JEE Main 2023MathematicsApplication of DerivativesHardNumerical

JEE Main 2023 — Application of Derivatives Question with Solution

JEE Main 2023 (08 Apr Shift 1)

Question

If aα is the greatest term in the sequence an=n3n4+147, n=1, 2, 3...., then α is equal to ______

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Let,

y=x3x4+147=fx

We know that, for increasing function dydx>0

So, differentiating the given function fx=x3x4+147 we get,

dydx=-x2x4-441(x4+147)2

⇒-x2x4-441(x4+147)2>0

⇒x2x4-441(x4+147)2<0

⇒x4<441

Now for maxima/minima dydx=0

⇒x4=441

⇒x=α, 4<α<5

⇒Maximum value of fx is at x=4 or x=5

f4=64403, f5=125772

∵f5>f4

⇒α=5

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About this question

This is a previous-year question from JEE Main 2023, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.