JEE MAIN - Mathematics (2021 - 25th July Evening Shift - No. 1)
The sum of all those terms which are rational numbers in the
expansion of (21/3 + 31/4)12 is :
expansion of (21/3 + 31/4)12 is :
89
27
35
43
Explanation
$${T_{r + 1}} = {}^{12}{C_r}{\left( {{2^{1/3}}} \right)^r}.{\left( {{3^{1/4}}} \right)^{12 - 4}}$$
Tr + 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
Tr + 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
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