JEE Main 2021MathematicsLimitsHardMCQ

JEE Main 2021 — Limits Question with Solution

JEE Main 2021 (18 Mar Shift 1)

Question

If limx→0sin-1x-tan-1x3x3 is equal to L, then the value of (6L+1) is

Choose an option

Show full solutionCorrect option: D
Correct answer
D2

Step-by-step explanation

Given limx→0sin-1x-tan-1x3x3

⇒limx→0x+x33!…-x-x33…3x3

⇒limx→01+3x23!…-1-3x23…9x2 (Use L'Hospital rule 00 form)

⇒limx→06x3!+…--6x3+…18x  (Use L'Hospital rule 00 form)

⇒limx→063!+…--63+…18=1+218=16

Given that, limx→0sin-1x-tan-1x3x3=L

∴ 16=L⇒6L=1

So, 6L+1=2

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About this question

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