In a system, there are three types of resources: $$E, F$$ and $$G.$$ Four processes $${P_0},$$ $${P_1},$$ $${P_2}$$ and $${P_3}$$ execute concurrently. At the outset, the processes have declared their maximum resource requirements using a matrix named Max as given below. For example, Max$$\left[ {{P_{2,}}F} \right]$$ is the maximum number of instances of $$F$$ that $${{P_{2,}}}$$ would require. The number of instances of the resources allocated to the various processes at any given state is given by a matrix named Allocation.

Consider a state of the system with the Allocation matrix as shown below, and in which $$3$$ instances of $$E$$ and $$3$$ instances of $$F$$ are the only resources available.

Allocation
	E	F	G
P0	1	0	1
P1	1	1	2
P2	1	0	3
P3	2	0	0

Max
	E	F	G
P0	4	3	1
P1	2	1	4
P2	1	3	3
P3	5	4	1

From the perspective of deadlock avoidance, which one of the following is true?

Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is $$M$$ units if the corresponding memory page is available in memory, and $$D$$ units if the memory access causes a page fault. It has been experimentally measured that the average time taken for a memory access in the process is $$X$$ units.

Which one of the following is the correct expression for the page fault rate experienced by the process?

Consider the following C code. Assume that unsigned long int type length is 64 bits.

unsigned long int fun(unsigned long int n){
     unsigned long int i, j = 0, sum = 0;
     for (i = n; i > 1; i = i/2) j++;
     for ( ; j > 1; j = j/2) sum++;
     return(sum);
}

The value returned when we call fun with the input $${2^{40}}$$ is

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 _____.