Explanation:

Page replacement algorithms are used to manage memory in operating systems. These algorithms replace the pages in main memory when there is a page fault. The aim is to minimize the number of page faults and improve the performance of the system. There are different page replacement algorithms available and each algorithm has its own advantages and disadvantages.

In this question, we are asked to identify the page replacement algorithm in which the page fault rate can increase even when the number of allocated frames increases. The correct answer is FIFO. Let's understand why.

FIFO (First In First Out) Algorithm:

FIFO is a page replacement algorithm that replaces the oldest page in memory with the new page when there is a page fault. It is a simple and easy-to-implement algorithm. In FIFO, pages are stored in a queue and the page that is first in the queue is the one that will be replaced.

How FIFO Can Increase Page Fault Rate?

When the number of allocated frames increases, we expect the page fault rate to decrease. However, in the case of FIFO, this may not be true. The reason is that FIFO suffers from the Belady's Anomaly problem. Belady's Anomaly is a phenomenon where increasing the number of allocated frames may actually increase the number of page faults.

Let's understand this with an example. Consider the following reference string of 5 pages:

2 3 4 2 1

Assume that we have only 3 frames allocated for the pages. The page fault rate for this reference string using FIFO algorithm will be as follows:

Page Fault Rate: 3/5 = 60%

Now, let's increase the number of frames to 4 and see what happens to the page fault rate:

Page Fault Rate: 4/5 = 80%

As we can see, the page fault rate has increased even though we have allocated more frames. This is because when we increase the number of frames, the old pages that were previously replaced by new pages may now be kept in memory. However, since FIFO only replaces the oldest page, these old pages may still be replaced by new pages, resulting in more page faults.

Conclusion:

In conclusion, FIFO is the only page replacement algorithm in which increasing the number of allocated frames may increase the page fault rate. This is due to the Belady's Anomaly problem, which causes old pages to be replaced even when more frames are available.