Virtual Memory & Page Replacement

Consider a demand paging system with three frames, and the following page reference string: 1 2 3 4 5 4 1 6 4 5 1 3 2. The contents of the frames are as follows initially and after each reference (from left to right). The first column is the initial state; each later column shows the frames after the reference in its header: $$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \textit{initially} & 1^* & 2^* & 3^* & 4^* & 5^* & 4 & 1 & 6^* & 4 & 5 & 1^* & 3^* & 2^* \\ \hline - & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 6 & 6 & 6 & 6 & 6 & 2 \\ - & - & 2 & 2 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 1 & 1 & 1 \\ - & - & - & 3 & 3 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 3 & 3 \\ \hline \end{array}$$ The *-marked references cause page replacements. Which one or more of the following could be the page replacement policy/policies in use?

Consider a 32-bit system with 4 KB page size and page table entries of size 4 bytes each. Assume 1 KB = $2^{10}$ bytes. The OS uses a 2-level page table for memory management, with the page table containing an outer page directory and an inner page table. The OS allocates a page for the outer page directory upon process creation. The OS uses demand paging when allocating memory for the inner page table, i.e., a page of the inner page table is allocated only if it contains at least one valid page table entry. An active process in this system accesses 2000 unique pages during its execution, and none of the pages are swapped out to disk. After it completes the page accesses, let $X$ denote the minimum and $Y$ denote the maximum number of pages across the two levels of the page table of the process. The value of $X + Y$ is __________

In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases?

A computer system implements a 40-bit virtual address, page size of 8 kilobytes, and a 128-entry translation look-aside buffer (TLB) organized into 32 sets each having four ways. Assume that the TLB tag does not store any process id. The minimum length of the TLB tag in bits is _____.

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.

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?