JEE Main 2024 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 29 January 2024, Shift 1, Maths Q30

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

If the mean and variance of the data

65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60

where

\alpha>\beta

, are 56 and 66.2 respectively, then

\alpha^2+\beta^2

is equal to ______.

Official answer

6344

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Finding Unknown Observations from Mean and Variance

Same idea in other shifts

Asked 22× in all

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
2 Apr 2025, Shift 2 · Q8If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then $a+b+ab$ is equal to :MediumSingle correct
3 Apr 2025, Shift 2 · Q9Let the Mean and Variance of five observations $x_1 = 1, x_2 = 3, x_3 = a, x_4 = 7$ and $x_5 = b,\ a > b$ , be 5 and 10 respectively. Then…MediumSingle correct
4 Apr 2025, Shift 2 · Q8Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and $\sqrt{2}$ respectively. Then the mean…MediumSingle correct
4 Apr 2024, Shift 1 · Q20Let $\alpha, \beta \in \mathbf{R}$ . Let the mean and the variance of 6 observations $-3, 4, 7, -6, \alpha, \beta$ be 2 and 23,…MediumSingle correct
8 Apr 2024, Shift 2 · Q30Let $a, b, c \in \mathbb{N}$ and $a < b < c$ . Let the mean, the mean deviation about the mean and the variance of the 5 observations…HardNumerical value
31 Jan 2024, Shift 2 · Q18Let the mean and the variance of 6 observations $a, b, 68, 44, 48, 60$ be 55 and 194, respectively. If $a>b$ , then $a+3b$ isMediumSingle correct
8 Apr 2023, Shift 1 · Q30Let the mean and variance of 8 numbers $x,y,10,12,6,12,4,8$ be 9 and 9.25 respectively. If $x>y$ , then $3x-2y$ is equal to __________.MediumNumerical value

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.