JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 29 July 2022, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let the mean and the variance of 20 observations

x_1, x_2, \ldots, x_{20}

be 15 and 9, respectively. For

\alpha \in \mathbf{R}

, if the mean of

(x_1 + \alpha)^2, (x_2 + \alpha)^2, \ldots, (x_{20} + \alpha)^2

is 178, then the square of the maximum value of

\alpha

is equal to __________.

Official answer

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Relationship Between RMS, Mean, and Variance

Same topic in other shifts

All Variance and SD questions

2 Apr 2026, Shift 1 · Q8If the mean of the data | Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | | Frequency | 2 | $k$ | 28 | 54 | $k+1$ | 5 | is $21$ ,…MediumSingle correct
2 Apr 2026, Shift 2 · Q9The mean and variance of $n$ observations are 8 and 16, respectively. If the sum of the first $(n - 1)$ observations is 48 and the sum of…EasySingle correct
4 Apr 2026, Shift 2 · Q8For 10 observations $x_1,x_2,\ldots,x_{10}$ , if $\sum_{i=1}^{10}(x_i+2)^2=180$ and $\sum_{i=1}^{10}(x_i-1)^2=90$ , then their standard…MediumSingle correct
6 Apr 2026, Shift 1 · Q9A data consists of 20 observations $x_1, x_2,\ldots, x_{20}$ . If $\sum_{i=1}^{20}(x_i+5)^2=2500$ and $\sum_{i=1}^{20}(x_i-5)^2=100$ , then…MediumSingle correct
6 Apr 2026, Shift 2 · Q8Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$ , $\alpha<\beta$ , be 8 and 16 respectively. Then the…MediumSingle correct
8 Apr 2026, Shift 2 · Q7A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of…EasySingle correct

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 108 of the 174 JEE Main shifts held from 2017 to 2026.