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Q.
The term independent of $x$ in the expansion of
$\left(\sqrt[6]{x}-\frac{1}{\sqrt[3]{x}}\right)^{9}$ is
Binomial Theorem
Solution:
$T _{ r +1}={ }^{9} C _{ r }(\sqrt[6]{ x })^{9- r }\left(-\frac{1}{\sqrt[3]{ x }}\right)^{ r }$
$={ }^{9} C _{ r }(-1)^{ r } . x ^{\frac{9- r }{6}-\frac{ r }{3}}={ }^{9} C _{ r } .x ^{\left(\frac{9-3 r }{6}\right)}$
Now $\frac{9-3 r}{6}=0 $
$\Rightarrow r=3$
Thus, term independent of $x =-{ }^{9} C _{3}$