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Q.
If the $17^{th}$ and the $18^{th}$ terms in the expansion of $(2+a)^{50}$ are equal, then the coefficient of $x^{35}$ in the expansion of $(a+x)^{-2}$ is
TS EAMCET 2019
Solution:
Given,
$17^{th}$ and $18^{th}$ terms in the expansion $(2+a)^{50}$ are equal
$\therefore \, T_{17}=T_{18} $
$\Rightarrow \, { }^{50} C_{16}(2)^{34}(a)^{16} ={ }^{50} C_{17}(2)^{33}(a)^{17} $
$\Rightarrow \, a=\frac{50}{50} C_{16} \times 2=1$
$\therefore $ Now, coefficient of $x^{35}$ in the expansion
$(1+x)^{-2}=-36$