GATE-CS-2014-(Set-2)

Question 21

A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. The level-order traversal of the heap after the insertion of the elements is:

• 10, 8, 7, 3, 2, 1, 5

• 10, 8, 7, 2, 3, 1, 5

• 10, 8, 7, 1, 2, 3, 5

• 10, 8, 7, 5, 3, 2, 1

Question 22

Which one of the following correctly determines the solution of the recurrence relation with T(1) = 1?

T(n) = 2T(n/2) + Logn 

• Θ(n)
• Θ(nLogn)
• Θ(n*n)
• Θ(log n)

Question 23

Consider the tree arcs of a BFS traversal from a source node W in an unweighted, connected, undirected graph. The tree T formed by the tree arcs is a data structure for computing.

• the shortest path between every pair of vertices.

• the shortest path from W to every vertex in the graph.

• the shortest paths from W to only those nodes that are leaves of T.

• the longest path in the graph

Question 24

Which one of the following is CORRECT?

• Only (I)
• Only (II)
• Both (I) and (II)
• Neither (I) nor (II)

Question 25

Let A ≤_m B denotes that language A is mapping reducible (also known as many-to-one reducible) to language B. Which one of the following is FALSE?

• If A ≤_m B and B is recursive then A is recursive.
• If A ≤_m B and A is undecidable then B is undecidable.
• If A ≤_m B and B is recursively enumerable then A is recursively enumerable.
• If A ≤_m B  and B is not recursively enumerable then A is not recursively enumerable.

Question 26

Consider the grammar defined by the following production rules, with two operators ∗ and +

    S --> T * P 
    T --> U | T * U
    P --> Q + P | Q
    Q --> Id
    U --> Id

Which one of the following is TRUE?

• + is left associative, while ∗ is right associative
• + is right associative, while ∗ is left associative
• Both + and ∗ are right associative
• Both + and ∗ are left associative

Question 27

Which one of the following is NOT performed during compilation?

• Dynamic memory allocation
• Type checking
• Symbol table management
• Inline expansion

Question 28

Which one of the following is TRUE?

• The requirements document also describes how the requirements that are listed in the document are implemented efficiently.

• Consistency and completeness of functional requirements are always achieved in practice.

• Prototyping is a method of requirements validation.

• Requirements review is carried out to find the errors in system design

Question 29

A FAT (file allocation table) based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size. Given a 100 x 10⁶ bytes disk on which the file system is stored and data block size is 10³ bytes, the maximum size of a file that can be stored on this disk in units of 10⁶ bytes is ____________.

• 99.55 to 99.65
• 100.5 to 101.4
• 97.2 to 98.5
• 89.1 to 91.2

Question 30

The maximum number of superkeys for the relation schema R(E,F,G,H) with E as the key is

• 5
• 6
• 7
• 8