The value of $$\int\limits_0^3 {\int\limits_0^x {\left( {6 - x - y} \right)dxdy\,\,\,} } $$ is _____.

A process executes the following code

for (i = 0; i < n; i + +) fork ( ); 

The total number of child processes created is

Which of the following is/are true of the auto-increment addressing mode?
$${\rm I}.\,\,\,$$ It is useful in creating self-relocating code
$${\rm II}.\,\,\,$$ If it is included in an Instruction Set Architecture, then an additional $$ALU$$ is required for effective address calculation.
$${\rm III}.\,\,\,$$ The amount of increment depends on the size of the data item accessed

The P and V operations on counting semaphores, where s is a counting semaphore, are defined as follows:

P(s): s = s-1; 
if s < 0 then wait; 
V(s) : s = s-1; 
ifs <= 0 then wakeup a process waiting on s;

Assume that P_b and V_b the wait and signal operations on binary semaphores are provided. Two binary semaphores X_b and Y_b are used to implement the semaphore operations P(s) and V(s) as follows:

  P(s): Pb (Xb);
        S = s - 1;
        if(s < 0){
          Vb(Xb);
          Pb(Yb);
        }
        Else Vb (Xb);
  V(s): Pb (Xb);
        S = s + 1;
        if(s <= 0) Vb(Yb);
        Vb(Xb);

The initial values of X_b and Y_b are respectively