JEE Main 2021MathematicsApplication of DerivativesEasyNumerical

JEE Main 2021 — Application of Derivatives Question with Solution

JEE Main 2021 (25 Jul Shift 2)

Question

Let a curve y=fx pass through the point 2,loge22 and have slope 2yxlogex for all positive real values of x. Then the value of fe is equal to _____.

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Correct answer
1

Step-by-step explanation

Let a curve y=fx pass through the point 2,loge22 and have slope 2yxlogex for all positive real values of x. 

Therefore, y'=2yxlnx

⇒dyy=2dxxℓnx

⇒ℓny=2ℓnℓnx+C

Put x=2,y=ℓn22

⇒c=0

⇒y=ℓnx2

⇒fe=1.

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About this question

This is a previous-year question from JEE Main 2021, 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.