Question

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

• A. 9
• B. 10
• C. 8
• D. 6

Answer 1

The correct option is A

9

We have $T_{r+1}$ = ${}^{21}{C}_r{\left(\sqrt[3]{3\frac{a}{\sqrt{b}}}\right)}^{21-r}{\left(\sqrt{\frac{b}{\sqrt[3]{3a}}}\right)}^r$

= ${}^{21}{C}_r{a}^{7-\left(\frac{r}{2}\right)}{b}^{\frac{2}{3}r-\left(\frac{7}{2}\right)}$

Since the powers of a and b are the same,

therefore

7 - $\frac{r}{2}$ = $\frac{2}{3}$r - $\frac{7}{2}$ ⇒ r = 9