Question

The number of irrational terms in the expansion of ${\left(4^{1/5}+7^{1/10}\right)}^{45}$ is

• A. 40
• B. 5
• C. 41
• D. none of these

Answer 1

Answer: (C)

Total number of terms in the expansion of
${\left(4^{1/5}+7^{1/10}\right)}^{45}$ is $45+1$, i.e., $46$ .
The general term in the expansion is
$T_{r+1}={}^{45}{C}_r\cdot 4^{\frac{45-r}{5}}\cdot 7^{\frac{r}{10}}$
$T_{r+1}$ is rational if $r=0,10,20,30,40$.
$\therefore$ Number of rational terms $=5$.
$\therefore$ Number of irrational terms $=46-5=41$.