JEE Main 2022MathematicsInverse Trigonometric FunctionsHardMCQ

JEE Main 2022 — Inverse Trigonometric Functions Question with Solution

JEE Main 2022 (24 Jun Shift 2)

Question

Let x×y=x2+y3 and x×1×1=x ×1×1. Then a value of 2sin-1x4+x2-2x4+x2+2 is

Choose an option

Show full solutionCorrect option: B
Correct answer
Bπ3

Step-by-step explanation

Given x×y=x2+y3

Now x×1× 1=x×1×1 

x2+13×1=x×12+13 

x2+12+13=x2+23

x4+1+2x2+1=x2+8 

x4+x2−6=0

Let x2=t   

t2+t-6=0 

t+3t−2=0

t≠−3 so t=2 or x2=2

Now 2sin-1x4+x2-2x4+x2+2=2sin-14+2-24+2+2
=2sin-112=π6×2=π3 

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About this question

This is a previous-year question from JEE Main 2022, covering the Inverse Trigonometric Functions 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.