JEE Main201912 Jan 2019Evening ShiftMathematicsBinomial TheoremActual

If n C 4 , n C 5 and n C 6 are in A.P., then n can be

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Correct answer

B. 14

Step-by-step solution

Since, n C 4 ,   n C 5 ,   n C 6 are in A.P. ⇒ 2 × n C 5 = n C 4 + n C 6 ⇒ 2 × n ! 5 ! n - 5 ! = n ! 4 ! n - 4 ! + n ! 6 ! n - 6 ! ⇒ 2 5 ! n - 5 ! = 30 + n - 5 n - 4 6 ! n - 4 ! ⇒ 6 × 2 n - 4 = 30 + n 2 - 9 n + 20 ⇒ n 2 - 21 n + 98 = 0 ⇒ n - 7 n - 14 = 0 ⇒ n = 7 or 14

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