Question

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

• A. $43$
• B. $27$
• C. $35$
• D. $89$

Answer 1

The correct option is A $43$

The general term of ${(2^{1/3}+3^{1/4})}^{12}$ is
$T_{r+1}={}^{12}{C}_r\cdot 2^{(12-r)/3}\cdot 3^{r/4}$
For rational terms, $r=0$ or $12$.
$\therefore$ Sum of rational terms
$={}^{12}{C}_0\cdot 2^4\cdot 3^0+{}^{12}{C}_{12}\cdot 2^0\cdot 3^3$
$=16+27$
$=43$