In the expansion of ([5]{3}+[3]{12})¹5}

Sum of all rational terms is 58

Sum o f all rational terms is greater than the sum of all irrational terms

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AP EAMCET Engineering 18 Sep 2020 Shift 1 Paper

Section: Mathematics

Question : 71 of 160

Marks: +1, -0

(\sqrt[5]{3}+\sqrt[3]{12})^{15}

Solution:

Given binomial is

(\sqrt[5]{3}+\sqrt[3]{2})^{15}

\because

The general term

T_{r+1}={}^{15}C_{r}3^{\frac{15-r}{5}}2^{\frac{r}{3}}

={}^{15}C_{r}3^{\frac{3-r}{5}}2^{\frac{r}{3}}

For rational terms

r

must be multiple of 15, so possible values of

r=0

and

15\;\;(\because 0\leq r\leq 15)

\therefore

Sum of rational terms

={}^{15}C_{0}3^{3}+{}^{15}C_{15}2^{5}

=27+32=59

\therefore

The sum of all irrational terms is greater than the sum of all rational terms.

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