The sum of all those terms which are rational | vedclass

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Question

$T_{r+1}=^{12} C_{r}\left(2^{1 / 3}ight)^{r} \cdot\left(3^{1 / 4}ight)^{12-r}$

$\mathrm{T}_{\mathrm{r}+1}$ will be rational number

$	ext {

Vedclass · Accepted Answer

$43$

Vedclass · Answer

$T_{r+1}=^{12} C_{r}\left(2^{1 / 3}ight)^{r} \cdot\left(3^{1 / 4}ight)^{12-r}$

$\mathrm{T}_{\mathrm{r}+1}$ will be rational number

$	ext { Where } r=0,3,6,9,12$

$\&\, r=0,4,8,12$

$\Rightarrow r=0,12$

$T_{1}+T_{13}=1 	imes 3^{3}+1 	imes 2^{4} 	imes 1$

$\Rightarrow 27+16=43$

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

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