JEE Main 2022MathematicsDifferentiationHardMCQ

JEE Main 2022 — Differentiation Question with Solution

JEE Main 2022 (24 Jun Shift 2)

Question

If y=tan-1secx3-tanx3,π2<x3<3π2, then

Choose an option

Show full solutionCorrect option: B
Correct answer
Bx2y''-6y+3π2=0

Step-by-step explanation

Given,

y=tan-1secx3-tanx3

=tan-11-sinx3cosx3

=tan-11-cosπ2-x3sinπ2-x3

=tan-1tanπ4-x32

Since π4-x32∈-π2,0 as π2<x3<3π2

So, y=π4-x32

Now differentiating we get,

y'=-3x22,y''=-3x

Now putting the value of x in term of y'' in 4y=π-2x3

We get,

4y=π-2x2-y''3

12y=3π+2x2y''

x2y''-6y+3π2=0

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About this question

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