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

48

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49

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54

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55

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Solution

The correct option is C $54$
${(7^{1 / 5} - 3^{1 / 10})}^{60}$
General term : $T_{r + 1} =^{60} C_{r} (- 1)^{r} (7^{1 / 5})^{60 - r} (3^{1 / 10})^{r}$

A term will be rational if its power is a multiple of $LCM (5, 10) = 10$
$∴ r = 0, 10, 20, 30, 40, 50, 60$ for rational terms.
$∴$ No. of irrational terms $= 61 - 7 = 54$

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