Binomial Theorem

Question
CBSEENMA11015496

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1 − Tn = 10, then the value of n is

  • 7

  • 5

  • 10

  • 8

Solution

B.

5

Given,Tn = nC3
Tn+1 = n+1C3
therefore,
Tn+1-Tn = n+1C3-nC3 =10
nC2 + nC3-nC3 = 10
[∵nCr +nCr-1 =n+1Cr]
nC2 =10
nC2 =5C2
n =5

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