The sum of all rational terms in the expansion of
` (3^(1//4) + 4^(1//3))^(12)` is

Options

A. 91
B. 251
C. 273
D. 283

Answer

d

Explanation

In the expansion of `(3^(1//4)+ 2^(2//3))^(12) ` , the general term is
`T_(r+1) = ""^(12)C_(r) (3^(1//4))^(12-r) (2^(2//3))^(r) = ""^(12)C_(r)3^(3-(r)/(4)) 2^((2r)/(3))`
Now , ` 0 lt r le 12 `
` therefore r = -0, 12 `
Rotional terms are ` T_(0+1) "and " T_(12 + 1)`
Now , ` T_(1) = ""^(12)C_(0) 3^(3) 2^(0) = 27`
`rArr T_(13) = ""^(12)C_(12) 3^(0) *2^(8) = 256`
` therefore ` Required sum `= T_(1) + T_(13) = 27 + 256 = 283` .