Find the number of terms which are free from radical signs in the expansion of `(y^(1//5)+x^(1//10))^(55)dot`

Options

A. 5
B. 6
C. 7
D. none of these

Answer

B

Explanation

`T_(r+1) = ""^(55)C_(r) (y^(1//5))^(55- r )(x ^(1//10))^(r)= ""^(55)C_(r)y^(11-r//5)x^(r//10)`
Clearly, `T_(r + 1)` will be indepandent of radical sings of `r//5` and
`therefore r = 0, 10, 20, 30, 40, 50 `
Hence, there are 6 terms in the expansion of the given
expression which are independent of radicals .