1.

Let `T_n`be the numberof all possible triangles formed by joining vertices of an n-sided regularpolygon. If `T_(n+1)-T_n=""10`, then thevalue of n is(1) 5(2) 10(3) 8(4) 7A. 7B. 5C. 10D. 8

Answer» Correct Answer - 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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