JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 31 January 2024, Shift 2, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

Let 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

(1)180Official answer
(2)190
(3)200
(4)210

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 8× 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
29 Jan 2024, Shift 1 · Q30If 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,…MediumNumerical value
29 Jun 2022, Shift 1 · Q20Let the mean and the variance of 5 observations $x_1, x_2, x_3, x_4, x_5$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean…MediumSingle correct
3 Aug 2021, Shift 2 · Q88The mean and variance of 7 observations are 7 and 18 respectively. If 5 of the observations are 2, 4, 10, 11, 13 and the remaining…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 42 of the 174 JEE Main shifts held from 2017 to 2026.