The number of terms with integral coefficient in the expansion of ${⎛ ⎜ ⎝ 17^{\frac{1}{3}} + 35^{\frac{1}{2}} ⎞ ⎟ ⎠}^{300}$ is

50

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100

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150

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51

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Solution

The correct option is D $51$
The number of rational terms will be
$1 + \frac{300}{L . C . M (3, 2)}$
$= 1 + \frac{300}{6}$
$= 1 + 50 = 51$ rational terms.

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