The number of integral terms in the expansion of $(3^{1 / 2} + 2^{1 / 2})^{500}$ is :

128

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129

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251

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512

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Solution

The correct option is D 251
$T_{r + 1} =^{500} C_{r} (3^{1 / 2})^{500 - r} [(2)^{1 / 2}]^{r}$
obviously $r$ should be even
$∴$ Total numbers $= 500 / 2 = 250$
But first term for $r = 0$ is also integral
$∴$ Total terms $= 250 + 1 = 251$

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