Question

Number of terms which are rational in the expansion of $(\sqrt[4]{45}+\sqrt[3]{34}{)}^{100}$ is

• A. $10$
• B. $8$
• C. $9$
• D. $11$

Answer 1

The correct option is A $10$

General term

$T_{r+1}={}^{100}{C}_2(5{)}^{\frac{100-r}{4}}\cdot (4{)}^{\frac{r}{3}}$

In this case, for rational tems., power of $5and4$ should be integer

.

$\therefore \frac{100-r}{4}and\frac{r}{3}$ should be integers

For $r=6,0,12,24,30,36,42,4.8,54,60$

powers will be integer.

$\therefore Ans=10$

option (a)