Question

The number of rational terms in the expansion of ${(3^{\frac{1}{4}}+7^{\frac{1}{6}})}^{144}$ is

• A. $33$
• B. $23$
• C. $12$
• D. $13$

Answer 1

The correct option is D $13$

$(3^{1/4}+7^{1/6}{)}^{144}$

general term$={}^{144}{C}_r{3}^{\frac{1}{4}(144-r)}{7}^{1/6\left(r\right)}$

$={}^{144}{C}_r{3}^{36-\frac{r}{4}}{7}^{\frac{r}{6}}$

For rational terms

$r=$LCM$(4,6)=12$

$r=0,12,24,36,.....144$

AP$\to$

$144=0+(n-1)12$

$n-1=\frac{144}{2}=12$

$n=13$

$\therefore$ $13$ rational term.