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JEE Advanced Mathematics question

MathematicsApplication of DerivativesJEE Advanced

The sum of infinite terms of a decreasing GP is equal to the greatest value of the function in the interval and the difference between the first two terms is . Then the common ratio of the GP is

Answer: (C)

Solution

, so is increasing and its greatest value on is . Also . Let the GP be with (decreasing, positive terms, convergent). Then

Missing argument for \frac\frac a{1-r}=27,

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Question ID VK-107866