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Official PYQ · 2018Q10Memory Management and Virtual MemoryMCQ1 mark

GATE CS 2018 Q10 — Memory Management and Virtual Memory

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Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is MM units if the corresponding memory page is available in memory, and DD units if the memory access causes a page fault. It has been experimentally measured that the average time taken for a memory access in the process is XX units.

Which one of the following is the correct expression for the page fault rate experienced by the process.

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Answer: B

To find the page fault rate, we can set up the equation for the effective memory access time (XX).

Let pp be the page fault rate (the probability that a memory access results in a page fault). Then, the probability that a page is found in memory (a page hit) is 1−p1 - p.

We are given:

  • Memory access time on page hit = MM
  • Memory access time on page fault = DD
  • Average (effective) memory access time = XX

The formula for the average memory access time is:

X=(1−p)⋅M+p⋅DX = (1 - p) \cdot M + p \cdot D

Now, we solve for pp:

X=M−p⋅M+p⋅DX = M - p \cdot M + p \cdot DX−M=p⋅(D−M)X - M = p \cdot (D - M)p=X−MD−Mp = \frac{X - M}{D - M}

Thus, the correct expression for the page fault rate is (X−M)/(D−M)(X - M) / (D - M), which corresponds to option B.

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