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GATE 2022: Semi Syllabus Quiz- 1

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Question 1

What will be the value of x for the following expression?

(135)x + (144)x = (323)x

Question 2

Consider the following Boolean expression E.

How many literals are there in the minimized expression of E?

Question 3

In an n bit Carry Look ahead Adder (CLA), if tp is the delay of each gate and all gates are available with multi bit inputs and Carry Look ahead Generator (CLG) is designed with two-level logic circuit. For computing the sum of two n bit numbers xn–1 xn–2 …. x0, yn–1 yn–2 …. y0together with input carry (C0), amount of delay required for generating final result of on cn sn–1 sn–2 … s0 is _____ .

(Note: EXOR gates are available with two inputs only)

Question 4

A 1-bit full adder takes 20 ns to generate carry-out bit. If the maximum rate of additions is 10 X 106 additions/sec then what is the value of ‘x’ ns for the sum bit when four 1-bit full adders are cascaded?

Question 5

Consider the MUX given below , and find the value for function F :

Question 6

What is the number of select lines required in a single input n-output demultiplexer?

Question 7

Consider 3 processes P1, P2 and P3 arriving at time 1, 2 and 4 and their execution duration in CPU is 6, 8 and 3 time units respectively. If Round Robin CPU scheduling is used by Operating System with time slice of 2 units, then the total waiting time of P3, is ______ .

Question 8

Suppose the following disk request sequence (track numbers) for a disk with 100 tracks is given: 45, 20, 90, 10, 50, 60, 80, 25, 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 and compared to the SCAN (Elevator) algorithm (assuming that SCAN algorithm moves towards 100 when it starts execution) is ______ tracks.

Question 9

Consider system having ‘m’ resources of the same type. These resources are shared by 3 processes A, B, C which have peak time demands of 7,8,9 respectively. The minimum value of ‘m’ that ensure that deadlock will never occur is

Question 10

Consider the following program.

#include<stdio.h>

#include<stdlib.h>

#include<unistd.h>

int main(void)

{

pid_t pid;

int var= 200;

pid=fork();

if (pid==0)

var=300;

fork();

printf(“%d”, var);

return 0;

}

Assuming all invocations of fork are successful, which of the following is a correct output when the program is executed on the UNIX OS?

Question 11

Consider a process with single CPU burst of 100 time units and a single disk IO burst of 1000 time units at the end. Suppose the time interval for the processor is 15 time units and the process scheduling algorithm is round robin scheduling algorithm. Then, atmost how many times a process entered into ready queue before entering to the termination state while its execution ____________

Question 12

Given below is a program which when executed spawns two concurrent processes:
Semaphore X:=0;
/*Process now forks into concurrent processes P1 & P2*/

Consider the following statements about processes P1 and P2:
I : It is possible for process P1 to starve.
II. It is possible for process P2 to starve.
Which of the following holds?

Question 13

Consider a paging system with a 32-bit virtual address space. Each address refers to a byte in memory.
Let the page size be 16 KB, and the main memory size be 256 MB. What is minimum size of page table? Assume page table entry has at least 2 protection bits.

Question 14

Consider a Ethernet network employing CSMA/CD, where Bw = 10 Mbps, length of the cable(L) is 200m and v = 2 x 108 m/sec. Calculate maximum frame size in bytes.

Question 15

Consider there to be five collision which are then to be followed by a progress in case of a ALOHA user producing 50 requests/sec and also time is been slotted in 40msec units, then after considering all of the above cases find the probability of the mentioned collisions?

Question 16

Consider the following statement:

(a) The minimum length of IPv4 and TCP header is 20 bytes

(b) The minimum length of IPv6 header is 40 Bytes

(c) IPv4 is connection-oriented protocol while IPv6 is not

(d) The size of the IP address in IPv6 is 8 bytes

The number of correct statement is ______?

Question 17

Consider a 1 Mbps Ethernet and find the throughput for slotted aloha at G=2 (channel load) in Kbps.

Question 18

Consider the following graph G:

The sum of edge weights of the spanning tree formed using Kruskal’s algorithm on graph G is ________.

Question 19

Consider a linked list which has 10 nodes and the nodes have value 1,2,3……10 in this order from head to last. Now this linked list is passed as parameter to the below given code :
 
Now suppose the value of n taken in above code is 4 , then what will be the value printed by above code _____________.

Question 20

A BFS algorithm is implemented on the following graph. Which of the following nodes will be traversed at last if the root is ‘E’ and consider lexicographic ordering while traversing?

Question 21

Let A[1, ......, n] be an array of ‘n’ elements. If there are inversions are present in ‘A’. Then which of the following statements are true?

I. Quick sort takes time complexity O(n2) for sorting elements of array A

II. Merge sort takes time complexity O(n2) for sorting elements of array A

Codes:

Question 22

Given the input sequence {11, 33, 43, 99, 79, 19} and hash table of size 10 with the hash function h(k) = k mod 10, if hash table uses quadratic probing, the number of collisions occurred while mapping the given sequence is ________.

Question 23

Consider the 5 items along with their weights and values.

The Knapsack has capacity W = 60, the maximum profit that can be achieved using fractional Knapsack is ________.

Question 24

Consider the following functions:

f(n) = 2log2n

g(n) = nlog2n

h(n) = n1/log2n

Which of the following statements about the asymptotic behavior of f(n), g(n) and h(n) is true?

Question 25

If an undirected graph ‘G’ has n-vertices and has ‘K’ edges . The number of components in the graph is at least.
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