Sum of all those terms which are rational numbers in expansion of left(2^{1 / 3}+3^{1 / 4}right)^{12

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7.Binomial Theorem

medium

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

$27$

B

$89$

C

$35$

D

$43$

(JEE MAIN-2021)

Solution

$T_{r+1}=^{12} C_{r}\left(2^{1 / 3}\right)^{r} \cdot\left(3^{1 / 4}\right)^{12-r}$

$\mathrm{T}_{\mathrm{r}+1}$ will be rational number

$\text { Where } r=0,3,6,9,12$

$\&\, r=0,4,8,12$

$\Rightarrow r=0,12$

$T_{1}+T_{13}=1 \times 3^{3}+1 \times 2^{4} \times 1$

$\Rightarrow 27+16=43$

Standard 11

Mathematics

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