The number of terms with integral coefficients in the expansion of ${(7^{1 / 3} + 5^{1 / 2} . x)}^{600}$ is

100

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50

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101

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none of these

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Solution

The correct option is C $101$
The number of integral terms will be
$1 + \frac{100}{L . C . M (2, 3)}$
$= 1 + \frac{600}{6}$
$= 1 + 100$
$= 101$

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