3+)*, where | is an alternation character and {+, *} are quantification characters, is:

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Q. Which of the following is FALSE ?

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Q. 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

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Q. Let Σ = {a, b} and language L = {aa, bb}. Then, the complement of L is

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Q. 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 ?

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Q. 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 ?

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Q. 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 :

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Q. 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:

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Q. The regular expression for the complement of the language L = {anbm|n≥4, m≤3} is:

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Q. Consider the following two languages:

L1 = {0i1j | gcd(i,j)=1}
L2 is any subset of 0*.

Which of the following is correct?

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Q. 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.

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