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Consider a hypothetical machine with $3$ pages of physical memory, $5$ pages of virtual memory, and $<A, B, C, D, A, B, E, A, B, C, D, E, B, A, B>$ as the stream of page reference by an application. If $P$ and $Q$ are the number of page faults that the application would incur with FIFO and LRU page replacement algorithms respectively, then $(P,Q)=$ _______(Assuming enough space for storing $3$ page frames)

  1. $(11,10)$
  2. $(12,11)$
  3. $(10,11)$
  4. $(11,12)$
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3 pages of physical memory means 3 frames (so at a time only max 3 page in  frames)

 5 pages of  virtual memory means 5 page

 A B C D A B  E A B C D E B A B

FIFO  Page Fault  for  A ,B ,C ,D  ,A ,B ,E, C ,D ,B,A   TOTAL= 11

LRU   Page Fault  for  A ,B ,C ,D  ,A ,B ,E, C ,D ,E,B,A   TOTAL= 12

Option 4 is the right ans

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