If the coefficients of the (n + 1)^th term and the (n + 3)^th term in the expansion of (1 + x)²⁰ are equal, then the value of n is
(a) 10
(b) 8
(c) 9
(d) none of these

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Solution

(c) 9
$Coefficient of (n + 1) th term = Coefficient of (n + 3) th W e h a v e : {}^{20}C_{n} = {}^{20}C_{n + 2} \Rightarrow 2 n + 2 = 20 [∵ if^{n} C_{x} =^{n} C_{y} \Rightarrow x = y or x + y = n] \Rightarrow n = 9$

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