JEE Main 2020MathematicsStatisticsMediumMCQ

JEE Main 2020 — Statistics Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

Let X=x∈N : 1≤x≤17 and Y=ax+b : x∈X and a, b∈R, a>0. If mean and variance of elements of Y are 17 and 216 respectively then a+b is equal to

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Show full solutionCorrect option: B
Correct answer
B-7

Step-by-step explanation

Yx¯=ax¯+b=a1+2+3+….+1717+b=17

a17×1817×2+b=17

9a+b=17

σX2=∑x2n-∑xn2

=12+22+…+17217-1+2+...+17172

=17·18·356·17-17·182·172

=105-81=24

∴ σY2=a2σX2=a2·24=216

⇒a2=21624=9

a=3

∴ b=17-27

∴ b=17-27

b=-10

∴ a+b=-7

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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.