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Question

If g(x)=200r=0αrxr and f(x)=200r=0βrxr,βr=1 for r100 and g(x)=f(1+x), then the greatest coefficient in these expansion of (1+x)201 is

A
α99
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B
α100
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C
α90
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D
α101
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Solution

The correct option is B α100
There will be 202 terms in the expansion of (1+x)201.
Hence the greatest coefficient will be the coefficient of the middle term.
Now there will be 2 middle terms.
T101 and T102
Hence the greatest coefficient is
=201C100
=α100.

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