GATE||TOC || Pyq (2010 to2025)

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Question 1

Consider the languages L1, L2 and L3 as given below.

LI= {0P1q |p, q∈N}

L2={0p1q |p, q∈ N and p=q} and

L3= {0P1q0r |p, q, r∈ N and p =q = r}

Which of the following statements is NOT TRUE?

[GATE | CS | 2011 |]

  • Push Down Automata (PDA) can be used to recognize L1 and L2

  • L1 is a regular language

  • All the three languages are context free

  • Turing machine can be used to recognize all the three languages

Question 2

Consider the regular grammar: S → Xa | Ya X → Za Z → Sa | ϵ Y → Wa W → Sa where S is the starting symbol, the set of terminals is {a} and the set of non-terminals is {S, W, X, Y, Z}. We wish to construct a deterministic finite automaton (DFA) to recognize the same language. What is the minimum number of states required for the DFA?

[GATE 2005]

  • 2

  • 3

  • 4

  • 5

Question 3

Let L = {w ∈ (0 + 1)* | w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expression below represents L?

[GATE 2010|| MCQ|| 2-mark]


  • (0 * 10 * 1)*

  • 0 * (10 * 10*)*

  • 0*(10 * 1*)*0*

  • 0 *1(10 * 1)*10*

Question 4

Let w be any string of length n is {0, 1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?

[GATE 2010|| MCQ|| 2-mark]



  • n-1

  • n

  • n+1

  • 2n-1

Question 5

Let P be a regular language and Q be a context-free language such that Q ⊆ P. (For example, let P be the language represented by the regular expression p*q* and Q be [pnqn | n ∈ N]). Then which of the following is ALWAYS regular?

[GATE 2011|| MCQ|| 1-mark]


  • P ∩ Q

  • P – Q

  • Σ* – P

  • Σ* – Q

Question 6

Which of the following pairs have DIFFERENT expressive power?

[GATE 2011||MCQ|| 1-mark]


  • Deterministic finite automata (DFA) and Non-deterministic finite automata (NFA)

  • Deterministic push down automata (DPDA) and Non-deterministic push down automata (NFDA)

  • Deterministic single-tape Turning machine and Non-deterministic single tape Turning machine

  • Single-tape Turning machine and multi-tape Turning machine

Question 7

Definition of a language L with alphabet {a} is given as following. L = {a nk | k > 0, and n is a positive integer constant} What is the minimum number of states needed in a DFA to recognize L?

[GATE 2011|| MCQ|| 2-mark]


  • k+1

  • n+1

  • 2 2𝑛+1

  • 2 𝑘+1

Question 8

A deterministic finite automation (DFA) D with alphabet Σ = {a, b} is given below.

Screenshot-2025-10-17-112700
.


Which of the following finite state machines is a valid minimal DFA which accepts the same language as D?

[GATE 2011|| MCQ|| 2-mark]


  • Screenshot-2025-08-11-111057
    .
  • Screenshot-2025-08-11-111134
    .
  • Screenshot-2025-08-11-111218
    .
  • Screenshot-2025-08-11-111252
    .

Question 9

What is the complement of the language accepted by the NFA shown below?
Assume Σ = {a} and ϵ is the empty string.

Screenshot-2025-08-11-112619
.

[GATE 2012|| MCQ|| 1-mark]


  • ∅

  • {ε}

  • a*

  • {a ,ε}

Question 10

Given the language L ={ab,aa,baa}, which of the following strings are in L *?
1)abaabaaabaa
2)aaaabaaaa
3)baaaaabaaaab
4)baaaaabaa

[GATE 2012|| MCQ|| 1-mark]


  • 1, 2 and 3

  • 2, 3 and 4

  • 1, 2 and 4

  • 1, 3 and 4

There are 108 questions to complete.

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