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  • In the expansion of <img alt="\left ( \sqrt[3]{\frac{a}{b}} + \sqrt[3]{\frac{b}{\sqrt{a}}} \right )^{21}" src="https://learn.careers360.com/latex-image/?%5Cleft%20%28%20%5Csqrt%5B3%5D%7B%5Cfrac%7Ba

In the expansion of \left ( \sqrt[3]{\frac{a}{b}} + \sqrt[3]{\frac{b}{\sqrt{a}}} \right )^{21}  the term containing same powers a and b is

Option: 1

11th


Option: 2

13th


Option: 3

12th


Option: 4

6th


Answers (1)

best_answer

 

General Term in the expansion of (x+a)^n -

T_{r+1}= ^{n}c_{r}\cdot x^{n-r}\cdot a^{r}
 

- wherein

Where r\geqslant 0 \, and \, r\leqslant n

r= 0,1,2,----n

 

 

t_{r+1}=^{21}\textrm{C}_{r}\left ( \frac{a}{b} \right )^{\frac{21-r}{3}}\frac{b^{\frac{r}{3}}}{a^{\frac{r}{6}}}=^{21}\textrm{C}_{r} a^{\frac{42-3r}{6}}b^{\frac{2r-21}{3}}

\therefore 42-3r=4r-42\; i.e.\;\; r=12

\therefore 13th term contains same powers of a  and  b

Posted by

vinayak

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