$1.$ Solve the following problem by using the Priority Scheduling algorithm, draw a Gantt Chart, and calculate the average waiting time.

Process Burst Time Priority

P$1103$

P$211$

P$324$

P$415$

P$552$

$2.$ Consider the following page reference string:

$3,2,3,4,2,1,3,4,2,1,4,3,2,1,5$

How many page faults would occur for the Least Recently Used $($LRU$),$ assuming three frames?

Page Faults $=$

$3.$ Considering a system with five processes P$0$ through P$4$ and three resource types A$,$ B$,$ C$.,$ Resource type A has $8$ instances, B has $6$ instances, and type C has $9$ instances. Suppose at time t$0$ following snapshot of the system has been taken:

Process Allocation Max Available

A B C A B C A B C

P$0111323221$

P$1213314$

P$2111112$

P$3100221$

P$4113343$

By applying the banker$$s algorithm

$1.$ What will be the content of the need matrix?

$2.$ Is the system in a safe state? If yes, then what is the safe sequence?