A virtual memory system uses First In First Out (FIFO) page replacement policy and allocates a fixed number of frames to a process. Consider the following statements:
$$P:$$ Increasing the number of page frames allocated to a process sometimes increases the page fault rate.
$$Q:$$ Some programs do not exhibit locality of reference.

Which one of the following is TRUE?

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 single processor system has three resource types X, Y and Z, which are shared by three processes. There are 5 units of each resource type. Consider the following scenario, where the column alloc denotes the number of units of each resource type allocated to each process, and the column request denotes the number of units of each resource type requested by a process in order to complete execution. Which of these processes will finish LAST?