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(B) The general term $T_{r+1}$ in the expansion of $\left(x-\frac{2}{\sqrt{x}}\right)^{21}$ is given by: $T_{r+1} = {}^{21}C_r (x)^{21-r} \left(-\frac

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${}^{21}C_{14} 2^{14}$

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(B) The general term $T_{r+1}$ in the expansion of $\left(x-\frac{2}{\sqrt{x}}\right)^{21}$ is given by: $T_{r+1} = {}^{21}C_r (x)^{21-r} \left(-\frac{2}{x^{1/2}}\right)^r$ $T_{r+1} = {}^{21}C_r (x)^{21-r} (-2)^r (x)^{-r/2}$ $T_{r+1} = {}^{21}C_r (-2)^r (x)^{21-r-r/2}$ $T_{r+1} = {}^{21}C_r (-2)^r (x)^{21-3r/2}$ For the term to be independent of $x$,the exponent of $x$ must be $0$: $21 - \frac{3r}{2} = 0$ $42 - 3r = 0$ $\Rightarrow 3r = 42$ $\Rightarrow r = 14$ Substituting $r = 14$ into the expression: $T_{14+1} = {}^{21}C_{14} (-2)^{14} = {}^{21}C_{14} 2^{14}$ Since ${}^{21}C_{14} = {}^{21}C_7$,the term is ${}^{21}C_{14} 2^{14}$.

The term independent of $x$ in the expansion of $\left(x-\frac{2}{\sqrt{x}}\right)^{21}$ is

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