GATE CS 2021 | Set 2

Question 41

​​​​​​Consider the following two statements about regular languages:

• S1: Every infinite regular language contains an undecidable language as a subset.
• S2: Every finite language is regular.

Which one of the following choices is correct?

• Only S1 is true
• Only S2 is true
• Both S1 and S2 are true
• Neither S1 nor S2 is true

Question 42

For two n-dimensional real vectors P and Q, the operation s(P,Q) is defined as follows: Let L be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P,Q∈L, s(P,Q)=0. What is the maximum cardinality possible for the set L?

• 9
• 10
• 11
• 100

Question 43

For a statement S in a program, in the context of liveness analysis, the following sets are defined:

• USE(S) : the set of variables used in S
• IN(S) : the set of variables that are live at the entry of S
• OUT(S) : the set of variables that are live at the exit of S

Consider a basic block that consists of two statements, S1 followed by S2. Which one of the following statements is correct?

• OUT(S1) = IN (S2)
• OUT (S1) = IN (S1) ∪ USE (S1)
• OUT (S1) = IN (S2) ∪ OUT (S2)
• OUT (S1) = USE (S1) ∪ IN (S2)

Question 44

Suppose the following functional dependencies hold on a relation U with attributes P,Q,R,S, and T:

P → QR
RS → T 

Which of the following functional dependencies can be inferred from the above functional dependencies?

• PS → T
• R → T
• P → R
• PS → Q

Question 45

For a string w, we define w^R to be the reverse of w. For example, if w = 01101 then w^R = 10110. Which of the following languages is/are context-free?

• {wxw^Rx^R ∣ w,x∈{0,1}*}
• {ww^Rxx^R ∣ w,x∈{0,1}*}
• {wxw^R ∣ w,x∈{0,1}*}
• {wxx^Rw^R ∣ w,x∈{0,1}*}

Question 46

Consider the following multi-threaded code segment (in a mix of C and pseudo-code), invoked by two processes P1 and P2, and each of the processes spawns two threads T1 and T2:

int x = 0;  // global
Lock L1;    // global
main () { 
    create a thread to execute foo( ); // Thread T1
    create a thread to execute foo( ); // Thread T2
    wait for the two threads to finish execution;
    print(x);}
    
    
foo() {
    int y = 0;
    Acquire L1;
    x = x + 1;
    y = y + 1;
    Release L1;
    print (y);} 

Which of the following statement(s) is/are correct?

• Both P1 and P2 will print the value of x as 2.
• At least of P1 and P2 will print the value of x as 4.
• At least one of the threads will print the value of y as 2.
• Both T1 and T2, in both the processes, will print the value of y as 1.

Question 47

Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and freeing of resources are done by holding a global lock (L). The following scheme is used to own a resource instance:

function OWNRESOURCE(Resource R)
    Acquire lock L // a global lock
    if R is available then
        Acquire R
        Release lock L
    else
        if R is owned by another process P then 
        Terminate P, after releasing all resources owned by P  
        Acquire R  
        Restart P
        Release lock L
        end if
    end if    
end function 

Which of the following choice(s) about the above scheme is/are correct?

• The scheme ensures that deadlocks will not occur
• The scheme may lead to live-lock
• The scheme may lead to starvation
• The scheme violates the mutual exclusion property

Question 48

If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?

• 0x6665
• 0x0001
• 0x4243
• 0x0100

Question 49

Consider a computer network using the distance vector routing algorithm in its network layer. The partial topology of the network is shown below. The objective is to find the shortest-cost path from the router R to routers P and Q. Assume that R does not initially know the shortest routes to P and Q. Assume that R has three neighbouring routers denoted as X, Y and Z. During one iteration, R measures its distance to its neighbours X, Y, and Z as 3, 2 and 5, respectively. Router R gets routing vectors from its neighbours that indicate that the distance to router P from routers X, Y and Z are 7, 6 and 5, respectively. The routing vector also indicates that the distance to router Q from routers X, Y and Z are 4, 6 and 8 respectively. Which of the following statement(s) is/are correct with respect to the new routing table o R, after updation during this iteration?

• The distance from R to P will be stored as 10
• The distance from R to Q will be stored as 7
• The next hop router for a packet from R to P is Y
• The next hop router for a packet from R to Q is Z

Question 50

Consider the following directed graph: Which of the following is/are correct about the graph?

• The graph does not have a topological order
• A depth-first traversal starting at vertex S classifies three directed edges as back edges
• The graph does not have a strongly connected component
• For each pair of vertices u and v, there is a directed path from u to v