Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is $$M$$ units if the corresponding memory page is available in memory, and $$D$$ units if the memory access causes a page fault. It has been experimentally measured that the average time taken for a memory access in the process is $$X$$ units.

Which one of the following is the correct expression for the page fault rate experienced by the process?

Consider a computer system with ten physical page frames. The system is provided with an access sequence $$\left( {{a_1},{a_2},....,{a_{20}},{a_1},{a_2},...,{a_{20}}} \right),$$ where each $${{a_i}}$$ is a distinct virtual page number. The difference in the number of page faults between the last-in-first-out page replacement policy and the optimal page replacement policy is _____________

Consider a computer system with $$40$$-bit virtual addressing and page size of sixteen kilobytes. If the computer system has a one-level page table per process and each page table entry requires $$48$$ bits, then the size of the per-process page table ____________ is megabytes.

Consider six memory partitions of sizes $$200$$ $$KB,$$ $$400$$ $$KB,$$ $$600$$ $$KB,$$ $$500$$ $$KB,$$ $$300$$ $$KB$$ and $$250$$ $$KB,$$ where $$KB$$ refers to kilobyte. These partitions need to be allotted to four processes of sizes $$357$$ $$KB,$$ $$210$$ $$KB,$$ $$468$$ $$KB$$ and $$491$$ $$KB$$ in that order. If the best fit algorithm is used, which partitions are NOT allotted to any process?