1. Given references to the following pages by a program, 0, 1, 4, 2, 0, 2, 6, 5, 1, 2, 3, 2, 1, 2, 6, 2, 1, 4, 6, 2, how many page faults will occur if the program has three-page frames available to it and uses: (a) FIFO replacement? (b) LRU replacement? (c) Optimal replacement? Show clearly how you got your results. Repeat the three algorithms for the scenario when the process has been allocated four frames. [2x2x3 points] 2. A memory manager has 116 free frames and it is requested by four processes with these memory requests A (spanning 40 pages), B (20 pages), C (48 pages), and D (96 pages). How many frames will be allocated to these processes if the memory allocation uses a) fixed allocation b) proportional allocation [2 points] 3. Calculate the average memory access time when memory access to cache on a cache hit is 180 ns and the average time to access the main memory is 2800 ns with a hit ratio of 85%. [2 points] 4. On a system with 1MB of memory using the Buddy System, draw a diagram showing memory allocation after each of the following events. Which would the first request to fail? Also indicate the internal and external fragmentation at the time of failure. [6 points] Process A, request 29K Process B, request 12K Process C, request 330K Process D, request 140K Process E, request 70K Process F, request 17K Process G, request 70K Process H, request 12K Process I, request 10K Process J, request 25K Process K, request 257K 5. For the processes listed below, draw a Gantt chart illustrating their execution using: (a) First-Come FirstServed (b) Shortest Job First (c) Shortest Remaining Time (d) Round Robin (quantum = 1) (e) Round Robin (quantum =2) Also calculate the turnaround time, wait time for the algorithms and average throughput for each of the algorithms. [5points] Process Arrival Time Processing Time A 0.000 4 B 0.003 7 C 0.009 3 D 1.001 2 E 1.002 3 F 3.001 2 6. For the processes listed below, draw a Gantt chart illustrating their execution using priority scheduling for: (a) Preemptive (b) Nonpreemptive cases. A larger priority number has higher priority. Also calculate the turnaround time, wait time for the algorithms and average throughput for each of the algorithms. [3 points] Process Arrival Time Burst Priority A 0.000 2 4 B 0.090 1 5 C 2.900 4 6 D 4.010 3 3 E 5.900 2 9 F 6.900 5 2