Question

The sum of rational term in the expansion of ${(3^{\frac{1}{5}}+2^{\frac{1}{3}})}^{15}$ is

• A. $31$
• B. $59$
• C. $51$
• D. $61$

Answer 1

The correct option is B $59$

Given that ,

${(3^{\frac{1}{5}}+2^{\frac{1}{3}})}^{15}$

General term is

$t_{r+1}{=}^{15}{C}_r{\left(3^{\frac{1}{5}}\right)}^{15-r}{\left(2^{\frac{1}{3}}\right)}^r$

${=}^{15}{C}_r{.3}^{\frac{15-r}{5}}{.2}^{\frac{r}{3}}$

For general term r=0,5

$t_{0+1}{=}^{15}{C}_0{.3}^3=27$

$t_{15+1}=t_{16}{=}^{15}{C}_{15}{3}^0.$$2^5$ =32

Hence, this is the required value = $27+32=59$