Number of terms in the expansion of $(1 + x)^{101} (1 + x^{2} - x)^{100}$ is

302

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301

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202

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101

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Solution

The correct option is C 202
$(1 + x)^{101} (1 + x^{2} - x)^{100} = (1 + x) (1 + x)^{100} (1 + x^{2} - x)^{100}$
$= (1 + x) ((1 + x) (1 + x^{2} - x))^{100}$
$= (1 + x) (1 + x^{3})^{100}$
There are two types of terms here:
$x^{3 k}$ type and $x^{(3 k + 1)}$ type
So, number of terms are $101 + 101 = 202$ terms

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