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The coefficient of x53 in ∑m=0100 100Cm(x−5)100−m(4)m is

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a

100C47

b

100C53

c

−100C53

d

253

answer is C.

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Detailed Solution

∑m=0100 100Cm(x−5)100−m(4)m=(x−5+4)100=(x−1)100∴ Coefficient of x53 is 100C53(−1)47=−100C53.

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The coefficient of x53 in ∑m=0100 100Cm(x−5)100−m(4)m is