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GATE 2022 Toppers Weekly Quiz 3

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Question 1Multiple Correct Options

Consider the following function written in a C like language:

int grade(int n)

{

   if (n < 2) return;

   else

   {

       int sum = 0;

       int i, j;

       for (i = 1; i< = 4; i++) grade(n/2);

       for (i = 1; i< = n; i++)

       {

          for (j = 1;j< = i;j++)

             {

                  sum = sum + 1;

             }

       }

   }

}

Now consider the following statements. Select all possible correct options.

Question 2

Consider a hash table of size 7 implemented using an array A[0 ... 6]. A modulo function (MOD 7) is used to map the keys and open addressing is used to handle collisions. If 53, 32, 43, 51, 99 are inserted into the hash table, the contents of array A is

Question 3

Consider the following statements:
S1 : If all edge weights of a graph are positive, then any subset of edges that connects all vertices and has minimum total weight is a tree.
S2 : Let p = <V0, V1, V2 ....., Vk> be the shortest path from vertex V0 to Vk and for all such that 0 ≤ i ≤ j ≤ k, let pij be the subpath of P from vertex Vi to Vj. Then p is a shortest path from Vi to Vj.

Which of the above statements is/are correct?

Question 4Multiple Correct Options

Consider the following statements with respect to user-level threads and kernel-level threads. Which of the statements is/are true? (Multi Select Question)

Question 5

In a computer a particular website is searched for 1sttime, it takes t1 time to load/access the site. After some time again same site is searched, now it takes t2 time to load/access that site. All the environment/factors (like net connection, bit rate, power supply etc)are same for both case. Then what is true ?

Question 6

Host X is sending a big file to host Y over a TCP connection. One way propagation time is 15 msec apart connected by a 512 Mbps link. Suppose that they are using a packet size of 500 bytes to transmit the file. For simplicity, do not consider acknowledgement packets. What should be the minimum window size (in terms packets)to have channel utilization to be greater than 75%?

Question 7Multiple Correct Options

Consider the given expressions for the function f(A, B). For the given functions to be true, it should be self-dual functions. Which of the functions is/are true?

Question 8

Consider the following sequence of instructions executed on a 5 stage pipelined processor. Data dependency is resolved by operand forwarding techniques. MOV instruction output present in 4th stage and ALU operation output present in 3rd stage.

I1 : MOV R0 , M[300]

I2 : SUB R0 , R1

I3 : ADD R2 , R1

I4 : MOV R3 , @ 200

I5 : MUL R2 , R3

What is the number of cycles required to complete the program? (Assume each stage takes 1 cycle time)

Question 9

Let G be a directed graph where vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j iff either j = i+1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is:

Question 10

Executing an algorithm with time complexity O(n2) exactly 10 times gives an algorithm with Big-Oh time complexity ___?
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Aug 9GATE & PSU CS