GATE CS 2016 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
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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 the relationship between the number of cycles to failure and the load be given by the exponential equation:Given:
1.At , .
2.When the load is halved, , .
Dividing equation (2) by equation (1):Taking natural logarithm on both sides:We need to find the load for which .Dividing equation (2) by equation (3):Taking natural logarithm:Substitute :Since :Using :Thus, the load is 46.02 units.Continue learning with Success Tracker
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