Question

The sum of all those terms which are rational numbers in the expansion of $\left(2^{1 / 3}+3^{1 / 4}\right)^{12}$ is:

• A. 89
• B. 27
• C. 35
• D. 43

Answer 1

Answer: (D)

$T_{r+1}={ }^{12} C_{r}\left(2^{1 / 3}\right)^{r} \cdot\left(3^{1 / 4}\right)^{12-r}$
$T_{r+1}$ will be rational number
when $r=0,3,6,9,12$
$\& r=0,4,8,12$
$\Rightarrow r=0,12$
$T_{1}+T_{13}=1 \times 3^{3}+1 \times 2^{4} \times 1$
$=24+16=43$