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The coefficient of $x^{53}$ in $\sum_{m = 0}^{100} 100 C_{m} (x - 5)^{100 - m} (4)^{m}$ is

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100C47

100C53

−100C53

253

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detailed solution

Correct option is C

∑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

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The coefficient of $x^{53}$ in $\sum_{m = 0}^{100} 100 C_{m} (x - 5)^{100 - m} (4)^{m}$ is