Question

The term independent of x in the expansion of $\left(\frac{2\sqrt{x}}{x}-\frac{1}{2x\sqrt{x}}\right)$ is

• A. 5th term
• B. 6th term
• C. 11 th term
• D. no term

Answer 1

Answer: (D)

Given expansion is ${\left(\frac{2\sqrt{x}}{5}-\frac{1}{2x\sqrt{x}}\right)}^{11}$
General term $T_{r+1}={(-1)}^r{}^{11}{C}_r{\left(\frac{2\sqrt{x}}{5}\right)}^{11-r}{\left(\frac{1}{2x^{3/2}}\right)}^r$
$=\frac{2^{11-2r}}{5^{11-r}}{(-1)}^r{}^{11}{C}_r{x}^{\frac{11-r}{2}-\frac{3r}{2}}$
For term independent of x put
$\frac{11-r}{2}-\frac{3r}{2}=0$
$\Rightarrow$ $\frac{11-4r}{2}=0$
$\Rightarrow$ $r=\frac{11}{4}\notin N$
$\therefore$ There is no term which is independent of x.