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 $r=0,3,6,9,12$
$\&r=0,4,8,12$
$\Rightarrow r=0,12$
$T_1+T_{13}=1\times 3^3+1\times 2^4\times 1$
$=24+16=43$