Question

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

• A. $-35$
• B. 35
• C. 36
• D. $-36$

Answer 1

Answer: (D)

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
$(1+x{)}^{-2}=-36$