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If 2 n1 Pn1 2 n1 Pn11 21 then n2n15 is equal to | null (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

If

{ }^{2 n+1} \mathrm{P}_{n-1}:{ }^{2 n-1} \mathrm{P}_{n}=11: 21

, then

n^{2}+n+15

is equal to :

Correct Answer:

45

Explanation

\frac{\frac{(2 n+1) !}{(n+2) !}}{\frac{(2 n-1) !}{(n-1) !}}=\frac{11}{21}

\\ \frac{(2 n+1) 2 n}{(n+2)(n+1) n}=\frac{11}{21}

\\ 84 n+42=11\left(n^{2}+3 n+2\right)

\\ 11 n^{2}-51 n-20=0

\\ (n-5)(11 n+4)=0 \\

n=5, \frac{-4}{11}

(Rejected

) \\

n^{2}+n+15=45

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