Question:
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
Solution:
(c) 9
Coefficient of $(n+1)$ th term $=$ Coefficient of $(n+3)$ th
We have :
${ }^{20} C_{n}={ }^{20} C_{n+2}$
$\Rightarrow 2 n+2=20 \quad\left[\because\right.$ if ${ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow x=y$ or $\left.x+y=n\right]$
$\Rightarrow n=9$
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