GATE CSE topic:computing PYQs & Answers — Page 8

Questions 71–80 of 975. Imported answers require independent review unless marked reviewed.

Consider the real valued variables X, Y and Z represented using the IEEE 754 single-precision floating-point format. The binary representations of X and Y in hexadecimal notation are as follows:

X: 35C00000 Y: 34A00000

Let

Which one of the following is the binary representation of Z, in hexadecimal notation?

Your answerChoose one option.

35C80000

35CC0000

35E80000

35EC0000

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Consider a complete graph

with

vertices (

). Note that multiple spanning trees can be constructed over

. Each of these spanning trees is represented as a set of edges. The Jaccard coefficient between any two sets is defined as the ratio of the size of the intersection of the two sets to the size of the union of the two sets.

Which one of the following options gives the lowest possible value for the Jaccard coefficient between any two spanning trees of

Your answerChoose one option.

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Consider a 2-bit saturating up/down counter that performs the saturating up count when the input P is 0, and the saturating down count when P is 1. The Next State table of the counter is as shown. The counter is built as a synchronous sequential circuit using D flip-flops.

[Table: Input P, Current State Q₁ Q₀, Next State Q₁⁺ Q₀⁺; rows (P,Q₁,Q₀ → Q₁⁺,Q₀⁺): (0,0,0→0,1), (0,0,1→1,0), (0,1,0→1,1), (0,1,1→1,1), (1,0,0→0,0), (1,0,1→0,0), (1,1,0→0,1), (1,1,1→1,0).]

Which one of the following options corresponds to the expressions for the inputs of the D flip-flops, D₁ and D₀?

Your answerChoose one option.

;

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Let

be a weighted directed acyclic graph with

edges and

vertices. Given

and a source vertex

, which one of the following options gives the worst case time complexity of the fastest algorithm to find the lengths of shortest paths from

to all vertices that are reachable from

Your answerChoose one option.

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The size of the physical address space of a processor is

bytes. The capacity of a cache memory unit is

bytes. The cache block size is 128 bytes. The cache memory unit can be built as a direct mapped cache or as a

-way set-associative cache, where

and

. Let the length of the TAG field be

bits for the direct mapped cache, and

bits for the set-associative cache.

Which one of the following options is true?

Your answerChoose one option.

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Consider an array

of integers of size

. The indices of

run from 1 to

. An algorithm is to be designed to check whether

satisfies the condition given below.

such that

Which one of the following gives the worst case time complexity of the fastest algorithm that can be designed for the problem?

Your answerChoose one option.

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Consider the following code snippet in C language that computes the number of nodes in a non-empty singly linked list pointed to by the pointer variable head.

struct node{

int elt;

struct node *next;

};

int getListSize (struct node *head)

{

if( E1 ) return 1;

return E2;

}

Which one of the following options gives the correct replacements for the expressions E1 and E2?

Your answerChoose one option.

E1: head == NULL; E2: 1 + getListSize(head)

E1: head->next == NULL; E2: 1 + getListSize(head->next)

E1: head == NULL; E2: 1 + getListSize(head->next)

E1: head->next == NULL; E2: 1 + getListSize(head)

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Consider a table

, where the elements

, represent the cost of the optimal solutions of different subproblems of a problem that is being solved using a dynamic programming algorithm. The recursive formulation to compute the table entries is as follows:

Consider the following two algorithms to compute entries of

. Assume that for both the algorithms, for all

has been initialized to 1.

Algorithm

: For

For

Algorithm

: For

For

Algorithm

is said to be correct if and only if it calculates the correct values of

, for all

, (as per the recursive formulation at the end of the execution of the algorithm

Which one of the following statements is true?

Your answerChoose one option.

Both algorithms

and

are correct

Algorithm

is correct, but algorithm

is incorrect

Algorithm

is correct, but algorithm

is incorrect

Both algorithms

and

are incorrect

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Let

be the set of all integers from 1 to 15. Consider any order of insertion of the elements of

into a binary search tree that creates a complete binary tree.

Which one of the following elements can NEVER be the third element that is inserted?

Your answerChoose one option.

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Consider the following 4-variable Boolean function

Consider

as MSB,

as LSB. Which one of the following options represents the minimal sum of products form for the above function?

Note:

is OR operation,

is AND operation,

is NOT operation

Your answerChoose one option.

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GATE CSE topic:computing PYQs

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