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If the coefficients of x4, x5 and x6 in the expansion of (1 + x)n are in the arithmetic progression, then the maximum value of n is:
(4) 14
nC4, nC5, nC6 are in A.P. 2 nC5 = nC4 + nC6
Divide by nC5 and use nCr-1nCr = rn - r + 1:
2 = 5n - 4 + n - 56
12(n - 4) = 30 + (n - 4)(n - 5)
n2 - 21n + 98 = 0 (n - 7)(n - 14) = 0
n = 7 or 14 ⇒ maximum n = 14
Answer: (4)
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