The coefficient of X53 in the following expansion∑m=0100 100Cm(x−3)100−m⋅2m is

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100C47

100C53

−100C53

−100C100

answer is C.

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Detailed Solution

The given sigma expansion ∑m=0100 100Cm(x−3)100−m⋅2m Can be written asx-3+2100=(x−1)100=(1−x)100∴ Coefficient of x53 in (1−x)100=(−1)53100C53=−100C53

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