GATE-CS-2014-(Set-1)

Question 11

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________

• 0.24 to 0.27
• 0.15 to 0.30
• 0.20 to 0.30
• 0.10 to 0.15

Question 12

Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ? 

• B
  

• A
  

• C
  

• D
  

Question 13

Consider the following system of equations:

3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0 

The number of solutions for this system is __________________

• 1
• 0
• 2
• 3

Question 14

The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is _____________________.

• 0
• 1
• -1
• 2

Question 15

• I only
• II only
• Both I and II
• Neither I nor II

Question 16

Consider the following Boolean expression for F:

F(P, Q, R, S) = PQ + P\'QR + P\'QR\'S

The minimal sum-of-products form of F is

• PQ + QR + QS
• P + Q + R + S
• P\' + Q\' + R\' + S\'
• P\'R + P\'R\'S + P

Question 17

The base (or radix) of the number system such that the following equation holds is____________.

312/20 = 13.1

• 3
• 4
• 5
• 6

Question 18

Consider the following program in C language:

C

#include <stdio.h>
main()
{
    int i;
    int *pi = &i;
    scanf(\"%d\", pi);
    printf(\"%d\\n\", i+5);
}

Which one of the following statements is TRUE?

• Compilation fails.
• Execution results in a run-time error.
• On execution, the value printed is 5 more than the address of variable i.
• On execution, the value printed is 5 more than the integer value entered.

Question 19

Let G be a graph with n vertices and m edges. What is the tightest upper bound on the running time on Depth First Search of G? Assume that the graph is represented using adjacency matrix.

• O(n)
• O(m+n)
• O(n²)
• O(mn)

Question 20

Consider a rooted Binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having having exactly 4 nodes O(n^a Logn ^b). Then the value of a + 10b is ________

• 1
• 11
• 12
• 21