GATE CS 2012

Question 11

A process executes the code

fork();
fork();
fork(); 

The total number of child processes created is

• 3
• 4
• 7
• 8

Question 12

Consider the function f(x) = sin(x) in the interval [π/4, 7π/4]. The number and location(s) of the local minima of this function are

• One, at π/2

• One, at 3π/2

• Two, at π/2 and 3π/2

• Two, at π/4 and 3π/2

Question 13

What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” 

[caption width="800"] [/caption]

• A

• B

• C

• D

Question 14

Given the basic ER and relational models, which of the following is INCORRECT?

• An attribute of an entity can have more than one value
• An attribute of an entity can be composite
• In a row of a relational table, an attribute can have more than one value
• In a row of a relational table, an attribute can have exactly one value or a NULL value

Question 15

The recurrence relation capturing the optimal execution time of the Towers of Hanoi problem with n discs is

• T(n) = 2T(n − 2) + 2
• T(n) = 2T(n − 1) + n
• T(n) = 2T(n/2) + 1
• T(n) = 2T(n − 1) + 1

Question 16

Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

• 6
  

• 5
  

• 4
  

• 3
  

Question 17

Let w(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. which of the following is ALWAYS TRUE?
(A) [Tex]A(n) = \\Omega(W(n))[/Tex]
(B) [Tex]A(n) = \\Theta(W(n))[/Tex]
(C) [Tex]A(n) = O(W(n))[/Tex]
(D) [Tex]A(n) = o(W(n))[/Tex]

• A
• B
• C
• D

Question 18

Which of the following graphs is isomorphic to

• A
• B
• C
• D

Question 19

The bisection method is applied to compute a zero of the function f(x) = x⁴ – x³ – x² – 4 in the 
interval [1,9]. The method converges to a solution after ––––– iterations

• 7
  

• 5
  

• 3
  

• 1
  

Question 20

Let G be a weighted graph with edge weights greater than one and G\'be the graph constructed by squaring the weights of edges in G. Let T and T\' be the minimum spanning trees of G and G\', respectively, with total weights t and t\'. Which of the following statements is TRUE?

• T\' = T with total weight t\' = t²
• T\' = T with total weight t\' < t²
• T\' != T but total weight t\' = t²
• None of the above