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The coefficient of x⁵ in the expansion of $(1 + x)^{21} + (1 + x)^{22} + \dots + (1 + x)^{30}$ is

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51C5

9C5

31C6−21C6

30C5+20C5

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detailed solution

Correct option is C

(1+x)21+(1+x)22+…+(1+x)30=(1+x)211+(1+x)1+…+(1+x)9=(1+x)21(1+x)10−1(1+x)−1=1x(1+x)31−(1+x)21∴ Coefficient of f in the given expression= Coefficient of x5 in 1x(1+x)31−(1+x)21= Coefficient of x6 in (1+x)31−(1+x)21=31C6−21C6

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The coefficient of x5 in the expansion of (1+x)21+(1+x)22+…+(1+x)30 is

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The coefficient of x⁵ in the expansion of $(1 + x)^{21} + (1 + x)^{22} + \dots + (1 + x)^{30}$ is