Q. $\{ n(n + 1)(2n + 1):n \in Z\} \subset$
A) $\{ 6k\ :k \in Z\}$
B) $\{ 12k\ :k \in Z\}$
C) $\{ 18k\ :k \in Z\}$
D) $\{ 24k\ :k \in Z\}$
Explanation
(a)
Let $A = \{ n(n + 1)(2n + 1):n \in Z\}$
Putting $n = \pm 1,\ \pm 2,\ \ldots.,$ we get $A = \{\ldots - 30,\ - 6,\ 0,\ 6,\ 30,\ \ldots\}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \left\{ n(n + 1)(2n + 1):n \in Z \right\} \subset \{ 6k:k \in Z\}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.