Binomial TheoremHard
Question
Let Tn denotes the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn+1 - Tn = 21, then n equals
Options
A.5
B.7
C.6
D.4
Solution
According to given condition Tn = nC3
and Tn+1 - Tn = 21
⇒ n+1C3 - nC3 = 21
⇒
(n + 1)(n)(n - 1) - n(n - 1)(n - 2) = 21
⇒
[(n + 1) - (n - 2)] = 21
⇒
= 21
⇒ n(n - 1) = 42
⇒ n = 7
and Tn+1 - Tn = 21
⇒ n+1C3 - nC3 = 21
⇒
(n + 1)(n)(n - 1) - n(n - 1)(n - 2) = 21⇒
[(n + 1) - (n - 2)] = 21⇒
= 21⇒ n(n - 1) = 42
⇒ n = 7
Create a free account to view solution
View Solution FreeMore Binomial Theorem Questions
The sum of the terms of the series [3.nC0 − 8.nC1 + 13.nC2 − 18. nC3 + .....+ (n + 1)] is-...The value of nCs sCr is -...If C0, C1, C2,.....Cn denote the binomial coefficients in the expansion of (1 + x)n, then the value of is -...Given positive integers r > 1, n > 2and the coefficient of (3r) th and (r + 2) th term in the binomial expansion of (1 +...The value of x , for which the 6th term in the expansion of is 84 is equal to -...