$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix containing coefficients has a non-trival solution when $$A$$ is.

$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$

A uni-processor computer system only has two processes, both of which alternate $$10$$ $$ms$$ $$CPU$$ bursts with $$90$$ $$ms$$ $${\rm I}/O$$ bursts. Both the processes were created at nearly the same time. The $${\rm I}/O$$ of both processes can proceed in parallel. Which of the following scheduling strategies will result in the least $$CPU$$ utilization (over a long period of time) for this system?

Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T. The code for the processes P and Q is shown below.

Process P:

while(1){
  W:
  Print '0';
  Print '0';
  X:
}

Process Q:

while(1){
  Y:
  Print '1';
  Print '1';
  Z:
}

Synchronization statements can be inserted only at points W, X, Y, and Z.

Which of the following will always lead to an output starting with 001100110011