Question

The number of rational terms in the binomial expansion of `(4^(1/4) + 5^(1/6))^120` is ______.

Options

• 20

• 21

• 22

• 23

Answer 1

The number of rational terms in the binomial expansion of `(4^(1/4) + 5^(1/6))^120` is 21.

Explanation:

General term of `(2^(1/2) + 5^(1/6))^120` is 

Given, by T_r+1 = `""^120C_r(2^(1/2))^(120-r)(5^(1/6))^r`

For rational term, r should be a multiple of 6 (i.e.) r∈{0, 6, 12, 18, ......, 120}

∴ 21 rational terms are there in the expansion `(2^(1/2) + 5^(1/6))^20`