JEE Main 2022MathematicsApplication of DerivativesMediumMCQ

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (26 Jun Shift 1)

Question

Let S be the set of all the natural numbers, for which the line xa+yb=2 is a tangent to the curve xan+ybn=2 at the point a,b, ab≠0. Then

Choose an option

Show full solutionCorrect option: D
Correct answer
DS=N

Step-by-step explanation

xan+ybn=2

Differentiating, we get, 

nxan−1⋅1a+n⋅ybn−1⋅1b⋅dydx=0

dydx=-1axan−11bybn−1=−baxbyan−1⇒dydxa,b=−baabban−1 =−ba

So, equation of the tangent to the curve at a,b will be y−b=−bax−a  ⇒yb−1=−xa+1

⇒xa+yb=2

i.e. S∈N

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About this question

This is a previous-year question from JEE Main 2022, 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.