A process has been allocated $$3$$ page frames. Assume that none of the pages of the process are available in the memory initially. The process makes the following sequence of page references (reference string): $$$1, 2, 1, 3, 7, 4, 5, 6, 3, 1$$$

Least Recently Used (LRU) page replacement policy is a practical approximation to optimal page replacement. For the above reference string, how many more page faults occur with LRU than with the optimal page replacement policy?

A process has been allocated $$3$$ page frames. Assume that none of the pages of the process are available in the memory initially. The process makes the following sequence of page references (reference string): $$$1, 2, 1, 3, 7, 4, 5, 6, 3, 1$$$

If optimal page replacement policy is used, how many page faults occur for the above reference string?

A Computer system supports $$32$$-bit virtual addresses as well as $$32$$-bit physical addresses. Since the virtual address space is of the same size as the physical address space, the operating system designers decide to get rid of the virtual memory entirely. Which one of the following is true?

Consider a System with a two-level paging scheme in which a regular memory access takes $$150$$ nanoseconds, and servicing a page fault takes $$8$$ milliseconds. An average instruction takes $$100$$ nanoseconds of $$CPU$$ time, and two memory accesses. The $$TLB$$ hit ratio is $$90$$% and the page fault rate is one in every $$10,000$$ instructions. What is the effective average instruction execution time?