GATE CS 2014 Set 1 — Question 43

NAT+2 / -0MediumPage Replacement AlgorithmsMemory ManagementOperating System

Operating System → Memory Management → Page Replacement Algorithms

Last updated 5 September 2026

Question

Assume that there are 3 page frames which are initially empty. If the page reference string is 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6, the number of page faults using the optimal replacement policy is__________.

Correct answer 7 to 7 Solution Optimal Page Replacement replaces the page that will not be used for the longest period of time. Frames: 3. Reference String: 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6. 1. Ref 1 : Miss. Frames: {1}. (Fault 1) 2. Ref 2 : Miss. Frames: {1, 2}. (Fault 2) 3. Ref 3 : Miss. Frames: {1, 2, 3}. (Fault 3) 4. Ref 4 : Miss. Frames full. Look ahead: 2, 1, 5, 3... 2 is needed next at index 4. 1 is needed next at index 5. 3 is needed next at index 7. 3 is the furthest. Replace 3. Frames: {1, 2, 4}. (Fault 4) 5. Ref 2 : Hit. Frames: {1, 2, 4}. 6. Ref 1 : Hit. Frames: {1, 2, 4}. 7. Ref 5 : Miss. Look ahead: 3, 2, 4, 6... 1 is not needed again. 2 is needed at index 8. 4 is needed at index 9. Replace 1. Frames: {5, 2, 4}. (Fault 5) 8. Ref 3 : Miss. Look ahead: 2, 4, 6... 5 is not needed again. 2 is needed at index 8. 4 is needed at index 9. Replace 5. Frames: {3, 2, 4}. (Fault 6) 9. Ref 2 : Hit. Frames: {3, 2, 4}. 10. Ref 4 : Hit. Frames: {3, 2, 4}. 11. Ref 6 : Miss. Look ahead: (none). Replace any (e.g., 3). Frames: {6, 2, 4}. (Fault 7) Total Page Faults = 7. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

Review answer and solution without JavaScript

Interactive answer checking needs JavaScript. The published solution is available below.

Correct answer 7 to 7 Solution Optimal Page Replacement replaces the page that will not be used for the longest period of time. Frames: 3. Reference String: 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6. 1. Ref 1 : Miss. Frames: {1}. (Fault 1) 2. Ref 2 : Miss. Frames: {1, 2}. (Fault 2) 3. Ref 3 : Miss. Frames: {1, 2, 3}. (Fault 3) 4. Ref 4 : Miss. Frames full. Look ahead: 2, 1, 5, 3... 2 is needed next at index 4. 1 is needed next at index 5. 3 is needed next at index 7. 3 is the furthest. Replace 3. Frames: {1, 2, 4}. (Fault 4) 5. Ref 2 : Hit. Frames: {1, 2, 4}. 6. Ref 1 : Hit. Frames: {1, 2, 4}. 7. Ref 5 : Miss. Look ahead: 3, 2, 4, 6... 1 is not needed again. 2 is needed at index 8. 4 is needed at index 9. Replace 1. Frames: {5, 2, 4}. (Fault 5) 8. Ref 3 : Miss. Look ahead: 2, 4, 6... 5 is not needed again. 2 is needed at index 8. 4 is needed at index 9. Replace 5. Frames: {3, 2, 4}. (Fault 6) 9. Ref 2 : Hit. Frames: {3, 2, 4}. 10. Ref 4 : Hit. Frames: {3, 2, 4}. 11. Ref 6 : Miss. Look ahead: (none). Replace any (e.g., 3). Frames: {6, 2, 4}. (Fault 7) Total Page Faults = 7.

Continue learning with Success Tracker

Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans

PYQs with solutions: Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts: Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support: Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.