JEE Main 2022MathematicsLimitsEasyMCQ

JEE Main 2022 — Limits Question with Solution

JEE Main 2022 (26 Jul Shift 2)

Question

Let β=limx→0αx-e3x-1αxe3x-1 for some α∈ℝ. Then the value of α+β is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C52

Step-by-step explanation

Given, limx→0αx-e3x-1αxe3x-1=β

⇒limx→0αx+1-e3xαxe3x-13x·3x=β

⇒limx→0αx+1-e3x3αx2=β as limx→0ex-1x=1

⇒limx→0α-3e3x6αx=β   [Using L' Hospital rule as 00 form]

Now for limit to exist, α=3

So, limx→03-3e3x6×3×x=β

So, β=limx→0-e3x-16x=limx→0-3e3x6=-12

∴  α+β=52

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About this question

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