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QJEEM21Mab286: JEE Main 2021 Mathematics - Class 11 JEEM21Mab286 Solution: The sum of all those terms which are rational numbers in the…

The sum of all those terms which are rational numbers in the

expansion of (2^1/3 + 3^1/4)¹² is :

Step-by-Step Verified Solution

{T_{r + 1}} = {}^{12}{C_r}{\left( {{2^{1/3}}} \right)^r}.{\left( {{3^{1/4}}} \right)^{12 - 4}}

T_{r + 1} will be rational number when r = 0, 3, 6, 9, 12 & r = 0, 4, 8, 12

\Rightarrow

r = 0, 12

T₁ + T₁₃ = 1

\times

3³ + 1

\times

2⁴

\times

1

= 24 + 16 = 43