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

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Solution

The correct option is C 50
$(2^{\frac{1}{5}} + 3^{\frac{1}{10}})^{55} = \sum_{r = 0}^{55}^{55} C_{r} 2^{\frac{r}{5}} 3^{\frac{55 - r}{10}}$

So, for all case where $r$ $m o d$ $10 = 5$ , it's terms are rational.
ie, no of rational terms $= 6$
Total no of terms $= 56$

$∴$ no of irrational terms $= 56 - 6 = 50$

So, Option C is the correct answer.

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