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  4. If the (3r)th and (r+2)th terms in the binomial expansion of (1 + x)2n are equal, then

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Q. If the $ (3r)^{th} \,and\, (r+2)^{th} $ terms in the binomial expansion of $ (1 + x)^{2n} $ are equal, then

AMUAMU 2012Binomial Theorem

Solution:

Given expansion is $(1+x)^{2 n}$.
According to the given condition,
${ }^{2 n} C_{3 r-1} { }^{2 n} C_{r+1} $
$\Rightarrow (2 n-3 r+1) =(r+1)$
$\Rightarrow 2 n =4 r $
$\Rightarrow n =2 r$