If in the expansion of

Question:

If in the expansion of (1 + x)20, the coefficients of rth and (r + 4)th terms are equal, then r is equal to

(a) 7

(b) 8

(c) 9

(d) 10

Solution:

(c) 9

Coefficients of the $r$ th and $(r+4)$ th terms in the given expansion are ${ }^{20} C_{r-1}$ and ${ }^{20} C_{r+3}$.

Here,

${ }^{20} C_{r-1}={ }^{20} C_{r+3}$

$\Rightarrow r-1+r+3=20 \quad\left[\because\right.$ if ${ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow x=y$ or $\left.x+y=n\right]$

$\Rightarrow r=2$ or $2 r=18$

$\Rightarrow r=9$

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