GATE-CS-2004

Question 41

What does the following algorithm approximate?

C

    x = m;
    y = 1;
    while (x - y > e)
    {
        x = (x + y)/2;
        y = m/x;
    }
    print(x);

(Assume m > 1, e > 0).

• log m
• m²
• m^1/2
• m^1/3

Question 42

Consider the following C program segment

c

struct CellNode
{
  struct CelINode *leftchild;
  int element;
  struct CelINode *rightChild;
}

int Dosomething(struct CelINode *ptr)
{
    int value = 0;
    if (ptr != NULL)
    {
      if (ptr->leftChild != NULL)
        value = 1 + DoSomething(ptr->leftChild);
      if (ptr->rightChild != NULL)
        value = max(value, 1 + DoSomething(ptr->rightChild));
    }
    return (value);
}

The value returned by the function DoSomething when a pointer to the root of a non-empty tree is passed as argument is

• The number of leaf nodes in the tree
• The number of nodes in the tree
• The number of internal nodes in the tree
• The height of the tree

Question 43

Suppose we run Dijkstra’s single source shortest-path algorithm on the following edge weighted directed graph with vertex P as the source. In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized?

• P, Q, R, S, T, U
• P, Q, R, U, S, T
• P, Q, R, U, T, S
• P, Q, T, R, U, S

Question 44

Consider the grammar with the following translation rules and E as the start symbol.

E → E1 # T { E.value = E1.value * T.value }
         | T{ E.value = T.value }
T → T1 & F { T.value = T1.value + F.value }
          | F{ T.value = F.value }
F → num { F.value = num.value } 

Compute E.value for the root of the parse tree for the expression: 2 # 3 & 5 # 6 & 4.

• 200
• 180
• 160
• 40

Question 45

Consider the following set of processes, with the arrival times and the CPU-burst times given in milliseconds

  Process   Arrival Time    Burst Time
    P1          0              5
    P2          1              3
    P3          2              3
    P4          4              1

What is the average turnaround time for these processes with the preemptive shortest remaining processing time first (SRPT) algorithm ?

• 5.50
• 5.75
• 6.00
• 6.25

Question 46

Consider a system with a two-level paging scheme in which a regular memory access takes 150 nanoseconds, and servicing a page fault takes 8 milliseconds. An average instruction takes 100 nanoseconds of CPU time, and two memory accesses. The TLB hit ratio is 90%, and the page fault rate is one in every 10,000 instructions. What is the effective average instruction execution time?

• 645 nanoseconds
• 1050 nanoseconds
• 1215 nanoseconds
• 1230 nanoseconds

Question 47

Consider two processes P1 and P2 accessing the shared variables X and Y protected by two binary semaphores SX and SY respectively, both initialized to 1. P and V denote the usual semaphore operators, where P decrements the semaphore value, and V increments the semaphore value. The pseudo-code of P1 and P2 is as follows : P1 :

 While true do {
   L1 : ................
   L2 : ................
   X = X + 1;
   Y = Y - 1;
   V(SX);
   V(SY);             
 }

P2 :

 While true do {
   L3 : ................   
   L4 : ................
   Y = Y + 1;
   X = Y - 1;
   V(SY);
   V(SX);            
}

In order to avoid deadlock, the correct operators at L1, L2, L3 and L4 are respectively

• P(SY), P(SX); P(SX), P(SY)

• P(SX), P(SY); P(SY), P(SX)

• P(SX), P(SX); P(SY), P(SY)

• P(SX), P(SY); P(SX), P(SY)

Question 48

A Unix-style i-node has 10 direct pointers and one single, one double and one triple indirect pointers. Disk block size is 1 Kbyte, disk block address is 32 bits, and 48-bit integers are used. What is the maximum possible file size ?

• 2²⁴ bytes
• 2³² bytes
• 2³⁴ bytes
• 2⁴⁸ bytes

Question 49

The relation scheme Student Performance (name, courseNo, rollNo, grade) has the following functional dependencies:

name, courseNo → grade
rollNo, courseNo → grade
name → rollNo
rollNo → name 

The highest normal form of this relation scheme is

• 2 NF
• 3 NF
• BCNF
• 4NF

Question 50

Consider the relation Student (name, sex, marks), where the primary key is shown underlined, pertaining to students in a class that has at least one boy and one girl. What does the following relational algebra expression produce? (Note: r is the rename operator). The condition in join is "(sex = female ^ x = male ^ marks ≤ m)"

• names of girl students with the highest marks
• names of girl students with more marks than some boy student
• names of girl students with marks not less than some boy students4)
• names of girl students with more marks than all the boy students