JEE Main 2020MathematicsLimitsMediumMCQ

JEE Main 2020 — Limits Question with Solution

JEE Main 2020 (05 Sep Shift 1)

Question

If α is the positive root of the equation, px=x2−x−2=0, then limx→α+1−cospxx+α−4is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B32

Step-by-step explanation

Given, px=0

⇒x2-x-2=0

⇒x-2x+1=0

⇒x=2,-1  ∴  α=2

Now,limx→2+1−cosx2−x−2x−2

=limx→2+2sin2x2−x−22x−2

=limx→2+2·sinx2-x-22x-2

=limx→2+2·sinx2-x-22x-2 (because x>2)

=limx→2+ 2sinx2-x-22x2-x-22·2·x2-x-2x-2

=limx→2+12·x-2x+1x-2

=32.

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 2020, 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.