Question

Numerically greatest term in the expansion of $(3-5x{)}^{11}whenx=\frac{1}{5}$ is:

• A. 55x3⁹
• B. 55x3⁸
• C. 55x3¹⁰
• D. None

Answer 1

The correct option is A

55x3⁹

$(3-5x{)}^{11}=3^{11}(1-\frac{5x}{3}{)}^{11}$

$\frac{(n+1)|x|}{|x|+1}=\frac{12\left(\frac{1}{3}\right)}{\frac{1}{3}+1}=3$
$\therefore$ Numerically greatest term is $T_3=55\times 3^9$