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 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?

A computer system implements $$8$$ kilobyte pages and a $$32$$-bit physical address space. Each page table entry contains a valid bit, a dirty bit, three permission bits, and the translation. If the maximum size of the page table of a process is $$24$$ megabytes, the length of the virtual address supported by the system is _______________ bits.

Consider a paging hardware with a TLB. Assume that the entire page table and all the pages are in the physical memory. It takes 10 milliseconds to search the TLB and 80 milliseconds to access the physical memory. If the TLB hit ratio is 0.6, the effective memory access time (in milliseconds) is______________.