JEE Main 2021MathematicsLimitsHardNumerical

JEE Main 2021 — Limits Question with Solution

JEE Main 2021 (01 Sep Shift 2)

Question

Let f(x)=x6+2x4+x3+2x+3, x∈R. Then the natural number n for which limx→1xnf(1)-f(x)x-1=44 is _____ .

Enter your answer

Show full solutionCorrect answer: 7
Correct answer
7

Step-by-step explanation

Given that: f(x)=x6+2x4+x3+2x+3, x∈R

So, f(1)=9

limx→19xn-x6-2x4-x3-2x-3x-1=44

⇒limx→19xn-9-x6+1-2x4+2-x3+1-2x+2x-1=44

⇒limx→19xn-1x-1-x6-1x-1-2x4-1x-1-x3-1x-1-2x-1x-1=44

As we know that, limx→axn-anx-a=nan-1

⇒9n-6-8-3-2=44

⇒n=7

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Limits chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.