Question

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

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

Answer 1

The correct option is C

41

The general term $T_{r+1}$ in the given expansion is given by ${}^{45C_r}\left(4^{1/5}{)}^{45-r}\right(7^{1/10}{)}^r$

For $T_{r+1}$ to be an integer, we must have $\frac{r}{5}$ and $\frac{r}{10}$ as integers i.e. $0\le r\le 45$

$\therefore$ r =0, 10,20,30 and 40

Hence, there are 5 rational and 41, i.e., 46-5, irrational terms.