Question

The term independent of $x$ in the expansion of $\left(\sqrt[6]{x}-\frac{1}{\sqrt[3]{x}}\right)^{9}$ is equal to

• A. $-{ }^{9} C _{3}$
• B. ${ }^{9} C _{4}$
• C. ${ }^{9} C _{2}$
• D. None of these

Answer 1

Answer: (A)

Here General term $T _{ r +1}={ }^{9} C _{ r }(\sqrt[6]{x})^{9-r}\left(\frac{1}{\sqrt[3]{x}}\right)^{r}$
$={ }^{9} C _{ r }(-1)^{ r } x^{\frac{9-3 r }{r}}$
For term independent of $x$ $\frac{9-3 r }{r}=0$
$ \Rightarrow r =3$,
required value ${ }^{-9} C _{3}$