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  • If the <img alt="(r+1)^{th}" src="https://entrancecorner.oncodecogs.com/gif.latex?%28r&pl

If the (r+1)^{th} term in the expansion of  \left(\sqrt[3]{\frac{a}{\sqrt{b}}}+\sqrt{\frac{b}{\sqrt[3]{a}}}\right)^{21} has the same power of a and b, then the value of r is

 

Option: 1

9


Option: 2

10


Option: 3

8


Option: 4

6


Answers (1)

best_answer

we have T_{r+1}={ }^{21} C_r\left(\sqrt[3]{\frac{a}{\sqrt{b}}}\right)^{21-r}\left(\sqrt{\frac{b}{\sqrt[3]{a}}}\right)^r

={ }^{21} C_r a^{7-(r / 2)} b^{(2 / 3) r-(7 / 2)}

Since the powers of a and b are the same, therefore
7-\frac{r}{2}=\frac{2}{3} r-\frac{7}{2} \Rightarrow r=9

Posted by

Divya Prakash Singh

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