Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is $M$ units if the corresponding memory page is available in memory, and $D$ 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 $X$ units. Which one of the following is the correct expression for the page fault rate experienced by the process?

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Solution

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Official answer: B) (X - M) / (D - M)

Memory Management and Virtual Memory

Let $p$ be the page fault rate (probability of a page fault).

The effective memory access time $X$ is given by:

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

Expanding and rearranging the terms:

X = M - pM + pD

X - M = p(D - M)

p = \frac{X - M}{D - M}

Hence, option (B) is the correct expression.

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This Memory Management and Virtual Memory previous year question is Q10 of the GATE CSE 2018 paper. Find more GATE CSE PYQs on Memory Management and Virtual Memory in Operating Systems, or browse all GATE CSE PYQs.

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Memory Management and Virtual Memory in GATE CSE

Memory Management and Virtual Memory has 32 GATE CSE PYQs across 22 papers from 2011 to 2026. 5 of them are 1-mark MCQs like this one, and it is the only one in GATE CSE 2018.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.