Question

The number of rational terms in the expansion of ${(x^{\frac{1}{5}}+y^{\frac{1}{10}})}^{45}$ is

• A. 5
• B. 6
• C. 4
• D. 7

Answer 1

The correct option is A 5

Given, ${(x^{\frac{1}{5}}+y^{\frac{1}{10}})}^{45}$

general term

$T_{r+1}={}^n{C}_r{x}^{n-r}{y}^r$

$T_{r+1}={}^{45}{C}_r\left(x^{\frac{1}{5}}{)}^{45-r}\right(y^{\frac{1}{10}})$

$T_{r+1}={}^{45}{C}_r{x}^{9-\frac{r}{5}}(y{)}^{\frac{r}{10}}$

Rational term when

$r=0,10,20,30,40$

so, there are $5$ rational numbers.