The number of different terms in the expansion of 1 - x 201 1 + x + x 2 200 is

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The number of different terms in the expansion of

{(1 - x)}^{201} {(1 + x + x^{2})}^{200}

is

MathematicsBinomial TheoremJEE Main

Options:

A $200$
B $201$
C $202$
D $402$

Solution:

1071 Upvotes Verified Answer

The correct answer is:

402

(1 - x) {(1 - x^{3})}^{200}

(1 - x) [{}^{200}C_{0} - {}^{200}C_{1} x^{3} + \dots \dots \dots \dots .]

So, number of required terms

= 2 \times 201 = 402

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