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The ratio of the coefficient of $x^{10}$ in ${(1 + x^{2})}^{10}$ and the term independent of $x$ in ${(x + \frac{2}{x})}^{10}$ is

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Correct option is B

Tr+1=(r+1) th term in 1+x210=10Crx2r∴ coefficient of x10 in 1+x210 is 10C5.Also, tr+1=(r+1) th term in x+2x10=10Cr(x)10−r2xr=10Cr2rx10−2rFor this term to be independent of x, set 10−2r=0or r=5.∴ term independent of x is 10C525

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The ratio of the coefficient of x10 in 1+x210 and the term independent of x in x+2x10 is

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The ratio of the coefficient of $x^{10}$ in ${(1 + x^{2})}^{10}$ and the term independent of $x$ in ${(x + \frac{2}{x})}^{10}$ is