GATE CSE format:nat PYQs & Answers — Page 23

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Questions 221–230 of 281. Imported answers require independent review unless marked reviewed.

Topic practice 281 questionsPage 23 of 29

The chromatic number of the following graph is ______.

Diagram for Computer Science and Information Technology question 18

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Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is ______.

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The postorder traversal of a binary tree is 8,9,6,7,4,5,2,3,1. The inorder traversal of the same tree is 8,6,9,4,7,2,5,1,3. The height of a tree is the length of the longest path from the root to any leaf. The height of the binary tree above is ____.

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Consider the following C program:

#include <stdio.h>

int counter = 0;

int calc (int a, int b) {

int c;

counter++;

if (b==3) return (a*a*a);

else {

c = calc(a, b/3);

return (c*c*c);

}

int main () {

calc(4, 81);

printf("%d", counter);

}

The output of this program is ____.

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Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops.

Diagram for Computer Science and Information Technology question 22

The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of “in” is ____.

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A 32-bit wide main memory unit with a capacity of 1 GB is built using 256 M × 4-bit DRAM chips. The number of rows of memory cells in the DRAM chip is

. The time taken to perform one refresh operation is 50 nanoseconds. The refresh period is 2 milliseconds. The percentage (rounded to the closest integer) of the time available for performing the memory read/write operations in the main memory unit is ________.

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Consider a system with 3 processes that share 4 instances of the same resource type. Each process can request a maximum of K instances. Resource instances can be requested and released only one at a time. The largest value of K that will always avoid deadlock is ____.

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Consider a long-lived TCP session with an end-to-end bandwidth of 1 Gbps (=

bits-per-second). The session starts with a sequence number of 1234. The minimum time (in seconds, rounded to the closest integer) before this sequence number can be used again is ________.

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Let G be a graph with

vertices, with each vertex labelled by a distinct permutation of the numbers 1, 2, ..., 100. There is an edge between vertices

and

if and only if the label of

can be obtained by swapping two adjacent numbers in the label of

. Let y denote the degree of a vertex in G, and z denote the number of connected components in G. Then,

_____.

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Consider Guahati (G) and Delhi (D) whose temperatures can be classified as high (H), medium (M) and low (L). Let

denote the probability that Guahati has high temperature. Similarly,

and

denote the probability of Guahati having medium and low temperatures respectively. Similarly, we use

and

for Delhi.

The following table gives the conditional probabilities for Delhi’s temperature given Guwahati’s temperature.


0.40	0.48	0.12
0.10	0.65	0.25
0.01	0.50	0.49

Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature (

) then the probability of Delhi also having a high temperature (

) is 0.40; i.e.,

. Similarly, the next two entries are

and

. Similarly for the other rows.

If it is known that

, and

, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _____.

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GATE CSE format:nat PYQs

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 43

Question 44