A function $$f:\,\,{N^ + } \to {N^ + },$$ defined on the set of positive integers $${N^ + },$$ satisfies the following properties: $$$\eqalign{ & f\left( n \right) = f\left( {n/2} \right)\,\,\,\,if\,\,\,\,n\,\,\,\,is\,\,\,\,even \cr & f\left( n \right) = f\left( {n + 5} \right)\,\,\,\,if\,\,\,\,n\,\,\,\,is\,\,\,\,odd \cr} $$$

Let $$R = \left\{ i \right.|\exists j:f\left( j \right) = \left. i \right\}$$ be the set of distinct values that $$f$$ takes. The maximum possible size of $$R$$ is _____________________.

Consider the recurrence relation $${a_1} = 8,\,{a_n} = 6{n^2} + 2n + {a_{n - 1}}.$$ Let $${a_{99}} = K \times {10^4}.$$ The value of $$K$$ is ____________.

Consider an arbitrary set of $$CPU$$-bound processes with unequal $$CPU$$ burst lengths submitted at the same time to a computer system. Which one of the following process scheduling algorithms would minimize the average waiting time in the ready queue?

Consider a disk queue with requests for $${\rm I}/O$$ to blocks on cylinders $$47, 38, 121, 191,$$ $$87, 11, 92, 10.$$ The $$C$$-$$LOOK$$ scheduling algorithm is used. The head is initially at cylinder number $$63,$$ moving towards larger cylinder numbers on its servicing pass. The cylinders are numbered from $$0$$ to $$199.$$ The total head movement (in number of cylinders) incurred while servicing these requests is _________________ .