A system uses $$3$$ page frames for storing process pages in main memory. It uses the Least Recently Used $$(LRU)$$ page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below? $$$4,7,6,1,7,6,1,2,7,2$$$

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______________.

A system contains three programs and each requires three tape units for its operation. The Minimum number of tape units which the system must have such that deadlocks never arise is _________.

An operating system uses $$shortest$$ $$remaining$$ $$time$$ $$first$$ scheduling algorithm for pre-emptive scheduling of processes. Consider the following set of processes with their arrival times and $$CPU$$ burst times (in milliseconds):

Process	Arrival Time	Burst Time
P1	0	12
P2	2	4
P3	3	6
P4	8	5

The average waiting time (in milliseconds) of the processes is ________.