GATE CS 2021 | Set 1

Question 21

Consider a linear list based directory implementation in a file system. Each directory is a list of nodes, where each node contains the file name along with the file metadata, such as the list of pointers to the data blocks. Consider a given directory foo. Which of the following operations will necessarily require a full scan of foo for successful completion?

• Creation of a new file in foo
• Deletion of an existing file from foo
• Renaming of an existing file in foo
• Opening of an existing file in foo

Question 22

In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is _________.

• 10
• 11
• 12
• 6

Question 23

Consider the following undirected graph with edge weights as shown: The number of minimum-weight spanning trees of the graph is ___________.

• 3
• 4
• 5
• 2

Question 24

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ____________.

• 0.37
• 0.25
• 0.50
• 0.18

Question 25

There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

• The fastest computer gets the toughest job and the slowest computer gets the easiest job.
• Every computer gets at least one job.

The number of ways in which this can be done is ___________.

• 65
• 81
• 36
• 16

Question 26

Consider the following expression. The value of the above expression (rounded to 2 decimal places) is ___________.

• 0.25

• 0.20

• 0.35

• 0.50

Question 27

Consider the following sequence of operations on an empty stack.

Push(54);push(52);pop();push(55);push(62);s=pop(); 

Consider the following sequence of operations on an empty queue.

enqueue(21);enqueue(24);dequeue();enqueue(28);enqueue(32);q=dequeue(); 

The value of s+q is ___________.

• 86

• 68

• 24

• 94

Question 28

Consider a computer system with a byte-addressable primary memory of size 2³² bytes. Assume the computer system has a direct-mapped cache of size 32 KB (1 KB = 2¹⁰ bytes), and each cache block is of size 64 bytes. The size of the tag field is __________ bits.

• 17
• 18
• 15
• 9

Question 29

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S : 1     E : 10000001      F : 11110000000000000000000 

Here, S,E and F denote the sign, exponent, and fraction components of the floating point representation. The decimal value corresponding to the above representation (rounded to 2 decimal places) is ____________.

• -7.75
• +7.75
• -5.57
• 5.75

Question 30

Three processes arrive at time zero with CPU bursts of 16, 20 and 10 milliseconds. If the scheduler has prior knowledge about the length of the CPU bursts, the minimum achievable average waiting time for these three processes in a non-preemptive scheduler (rounded to nearest integer) is _____________ milliseconds.

• 12
• 36
• 46
• 10