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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrEasy2 minPYQ_2013

MathematicsEasysingle choice

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 :

Options:

Answer:

Solution:

Number of triangles $= {}^{n}C_{3}$

Given: ${}^{n + 1}C_{3} - {}^{n}C_{3} = 10$

$\Rightarrow n^{2} - n - 20 = 0$

$\Rightarrow (n - 5) (n + 4) = 0$

$\Rightarrow n = 5, (∵ n \neq 0)$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: PYQ_2013

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