In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases?

A computer system implements a $$40$$-bit virtual address, page size of $$8$$ kilobytes, and a $$128$$-entry translation look-aside buffer $$(TLB)$$ organized into $$32$$ sets each having four ways. Assume that the $$TLB$$ tag does not store any process id. The minimum length of the $$TLB$$ tag in bits is ________________.

Consider a system with byte-addressable memory, 32-bit logical addresses, 4 kilobyte page size and page table entries of 4 bytes each. The size of the page table in the system in megabytes is ________.

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? $$$4,7,6,1,7,6,1,2,7,2$$$