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JEE Advanced2013MathematicsBinomial TheoremActual

The coefficients of three consecutive terms of 1 + x n + 5 are in the ratio 5 : 10 : 14 . Then n =

Correct answer

6

Step-by-step solution

n + 5 C r - 1  :  n + 5 C r  :  n + 5 C r + 1 = 5 : 10 :14 ⇒ n + 5 ! r - 1 ! n - r + 6 ! : n + 5 ! r ! n - r + 5 ! : n + 5 ! r + 1 ! n - r + 4 ! = 5 : 10 :14 ⇒ 1 r - 1 ! n - r + 6 ! : 1 r ! n - r + 5 ! : 1 r + 1 ! n - r + 4 ! = 5 : 10 :14 ⇒ r + 1 r n - r + 6 ! : r + 1 n - r + 5 ! : 1 n - r + 4 ! = 5 : 10 :14 ⇒ r + 1 r   :   r + 1 n - r + 6   :   n - r + 6 n - r + 5 = 5 : 10 :14 ⇒ r + 1 n - r + 6 r + 1 r = 1 0 5 and n - r + 6 n - r + 5 r + 1 n - r

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