JEE Main 2023MathematicsSets and RelationsEasyNumerical

JEE Main 2023 — Sets and Relations Question with Solution

JEE Main 2023 (10 Apr Shift 1)

Question

The number of elements in the set n∈ℤ:n2-10n+19<6 is _______ . 

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Show full solutionCorrect answer: 6
Correct answer
6

Step-by-step explanation

Given,

n2-10n+19<6

Now we know that,

x<a⇒-a<x<a

Now using above formula we get,

⇒-6<n2-10n+19<6

⇒n2-10n+25>0 and n2-10n+13<0

⇒n-52>0 and n-5-23n-5+23<0

⇒n∈ℤ-5 and n∈2, 3, 4, 5, 6, 7, 8

Hence, n=2, 3, 4, 6, 7, 8

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About this question

This is a previous-year question from JEE Main 2023, covering the Sets and Relations 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.