Question

Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1}-T_n=10$, then the value of N is

• A. 7
• B. 5
• C. 10
• D. 8

Answer 1

The correct option is B 5

Given, $T_n={}^n{C}_3\Rightarrow T_{n+1}={}^{n+1}{C}_3$
$\therefore T_{n+1}-T_n={}^{n+1}{C}_3{-}^n{C}_3=10$ [given]
$\Rightarrow {}^n{C}_2+{}^n{C}_3-{}^n{C}_3=10$ $[\because {}^n{C}_r+{}^n{C}_{r+1}={}^{n+1}{C}_{r+1}]$
$\Rightarrow {}^n{C}_2=10\Rightarrow n=5$