JEE Main 2022MathematicsDefinite IntegrationHardMCQ

JEE Main 2022 — Definite Integration Question with Solution

JEE Main 2022 (25 Jul Shift 2)

Question

limn→∞12n11-12n+11-22n+11-32n+….+11-2n-12n is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C2

Step-by-step explanation

Let I=limn→∞12n11-12n+11-22n+11-32n+….+11-2n-12n

Let 2n=t and if n→∞ then t→∞

I=limn→∞1t∑r=1t-111-rt

I=∫01dx1-x (Using definite integral as limit of sum)

Applying ∫0afxdx=∫0afa-xdx, we get

I=∫01dxx 

=2x01=2

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About this question

This is a previous-year question from JEE Main 2022, covering the Definite Integration 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.