JEE Main 2022MathematicsLimitsMediumNumerical

JEE Main 2022 — Limits Question with Solution

JEE Main 2022 (27 Jun Shift 2)

Question

Let t denote the greatest integer ≤t and t denote the fractional part of t. Then integral value of α for which the left hand limit of the function fx=1+x+α2x+x+x-12x+x at x=0 is equal to α-43 is _____

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Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

Given,

fx=1+x+α2x+x+x-12x+x

limx→0-fx=α-43

limx→0-1+x+αx+x+x+x-12x+x=α-43

⇒0+α-1-2-1=α-43

⇒2-1α=α-43

⇒α+1α=103

On solving above equation we get,

⇒α=3;α∈I

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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.