JEE Main 2020MathematicsLimitsHardNumerical

JEE Main 2020 — Limits Question with Solution

JEE Main 2020 (03 Sep Shift 1)

Question

If limx→01x81−cosx22−cosx24+cosx22cosx24=2−k then the value of k is

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Show full solutionCorrect answer: 8
Correct answer
8

Step-by-step explanation

limx→01x81−cosx22−cosx24+cosx22cosx24

=limx→01−cosx221−cosx24x8

=limx→01−cosx22x4×1−cosx24x4

=limx→01−cosx224×x44×1−cosx2416×x416

Using limx→01-cosxx2=12

=12×14×12×116=1256=2-8

⇒2-8=2-k   ⇒k=8

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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.