Computer Science Gate 2015 Set 1 Questions

For any two languages L₁ and L₂ such that L₁ is context free and L₂ is recursively enumerable but not recursive, which of the following is/are necessarily true?

a) I only
b) III only
c) III and IV only
d) I and IV only

The output of the following C program is __________.

Which of following statements is/are False?

I. XML overcomes the limitations in HTML to support a structured way of organizing content.
II. XML specification is not case sensitive while HTML specification is case sensitive.
III. XML supports user defined tags while HTML uses pre-defined tags.
IV. XML tags need not be closed while HTML tags must be closed.

a) II only
b) I only
c) I and IV only
d) III and IV only

Consider a system with byte-addressable memory, 32 bit logical addresses, 4 kilobyte page size and page table entries of 4 bytes each. The size of the page table in the system in megabytes is_________

For computers based on three-address instruction formats, each address field can be used to specify which of the following:

S₁: A memory operand
S₂: A processor register
S₃: An implied accumulator register

a) Either S₁ or S₂
b) Either S₂ or ₃
c) Only S₂ and  ₃
d) All of S₁, S₂ and S₃

Which one of the following is True at any valid state in shift-reduce parsing?

a) Viable prefixes appear only at the bottom of the stack and not inside
b) Viable prefixes appear only at the top of the stack and not inside
c) The stack contains only a set of viable prefixes
d) The stack never contains viable prefixes

Consider a LAN with four nodes S₁, S₂, S₃ and S₄. Time is divided into fixed-size slots, and a node can begin its transmission only at the beginning of a slot. A collision is said to have occurred if more than one node transmit in the same slot. The probabilities of generation of a frame in a time slot by S₁, S₂, S₃ and S₄ are 0.1, 0.2, 0.3 and 0.4, respectively. The probability of sending a frame in the first slot without any collision by any of these four stations is_________

Suppose two hosts use a TCP connection to transfer a large file. Which of the following statements is/are False with respect to the TCP connection?

I. If the sequence number of a segment is m, then the sequence number of the subsequent segment is always m+1.
II. If the estimated round trip time at any given point of time is t sec, the value of the retransmission timeout is always set to greater than or equal to t sec.
III. The size of the advertised window never changes during the course of the TCP connection.
IV. The number of unacknowledged bytes at the sender is always less than or equal to the advertised window.

Which one of the following fields of an IP header is NOT modified by a typical IP router?

a) Checksum
b) Source address
c) Time to Live (TTL)
d) Length

Suppose that everyone in a group of N people wants to communicate secretly with the N–1 others using symmetric key cryptographic system. The communication between any two persons should not be decodable by the others in the group. The number of keys required in the system as a whole to satisfy the confidentiality requirement is

a) 2N
b) N(N – 1)
c) N(N – 1)/2
d) (N – 1)²

In one of the pairs of protocols given below, both the protocols can use multiple TCP connections between the same client and the server. Which one is that?

a) HTTP, FTP
b) HTTP, TELNET
c) FTP, SMTP
d) HTTP, SMTP

Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n ( ≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.

a) T(n)=2T(n/2)+cn
b) T(n)=T(n–1)+T(0)+cn
c) T(n)=2T(n–2)+cn
d) T(n)=T(n/2)+cn

Match the following

a) P-iii, Q-ii, R-iv, S-i
b) P-i, Q-ii, R-iv, S-iii
c) P-ii, Q-iii, R-iv, S-i
d) P-ii, Q-i, R-iii, S-iv

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

a) 63 and 6, respectively
b) 64 and 5, respectively
c) 32 and 6, respectively
d) 31 and 5, respectively

What are the worst-case complexities of insertion and deletion of a key in a binary search tree?

a) Θ(logn) for both insertion and deletion
b) Θ(n) for both insertion and deletion
c) Θ(n) for insertion and Θ(logn) for deletion
d) Θ(logn) for insertion and Θ(n) for deletion

Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)?

I. 3, 5, 7, 8, 15, 19, 25
II. 5, 8, 9, 12, 10, 15, 25
III. 2, 7, 10, 8, 14, 16, 20
IV. 4, 6, 7, 9, 18, 20, 25

a) I and IV only
b) II and III only
c) II and IV only
d) II only

A file is organized so that the ordering of data records is the same as or close to the ordering of data entries in some index. Then that index is called

a) Dense
b) Sparse
c) Clustered
d) Unclustered

Select operation in SQL is equivalent to

a) the selection operation in relational algebra
b) the selection operation in relational algebra, except that select in SQL retains duplicates
c) the projection operation in relational algebra
d) the projection operation in relational algebra, except that select in SQL retains duplicates

Consider a 4 bit Johnson counter with an initial value of 0000. The counting sequence of this counter is

a) 0,1,3,7,15,14,12,8,0
b) 0,2,4,6,8,10,12,14,0
c) 0,8,12,14,15,7,3,1,0
d) 0,1,3,5,7,9,11,13,15,0

Which one of the following is NOT equivalent to p ↔ q?

a) (┐p ˅ q) ˄ (p ˅ ┐q)
b) (┐p ˅ q) ˄ (q → p)
c) (┐p ˄ q) ˅ (p ˄ ┐q)
d) (┐p ˄ ┐q) ˅ (p ˄ q)

For a set A, the power set of A is denoted by 2^A. If A = {5,{6},{7}}, which of the following options are TRUE?
I. ∅ ∈ 2^A
II. ∅ ⊆ 2^A
III. {5,{6}} ∈ 2^A
IV. {5,{6}} ⊆ 2^A

a) I and III only
b) II and III only
c) I, II and III only
d) I, II and IV only

Suppose the following disk request sequence (track numbers) for a disk with 100 tracks is given: 45, 20, 90, 10, 50, 60, 80, 25, 70. Assume that the initial position of the R/W head is on track 50. The additional distance that will be traversed by the R/W head when the Shortest Seek Time First (SSTF) algorithm is used compared to the SCAN (Elevator) algorithm (assuming that SCAN algorithm moves towards 100 when it starts execution) is _________ tracks

The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently.