Number of terms free from radical sign in the expansion of ${(1 + 3^{1 / 3} + 7^{1 / 7})}^{10}$ is -

4

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5

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6

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8

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Solution

The correct option is A $4$
$(1 + 3^{1 / 3} + 7^{1 / 7})^{10}$
general term $= \frac{10!}{α_{1}! α_{2}! α_{3}!} 3^{α_{2} / 3} 7^{α_{3} / 7}$
form term to free from radical sign $\to$
$α_{2} = 0, α_{3} = 0, α_{1} = 10$
$α_{2} = 3, α_{3} = 7, α_{1} = 0$
$α_{2} = 3, α_{3} = 0, α_{1} = 7$
$α_{2} = 0, α_{3} = 7, α_{1} = 3$
$∴ 4 t e r m s$

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