let `T_(n)` be the number of all possible triangels formed by joining vertices of an n-sided regular polygon. Iff `T_(n+1)-T_(n)=10`, the value of n is

Options

A. 7
B. 5
C. 10
D. 8

Answer

B

Explanation

Clearly, `T_(n)=""^(n)C_(3)`
`:.T_(n+1)-T_(n)=10`
`implies""^(n+1)C_(3)-""^(n)C_(3)=10`
`implies(""^(n)C_(2)+""^(n)C_(3))-""^(n)C_(3)=10`
`implies""^(n)C_(2)=10implies(n(n-1))/(2)=10`
`impliesn^(2)-n-20=0implies(n-5)(n+4)=0impliesn=5`