The term independent of x in the expansion ofx-2x18 is

r=npp+q=181212+12=9∴ The term independent of x isT10=T9+1=18C9-29=29.18C9

The term independent of x in the expansion ofx-2x18 is

r=npp+q=181212+12=9∴ The term independent of x isT10=T9+1=18C9-29=29.18C9

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The term independent of x in the expansion of
${(\sqrt{x} - \frac{2}{\sqrt{x}})}^{18}$ is

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${18_{C}}_{8} 2^{12}$

${18_{C}}_{8} 2^{8}$

${18_{C}}_{9} 2^{9}$

${18_{C}}_{6} 2^{8}$

answer is B.

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Detailed Solution

$r = \frac{n p}{p + q} = \frac{18 (\frac{1}{2})}{\frac{1}{2} + \frac{1}{2}} = 9$

$∴$ The term independent of x is

$T_{10} = T_{9 + 1} = {18_{C}}_{9} {(- 2)}^{9} = 2^{9} . {18_{C}}_{9}$

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The term independent of x in the expansion of
${(\sqrt{x} - \frac{2}{\sqrt{x}})}^{18}$ is