GATE CSE kind:question PYQs & Answers — Page 45

Questions 441–450 of 975. Imported answers require independent review unless marked reviewed.

Let

be a set and

denote the powerset of

. Define a binary operation

as follows:

Let

. Which of the following statements about

is/are correct?

Your answerSelect all correct options. You can choose more than one.

is a group.

Every element in

has an inverse, but

is NOT a group.

For every

, the inverse of

is the complement of

For every

, the inverse of

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Suppose in a web browser, you click on the

www.gate-2023.in

URL. The browser cache is empty. The IP address for this URL is not cached in your local host, so a DNS lookup is triggered (by the local DNS server deployed on your local host) over the 3-tier DNS hierarchy in an iterative mode. No resource records are cached anywhere across all DNS servers. Let RTT denote the round trip time between your local host and DNS servers in the DNS hierarchy. The round trip time between the local host and the web server hosting

www.gate-2023.in

is also equal to RTT. The HTML file associated with the URL is small enough to have negligible transmission time and negligible rendering time by your web browser, which references 10 equally small objects on the same web server. Which of the following statements is/are CORRECT about the minimum elapsed time between clicking on the URL and your browser fully rendering it?

Your answerSelect all correct options. You can choose more than one.

7 RTTs, in case of non-persistent HTTP with 5 parallel TCP connections.

5 RTTs, in case of persistent HTTP with pipelining.

9 RTTs, in case of non-persistent HTTP with 5 parallel TCP connections.

6 RTTs, in case of persistent HTTP with pipelining.

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Consider a random experiment where two fair coins are tossed. Let

be the event that denotes HEAD on both the throws,

be the event that denotes HEAD on the first throw, and

be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

and

are independent.

and

are independent.

and

are independent.

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Consider functions Function_1 and Function_2 expressed in pseudocode as follows:

Function_1 while

do for

; end for

; end while

Function_2 for

; end for

Let

and

denote the number of times the statement “

” is executed in Function_1 and Function_2, respectively. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

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Let

be a simple, finite, undirected graph with vertex set

. Let

denote the maximum degree of

and let

denote the set of all possible colors. Color the vertices of

using the following greedy strategy: for

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

This procedure results in a proper vertex coloring of

The number of colors used is at most

The number of colors used is equal to the chromatic number of

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Let

. Let

denote the power set of

. Consider an undirected graph

whose vertex set is

. For any

is an edge in

if and only if (i)

, and (ii) either

. For any vertex

, the set of all possible orderings in which the vertices of

can be visited in a Breadth First Search (BFS) starting from

is denoted by

. If

denotes the empty set, then the cardinality of

is ________.

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Consider the following two-dimensional array D in the C programming language, which is stored in row-major order:

int D[128][128];

Demand paging is used for allocating memory and each physical page frame holds 512 elements of the array D. The Least Recently Used (LRU) page-replacement policy is used by the operating system. A total of 30 physical page frames are allocated to a process which executes the following code snippet:

for (int i = 0; i < 128; i++) for (int j = 0; j < 128; j++) D[j][i] *= 10;

The number of page faults generated during the execution of this code snippet is ________.

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Consider a computer system with 57-bit virtual addressing using multi-level tree-structured page tables with

levels for virtual to physical address translation. The page size is 4 KB (1 KB = 1024 B) and a page table entry at any of the levels occupies 8 bytes.

The value of

is ________.

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Consider a sequence

of elements

, and

. The following operations are performed on a stack

and a queue

, both of which are initially empty.

I: push the elements of

from

in that order into

II: enqueue the elements of

from

in that order into

III: pop an element from

IV: dequeue an element from

V: pop an element from

VI: dequeue an element from

VII: dequeue an element from

and push the same element into

VIII: Repeat operation VII three times.

IX: pop an element from

X: pop an element from

The top element of

after executing the above operations is __________.

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Consider the syntax directed translation given by the following grammar and semantic rules. Here

and

are non-terminals.

is the starting non-terminal, and #, 0 and 1 are lexical tokens corresponding to input letters “#”, “0” and “1”, respectively.

denotes the synthesized attribute (a numeric value) associated with a non-terminal

and

denote occurrences of

and

on the right hand side of a production, respectively. For the tokens 0 and 1,

and

Production	Semantic rule

The value computed by the translation scheme for the input string

is __________. (Rounded off to three decimal places)

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