JEE Main 2022MathematicsStatisticsMediumMCQ

JEE Main 2022 — Statistics Question with Solution

JEE Main 2022 (29 Jun Shift 2)

Question

The number of values of a∈N such that the variance of 3, 7, 12, a, 43-a is a natural number is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A0

Step-by-step explanation

Calculating Mean =3+7+12+a+43-a5=13

Variance =9+49+144+a2+43-a25-132∈N

⇒2a2-a+15=n (where n∈N)

⇒2a2-a+1-5n=0 must have solution as natural numbers

So, D=40n-7 always has 3 at unit place for any value of n

⇒D can't be perfect square

So, a can't be integer.

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About this question

This is a previous-year question from JEE Main 2022, 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.