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JEE Main 201610 AprilOnline

Exam: JEE Main
Year: 2016
Date: 10 April
Mode: Online
Subject: Mathematics
Chapter: Permutation and Combination

JEE Main 2016 · 10 April · Online · Mathematics · Permutation and Combination

If ^ n + 2 C _ 6 ^ n - 2 P _ 2 = 11 , then n satisfies the equation:

If

\dfrac{{}^{n + 2}{C}_{6}}{{}^{n - 2}{P}_{2}} = 11

, then

n

satisfies the equation:

Options

A ${n}^{2} + n - 110 = 0$
B ${n}^{2} + 2n - 80 = 0$
C ${n}^{2} + 3n - 108 = 0$
D ${n}^{2} + 5n - 84 = 0$

Correct answer

C. ${n}^{2} + 3n - 108 = 0$

Step-by-step solution

\dfrac{{}^{n + 2}{C}_{6}}{{}^{n - 2}{P}_{2}} = 11

⇒ \dfrac{\dfrac{\left(n + 2\right)\left(n + 1\right)n\left(n - 1\right)\left(n - 2\right)\left(n - 3\right)}{6 . 5 . 4 . 3 . 2 . 1}}{\left(n - 2\right)\left(n - 3\right)} = 11

⇒ \left(n + 2\right)\left(n + 1\right)n\left(n - 1\right) = 11.10.9 . 8

⇒ n = 9

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