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If $A$ and $B$ are coefficients of $x^{n}$ in the expansions of $(1 + x)^{2 n}$ and $(1 + x)^{2 n - 1}$ respectively, then

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A=B

A=2B

2A=B

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detailed solution

Correct option is B

We know that coefficient of xr in the expansion of (1+x)m is mCr.Thus, A=2nCn and B=2n−1Cn We have AB= 2nCn 2n−1Cn=(2n)!n!n!(n!)(n−1)!(2n−1)!=2nn=2⇒ A=2B

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If A and B are coefficients of xn in the expansions of (1+x)2n and (1+x)2n−1respectively, then

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Ready to Test Your Skills?

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If $A$ and $B$ are coefficients of $x^{n}$ in the expansions of $(1 + x)^{2 n}$ and $(1 + x)^{2 n - 1}$ respectively, then