GATE CS 2019

Question 61

Consider the following relation P(X, Y, Z), Q(X, Y, T) and R(Y, V):

How many tuples will be returned by the following relational algebra query?

πx(σ(P.Y = R.Y ∧ R.V = V(P X R))) - πx(σ(Q.Y = R.Y ∧ Q.T > 2(Q X R))) 

Note: This was Numerical Type question.

• 3
• 1
• 2
• 4

Question 62

Consider the following C program:

C

#include<stdio.h> 

int main() { 
  int a[] = {2, 4, 6, 8, 10}; 
  int i, sum = 0, *b = a + 4; 

  for (i = 0; i < 5; i++ ) 
  sum = sum + (*b - i) - *(b - i); 

  printf(\"%d\\n\", sum); 
  return 0; 
} 

The output of above C program is __________ . Note: This was Numerical Type question.

• 10
• 8
• 6
• 3

Question 63

If L is a regular language over ∑ = {a, b}, which one of the following languages is NOT regular?

• L⋅ L^R {xy ⏐ x ∈ L, y^R∈ L}
• Suffix (L) = {y ∈ ∑* ⏐ ∃x ∈ ∑* such that xy ∈ L}
• Prefix (L) = {x ∈ ∑* ⏐ ∃y ∈ ∑* such that xy ∈ L}
• {ww^R ⏐ w ∈ L}

Question 64

Which of the following protocol pairs can be used to send and retrieve e-mails (in that order)?

• IMAP POP3

• SMTP, POP3

• SMTP, MIME

• IMAP, SMTP

Question 65

Consider the following sets:

• S₁: Set of all recursively enumerable languages over the alphabet {0, 1}.
• S₂: Set of all syntactically valid C programs.
• S₃: Set of all languages over the alphabet {0, 1}.
• S₄: Set of all non-regular languages over the alphabet {0, 1}.

Which of the above sets are uncountable?

• S₁ and S₂
• S₃ and S₄
• S₁ and S₄
• S₂ and S₃