JEE Main 2020MathematicsDefinite IntegrationHardNumerical

JEE Main 2020 — Definite Integration Question with Solution

JEE Main 2020 (04 Sep Shift 2)

Question

Let x and x denote the fractional part of x and the greatest integer ≤x respectively of a real number x. if ∫0nxdx, ∫0nxdx and 10n2-n,(n∈N,n>1) are three consecutive terms of a G.P. then n is equal to__

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Show full solutionCorrect answer: 21
Correct answer
21

Step-by-step explanation

∫0nxdx=n∫01xdx=nx2201=n2
and ∫0nxdx=∫0nx-xdx=x220n-∫0nxdx=n22-n2
Now, n2,n2-n2 and 10n2-n are in Geometric progression

So,n2-n22=n2·10n2-n
⇒n2(n-1)24=5.n2(n-1)
⇒n-1=20⇒n=21 ∵n≠1

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About this question

This is a previous-year question from JEE Main 2020, 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.