GATE CE 2016 Set 1 — Question 10
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumRatios, Percentages, Powers, Exponents & LogarithmsQuantitative AptitudeGeneral Aptitude
General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
Last updated
Question
In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.
Correct answer
(B) 46.02
Solution
Let be the number of cycles to failure and be the load. The problem states that decreases exponentially with an increase in , which can be modeled as:
Taking the natural logarithm on both sides:
Given data:
Using :
Therefore, the load is 46.02 units. The correct option is (B).
Taking the natural logarithm on both sides:
Given data:
1.At units, cycles:
--- (Eq. 1)2.When the load is halved ( units), cycles:
--- (Eq. 2)Subtracting Eq. 1 from Eq. 2:3.We need to find the load for which cycles:
--- (Eq. 3)From Eq. 2, we have . Substituting this into Eq. 3:Using :
Therefore, the load is 46.02 units. The correct option is (B).
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE 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.
Also appeared in
More questions on Quantitative Aptitude
2026 Set 2 Q1'The team ____ more than 300 runs in 20 overs ____ rains. However, some players needed to…2026 Set 1 Q1‘The shopkeeper sells lemons.’ In this sentence, the word ‘lemons’ is the ________.2026 Set 2 Q2If a positive real satisfies the following equation then…2026 Set 1 Q2The figure below is supposed to show three non-overlapping shapes – one oval and two triangles.…2026 Set 2 Q3The next figure (indicated by ‘?’) in the sequence is