Question

The sum of all those terms which are rational numbers in the expansion of (2^1/3+3^1/4)¹² is:

(1) 89

(2) 27

(3) 35

(4) 43

Answer 1

Answer is: (4) 43

T_r+1 = ¹²C_r(2^1/3)^r.(3^1/4)^12-r

T_r+1 will be rational number

when r = 0, 3, 6, 9, 12

& r = 0, 4, 8, 12

⇒ r = 0, 12

T₁ + T₁₃ = 1 × 3³ + 1 × 2⁴ × 1

= 24 + 16 = 43