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Welcome to the Theory of Computation(TOC) MCQs Page

Dive deep into the fascinating world of Theory of Computation(TOC) with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Theory of Computation(TOC), a crucial aspect of UGC CBSE NET Exam. In this section, you will encounter a diverse range of MCQs that cover various aspects of Theory of Computation(TOC), from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within UGC CBSE NET Exam.

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Check out the MCQs below to embark on an enriching journey through Theory of Computation(TOC). Test your knowledge, expand your horizons, and solidify your grasp on this vital area of UGC CBSE NET Exam.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Theory of Computation(TOC). You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Theory of Computation(TOC) MCQs | Page 3 of 16

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Q21.
Regular expression for the complement of language L = {a^n b^m I n ≥ 4, m ≤ 3} is

a.

(a + b)* ba(a + b)*

b.

a* bbbbb*

c.

(λ + a + aa + aaa)b* + (a + b)* ba(a + b)*

d.

None of the above

Discuss
Answer: (d).None of the above
Q22.
We can show that the clique problem is NP-hard by proving that

a.

CLIQUE ≤ P 3-CNF SAT

b.

CLIQUE ≤ PVERTEX_COVER

c.

CLIQUE ≤  P SUBSET_SUM

d.

None of the above

Discuss
Answer: (d).None of the above
Q23.
Given the recursively enumerable language (LRE), the context sensitive language (LCS) the recursive language (LREC) the context free language (LCF) and deterministic context free language (LDCF) The relationship between these families is given by

a.

LCF ⊆ LDCF ⊆ LCS ⊆ LRE ⊆ LREC

b.

LCF ⊆ LDCF ⊆ LCS ⊆ LREC ⊆ LRE

c.

LDCF ⊆ LCF ⊆ LCS ⊆ LRE ⊆ LREC

d.

LDCF ⊆ LCF ⊆ LCS ⊆ LREC ⊆ LRE

Discuss
Answer: (b).LCF ⊆ LDCF ⊆ LCS ⊆ LREC ⊆ LRE
Q24.
Match the following:

       List- I                                                List -II
a. Context free grammar               i. Linear bounded automaton
b. Regular grammar                     ii. Pushdown automaton
c. Context sensitive grammar     iii. Turing machine
d. Unrestricted grammar             iv. Deterministic finite automaton

code:
a   b    c    d

a.

 ii    iv   iii    i

b.

ii    iv    i    iii

c.

iv    i     ii    iii

d.

i    iv   iii    ii

Discuss
Answer: (b).ii    iv    i    iii
Q25.
According to pumping lemma for context free languages:
Let L be an infinite context free language, then there exists some positive integer m such that any w ∈ L with I w I ≥ m can be decomposed as w = u v x y z

a.

with I vxy I ≤ m such that uvi xyi z ∈ L for all i = 0,1,2

b.

with I vxy I ≤ m and I vy I ≥ 1 such that uvi xyi z ∈ L for all i = 0,1,2,.....

c.

with I vxy I ≥ m and I vy I ≤ 1 such that uvi xyi z ∈ L for all i = 0,1,2,.....

d.

with I vxy I ≥ m and I vy I ≥ 1 such that uvi xyi z ∈ L for all i = 0,1,2,.....

Discuss
Answer: (d).with I vxy I ≥ m and I vy I ≥ 1 such that uvi xyi z ∈ L for all i = 0,1,2,.....
Q26.
The equivalent production rules corresponding to the production rules

S → Sα1 | Sα2 | β1 | β2 

a.

S → β1 | β2 ,  A   → α1A | α2 A | λ

b.

S → β1 | β2  | β1 A | β2 A , A   → α1A | α2 A 

c.

S → β1 | β2 ,  A   → α1A | α2 A 

d.

S → β1 | β2  | β1A |  β2A , A   → α1A | α2 A  | λ

Discuss
Answer: (d).S → β1 | β2  | β1A |  β2A , A   → α1A | α2 A  | λ
Q27.
If all the production rules have single non - terminal symbol on the left side, the grammar defined is :

a.

context free grammar

b.

context sensitive grammar

c.

unrestricted grammar

d.

phrase grammar

Discuss
Answer: (a).context free grammar
Q28.
Minimal deterministic finite automaton for the language L = {0n | n ≥ 0 , n ≠ 4} will have

a.

4 final states among 5 states

b.

1 final state among 6 states

c.

3 final state among 6 states

d.

5 final state among 6 states

Discuss
Answer: (d).5 final state among 6 states
Q29.
The regular expression corresponding to the language L where L = { x ∈{0, 1}* | x ends with 1 and does not contain substring 00 } is :

a.

(1 + 01)* (10 + 01)

b.

(1 + 01)* 01

c.

(1 + 01)* (1 + 01)

d.

(10 + 01)* 01

Discuss
Answer: (c).(1 + 01)* (1 + 01)
Q30.
A context free grammar for L = { w | n0 (w) > n1 (w)} is given by :

a.

S → 0 | 0 S | 1 S S

b.

S → 0 S | 1 S | 0 S S | 1 S S | 0 | 1

c.

S → 0 | 0 S | 1 S S | S 1 S |S S 1

d.

S → 0 S | 1 S | 0 | 1

Discuss
Answer: (c).S → 0 | 0 S | 1 S S | S 1 S |S S 1
Page 3 of 16

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