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 i - Mathematics MCQ JEE Main 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

T_{n} = (3 n) .Given: (3 n + 1) - (3 n) = 10 .Using the identity (r n) + (r - 1 n) = (r n + 1), we have: (2 n) = 10 . \frac{n ( n - 1 )}{2} = 10 \Rightarrow n^{2} - n - 20 = 0 \Rightarrow (n - 5) (n + 4) = 0 .Since n > 0, n = 5 .

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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:

5

10

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7

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