Question

The total number of irrational terms in the binomial expansion of $(7^{\frac{1}{5}}-3^{\frac{1}{10}}{)}^{60}$ is :

• A. $55$
• B. $49$
• C. $48$
• D. $54$

Answer 1

The correct option is D $54$

Given $(7^{\frac{1}{5}}-3^{\frac{1}{10}}{)}^{60}$ has $61$ terms

General term $T_{r+1}{=}^{60}{C}_r{7}^{\frac{60-r}{5}}{3}^{\frac{r}{10}}$

$\therefore$ for rational term, $r=0,10,20,30,40,50,60$$\Rightarrow$ no of rational terms $=7$

$\therefore$ number of irrational terms$=61-7=54$