GATE CS 2013

Question 11

Which of the following statements is/are FALSE?

1. For every non-deterministic Turing machine, 
   there exists an equivalent deterministic Turing machine.
2. Turing recognizable languages are closed under union 
   and complementation.
3. Turing decidable languages are closed under intersection 
   and complementation.
4. Turing recognizable languages are closed under union 
   and intersection. 

• 1 and 4 only

• 1 and 3 only

• 2 only

• 3 only

Question 12

Which of the following statements are TRUE?

1. The problem of determining whether there exists
   a cycle in an undirected graph is in P.
2. The problem of determining whether there exists
   a cycle in an undirected graph is in NP.
3. If a problem A is NP-Complete, there exists a 
   non-deterministic polynomial time algorithm to solve A. 

• 1, 2 and 3
• 1 and 2 only
• 2 and 3 only
• 1 and 3 only

Question 13

What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices?

• A
• B
• C
• D

Question 14

In a k-way set associative cache, the cache is divided into v sets, each of which consists of k lines. The lines of a set are placed in sequence one after another. The lines in set s are sequenced before the lines in set (s+1). The main memory blocks are numbered 0 onwards. The main memory block numbered j must be mapped to any one of the cache lines from.

• (j mod v) * k to (j mod v) * k + (k-1)
• (j mod v) to (j mod v) + (k-1)
• (j mod k) to (j mod k) + (v-1)
• (j mod k) * v to (j mod k) * v + (v-1)

Question 15

Which one of the following expressions does NOT represent exclusive NOR of x and y?

• xy+x\'y\'
• x⊕y\'
• x\'⊕y
• x\'⊕y\'

Question 16

Which one of the following functions is continuous at x = 3? 

[caption width="800"] [/caption]

• C
  

• D
  

• B
  

• A
  

Question 17

Function f is known at the following points: 

• 9.003 
  

• 9.017 
  

• 8.983 
  

• 9.045
  

Question 18

Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?

• 7
  

• 1
  

• 1/8
  

• 8
  

Question 19

Which of the following statements is/are TRUE for undirected graphs? 

P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even. 

• Neither P nor Q
  

• Both P and Q
  

• Q only
  

• P only
  

Question 20

The line graph L(G) of a simple graph G is defined as follows: · There is exactly one vertex v(e) in L(G) for each edge e in G. · For any two edges e and e\' in G, L(G) has an edge between v(e) and v(e\'), if and only if e and e\'are incident with the same vertex in G. Which of the following statements is/are TRUE?

(P) The line graph of a cycle is a cycle.
(Q) The line graph of a clique is a clique.
(R) The line graph of a planar graph is planar.
(S) The line graph of a tree is a tree. 

• P only
• P and R only
• R only
• P, Q and S only