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7.Binomial Theorem
easy
The term independent of $x$ in ${\left( {\sqrt x - \frac{2}{x}} \right)^{18}}$ is
A
$^{18}{C_6}{2^6}$
B
$^{18}{C_6}{2^{12}}$
C
$^{18}{C_{18}}{2^{18}}$
D
None of these
Solution
(a) ${T_{r + 1}} = {\,^{18}}{C_r}{(\sqrt x )^{18 – r}}{\left( { – \frac{2}{x}} \right)^r} = {\,^{18}}{C_r}{x^{9 – r/2 – r}}{( – 2)^r}$
If ${T_{r + 1}}$ is independent of $x$, then $9 – \frac{r}{2} – r = 0 \Rightarrow r = 6$.
So term independent of $x = {T_7} = {\,^{18}}{C_6}{2^6}$
Standard 11
Mathematics
