The term independent of x in expansion of {le | vedclass

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Question

$\left(\left(x^{1 / 3}+1\right)-\left(\frac{\sqrt{x}+1}{\sqrt{x}}\right)\right)^{10}$

$\left(x^{13}-x^{-1 / 2}\right)^{10}$

${T_{r + 1}}{ = ^{10

Vedclass · Accepted Answer

$210$

Vedclass · Answer

$\left(\left(x^{1 / 3}+1ight)-\left(\frac{\sqrt{x}+1}{\sqrt{x}}ight)ight)^{10}$

$\left(x^{13}-x^{-1 / 2}ight)^{10}$

${T_{r + 1}}{ = ^{10}}{C_r}{({x^{1/3}})^{10 - r}}{( - {x^{ - 1/2}})^r}$

$\frac{10-r}{3}-\frac{r}{2}=0$

$\Rightarrow \quad 20-2 r-3 r=0$

$\Rightarrow \quad r=4$

$T_{5}=^{10} C_{4}=\frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1}=210$

The term independent of $x$ in expansion of ${\left( {\frac{{x + 1}}{{{x^{2/3}} - {x^{\frac{1}{3}}} + 1\;}}--\frac{{x - 1}}{{x - {x^{1/2}}}}} \right)^{10}}$ is

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