The total number of irrational terms in the binomial expansion of 71/5−31/1060 is

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

A
55
B
54
C
48
D
49

Solution:

Given expression is $_{} {(7^{1 / 5} - 3^{1 / 10})}^{60}$

General terms of this expansion is $T_{r + 1} = (- 1)^{r} (^{60} C_{r} {(7^{\frac{1}{5}})}^{60 - r} {({\overset{}{3}}^{\frac{1}{10}})}^{r})$

For rational terms $r = 0, 10, 20, 30, 40, 50, 60$

So, number of rational terms = 7

$∴$ Number of irrational terms = 61 -7 =54

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