Question

Value of the numerically greatest term in the expansion of
$\sqrt{3}{(1+\frac{1}{\sqrt{3}})}^{20}$ is

• A. ${}^{20}{C}_7.\frac{1}{27\sqrt{3}}$
• B. ${}^{20}{C}_8.\frac{1}{27}$
• C. ${}^{20}{C}_8.\frac{1}{27\sqrt{3}}$
• D. ${}^{20}{C}_7.\frac{1}{27}$

Answer 1

Answer: (D)

${}^{20}{C}_7.\frac{1}{27}$

We know that $\sqrt{3}=1.732$
Therefore numerically greatest term is given by.
$\frac{n+1\left(|x|\right)}{1+|x|}$
Substituting $|x|=\frac{1}{\sqrt{3}}$ we get
$\frac{21}{1+\sqrt{3}}$
$=\frac{21}{2.732}$
$=7.68$
Since we do not consider the fractional value as the term number has to be a natural number.
Therefore numerically greatest term is
$\sqrt{3}\times {}^{20}{C}_7\frac{1}{27\sqrt{3}}$
$={}^{20}{C}_7\frac{1}{27}$