JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2026, Shift 2, Maths Q8

Question 8 of 75 in this shift, Maths question 8 of 25, Section A.

Let the mean and the variance of seven observations

2, 4, \alpha, 8, \beta, 12, 14

\alpha<\beta

, be 8 and 16 respectively. Then the quadratic equation whose roots are

3\alpha+2

and

2\beta+1

is :

(1) $x^2-35x+306=0$
(2) $x^2-41x+420=0$ Official answer
(3) $x^2-45x+506=0$
(4) $x^2-37x+342=0$

Official answer

Option 2

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

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
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
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.