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nCr Definitions and Properties

In T n denote...

Question

In $T_{n}$ denotes the number of triangles which can be formed using the vertices of a regular polygon of ‘n’ sides.If $T_{n + 1} - T_{n} = 21$ then n equal

A

5

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B

7

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C

6

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D

4

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Solution

The correct option is B 7
$^{n + 1} C_{3} - n c 3 = 21 \Rightarrow^{n} C_{2} = 21$
$\Rightarrow \frac{n (n - 1)}{2} = 21 \Rightarrow n = 7$

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