A cycle on $$n$$ vertices is isomorphic to its complement. The value of $$n$$ is __________.

The product of the non-zero eigenvalues of
the matrix $$\left[ {\matrix{ 1 & 0 & 0 & 0 & 1 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 1 & 0 & 0 & 0 & 1 \cr } } \right]$$ is ____ .

The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functinal be denoted by p. Then 100p = __________________.

A computer has twenty physical page frames which contain pages numbered $$101$$ through $$120.$$ Now a program accesses the pages numbered $$1, 2, …, 100$$ in that order, and repeats the access sequence THRICE. Which one of the following page replacement policies experiences the same number of page faults as the optimal page replacement policy for this program?