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JEE Main202331 Jan 2023Evening ShiftMathematicsBinomial TheoremActual

If P n - 1 2 n + 1 : P n 2 n - 1 = 11 : 21 , then n 2 + n + 15 is equal to :

Correct answer

0

Step-by-step solution

Given, P n - 1 2 n + 1 P n 2 n - 1 = 11 21 ⇒ 2 n + 1 ! n + 2 ! 2 n - 1 ! n - 1 ! = 11 21 ⇒ 21 × 2 n + 1 2 n 2 n - 1 ! n + 2 n + 1 n n - 1 ! = 11 × 2 n - 1 ! n - 1 ! ⇒ 21 × 2 2 n + 1 = 11 n + 2 n + 1 ⇒ 2 n + 1 n + 2 n + 1 = 11 42 Now on comparing both side we get, n = 5 So, the value of n 2 + n + 15 = 5 2 + 5 + 15 = 45

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