Let $x_1,x_2,x_3,\ldots,x_{20}$ be in geometric progression with $x_1=3$ and the common ratio $\frac{1}{2}$. A new data is constructed replacing each $x_i$ by $(x_i-i)^2$. If $\bar{x}$ is the mean of new data, then the greatest integer less than or equal to $\bar{x}$ is __________.

JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 28 July 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let

x_1,x_2,x_3,\ldots,x_{20}

be in geometric progression with

x_1=3

and the common ratio

\frac{1}{2}

. A new data is constructed replacing each

x_i

(x_i-i)^2

. If

\bar{x}

is the mean of new data, then the greatest integer less than or equal to

\bar{x}

is __________.

Official answer

142

NTA final key (2022 Session 2).

Chapter: Statistics
Topic: AP and GP
Idea tested: GP Sum of Squares

Same topic in other shifts

All AP and GP questions

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4 Apr 2026, Shift 2 · Q7Let $\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty$ and $\beta=\frac13+\frac19+\frac1{27}+\ldots\infty$ . Then the value of…EasySingle correct
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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.