The term independent of

Question:

The term independent of $\mathrm{x}$ in the expansion of

$\left\lceil\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right]^{10}, x \neq 1$, is equal to___________.

Solution:

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

$\left(x^{1 / 3}-x^{-1 / 2}\right)^{10}$

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

$\frac{10-r}{3}-\frac{r}{2}=0 \Rightarrow 20-2 r-3 r=0$

$\Rightarrow r=4$

$T_{5}={ }^{10} C_{4}=\frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1}=210$

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now