If 2n + 1Pn - 1 : 2n - 1Pn = 3 : 5, then n is equal to

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If ^{2n + 1}P_{n - 1} : ^{2n - 1}P_n = 3 : 5, then n is equal to ?

1. 4
2. 6
3. 3
4. 8

Correct Option: A

We have If ^{2n + 1}P_{n - 1} / ^{2n - 1}P_n = 3/5
⇒ 5 x ^{2n + 1}P_{n - 1} = 3 x ^{2n - 1}P_n
⇒ {5 x (2n + 1)!} / {(n + 2 )!} = 3 x {(2n - 1)!} / {(n - 1)!}
⇒ 10(2n + 1) = 3(n + 2) (n + 1)
⇒ 3n² - 11n - 4 = 0
⇒(3n + 1 ) (n - 4) = 0
∴ n = 4