Question

In the expansion, the term which does not contain x, is equal to:

${(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}})}^{10}$

• A. $10C_6$
• B. $10C_7$
• C. $10C_4$
• D. $10C_8$
  

Answer 1

The correct option is A $10C_6$

Given,

${(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}})}^{10}$

$={\left(\right(x^{\frac{1}{3}}+1)-\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}-1)})}^{10}$

$={(x^{\frac{1}{3}}+1-1-x^{\frac{-1}{2}})}^{10}$

$=(x^{\frac{1}{3}}-x^{\frac{-1}{2}})$

The general term is

$(\frac{10}{r})x^{\frac{r}{3}}{x}^{-\frac{(10-r)}{2}}$

$\therefore \frac{r}{3}-\frac{(10-r)}{2}=0$

we get, $r=6$

$(\frac{10}{6})=(\frac{10}{4})=210$