GATE CS 2019

Question 21

Which one of the following is NOT a valid identity?

• (x ⊕ y) ⊕ z = x ⊕ (y ⊕ z)

• (x + y) ⊕ z = x ⊕ (y + z)

• x ⊕ y = x + y, if xy = 0

• x ⊕ y = (xy + x′y′)′

Question 22

Compute

• Limit does not exist
• 1
• 53/12
• 108/7

Question 23

Which one of the following statements is NOT correct about the B+ tree data structure used for creating an index of a relational database table?

• B+ Tree is a height-balanced tree
• Non-leaf nodes have pointers to data records
• Key values in each node are kept in sorted order
• Each leaf node has a pointer to the next leaf node

Question 24

For Σ = {a, b}, let us consider the regular language

L = {x ∣ x = a2 + 3k or x = b10 + 12k, k ≥ 0} 

Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?

• 3

• 5

• 9

• 24

Question 25

The following C program is executed on a Unix / Linux system:

C

#include <unistd.h>
  int main() {
    int i;
    for (i = 0; i < 10; i++)
      if (i % 2 == 0) fork();
    return 0;
  }

The total number of child process created is __________ . Note - This was Numerical Type question.

• 31
• 63
• 5
• 6

Question 26

Consider the following C program:

C

#include <stdio.h>
  int jumble(int x, int y) {
    x = 2 * x + y;
    return x;
  }
int main() {
  int x = 2, y = 5;
  y = jumble(y, x);
  x = jumble(y, x);
  printf(\"%d\\n\", x);
  return 0;

}

The value printed by program is __________ . Note: This was Numerical Type question.

• 26
• 2
• 5
• 12

Question 27

Consider the following given grammar:

S → Aa
A → BD
B → b|ε
D → d|ε 

Let a, b, d and $ be indexed as follows:
Compute the FOLLOW set of the non-terminal B and write the index values for the symbols in the FOLLOW set in the descending order. (For example, if the FOLLOW set is {a, b, d, $}, then the answer should be 3210). Note: This was Numerical Type question.

• 31
• 310
• 230
• 23

Question 28

Two numbers are chosen independently and uniformly at random from the set {1, 2, ..., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ___________. Note: This was Numerical Type question.

• 0.5029
• 0.538
• 0.461
• 0.248

Question 29

An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is _________. Note: This was Numerical Type question.

• 0.08
• 0.0016
• 0.04
• 0.0008

Question 30

The value of 3⁵¹ mod 5 is _________ . Note: This was Numerical Type question.

• 1
• 2
• 3
• 4