JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 1
Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon. If $p_{n+1}-p_n=66$, then the sum of all distinct prime divisors of $n$ is :
Permutation and Combination
Solution
$p_n=\binom n3$, so $p_{n+1}-p_n=\binom n2=66\Rightarrow n(n-1)=132\Rightarrow n=12$. $12=2^2\cdot3$, prime divisors sum $2+3=5$. Option C.