JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q17

MathematicsSingle correct+4 / -1Question 17 of 90

The number of values of $a\in\mathbb N$ such that the variance of $3,7,12,a,43-a$ is a natural number is:

infinite

Answer and worked solution

Official answer: A

Mean 13. Variance $=\dfrac{2a^2-86a+1206}5$ .

Mod 5. $2a^2+4a+1$ takes values $1,2,2,1,4$ : never 0. No value works.

(A)

Topics:Variance and standard deviation Number systems

JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 17