JEE Main 2020MathematicsStatisticsEasyNumerical

JEE Main 2020 — Statistics Question with Solution

JEE Main 2020 (07 Jan Shift 1)

Question

If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then the value of  m+n is equal to

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Show full solutionCorrect answer: 18
Correct answer
18

Step-by-step explanation

var1,2,…n=10⇒12+22+…+n2n-1+2+…+nn2=10

⇒n+12n+16-n+122=10

⇒n2-1=120⇒n=11

var2,4,6….,2m=16⇒var1,2….,m=4

⇒m2-1=48⇒m=7⇒m+n=18

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About this question

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