Question

The number of irrational terms in the expansion of ${(2^{\frac{1}{5}}+3^{\frac{1}{10}})}^{55}$ is

• A. $47$
• B. $56$
• C. $50$
• D. $48$

Answer 1

The correct option is C $50$

For the above question
$T_{r+1}={}^{55}{C}_r{2}^{11-\frac{r}{5}}{3}^{\frac{r}{10}}$
Hence we will have rational terms at $r=0,10,20,30,40,50$ respectively.
Hence there will be $6$ rational terms.
The total number of terms will be
$55+1$
$=56$ terms.
Hence the number of irrational terms will be
$56-6$
$=50$ terms.