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

32 : 1

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1 : 32

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16 : 1

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None of these

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Solution

The correct option is B $1 : 32$
Coefficient of $T_{5}$ of $(1 - x^{2})^{10}$
$=^{10} C_{5}$
$= 252$ ...(i)
The coefficient of Term independent of x is
$^{10} C_{5} 2^{5}$
$= 252 (32)$ ..(ii)
Taking the ratio
$i : i i$
$= 1 : 32$

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