Question

Number of rational terms in the expansion of $(3^{\frac{1}{8}}+5^{\frac{1}{3}}{)}^{400}$ is

• A. $17$
• B. $20$
• C. $102$
• D. $150$

Answer 1

The correct option is A $17$

$T_{r+1}{=}^{400}{C}_r\cdot 3^{(50-\frac{r}{8})}\cdot 5^{\frac{r}{3}}$
so, $r=0,24,....24\times 16$
Hence, Total terms $=17$