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

Correct option is 331C6−21C 6

Questions

$The coefficient of x^{5} in the expansion of (1 + x)^{21} + (1 + x)^{22} + \dots + (1 + x)^{30} is$

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51C5

9C5

31C6−21C 6

30C5+ 20C 5

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detailed solution

Correct option is C

coefficientof x5 in (1+x)21+(1+x)22+…+(1+x)30 =coefficientof x5 in (1+x)21(1+x)10-1(1+x)-1 =coefficient of x6 in (1+x)31-(1+x)21

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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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$The coefficient of x^{5} in the expansion of (1 + x)^{21} + (1 + x)^{22} + \dots + (1 + x)^{30} is$