IIT-JEE 2001 ScreeningQuestion 1
Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n+1}-T_n=21$, then $n$ equals
Permutation and Combination
Solution
$T_{n+1}-T_n=\binom n2=21\Rightarrow n=7$.