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Let Tn be the number of all possible ...

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 (1) 5 (2) 10 (3) 8 (4) 7

A

7

B

5

C

10

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `T_(n) = ""^(n)C_(3) rArr T_(n + 1) = ""^(n + 1)C_(3)`
`therefore" " T_(n + 1) - T_(n) = ""^(n + 1)C_(3) = ""^(n)C_(3) = 10" "` [given]
`rArr ""^(n)C_(2) + ""^(n)C_(3) - ""^(n)C_(3) = 10 " "[because ""^(n)C_(r) + ""^(n)C_(r + 1) = ""^(n + 1)C_(r + 1)]`
`rArr " "^(n)C_(2) = 10`
`rArr` n = 5
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