Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right].$$
If the eigen values of $$A$$ are $$4$$ and $$8$$ then

What is the probability that divisor of $${10^{99}}$$ is a multiple of $${10^{96}}$$ ?

A system uses FIFO policy for page replacement. It has $$4$$ pages frames with no pages loaded to begin with. The system first accesses $$100$$ distinct pages in some order and then accesses the same $$100$$ pages but now in the reverse order. How many page faults will occur?

A system has n resources R₀,.....,R_n-1, and k processes P₀,.....,P_k-1. The implementation of the resource request logic of each process P_i, is as follows:

if (i%2==0) {
  if (i < n) request Ri;
  if (i+2 < n) request Ri+2 ;
}
else {
  if (i < n) request Rn-i;
  if (i+2 < n) request Rn-i-2;
}

In which one of the following situations is a deadlock possible?