Term independent of x in expansion of {left( {2x - frac{3}{x}} right)^6} is

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7.Binomial Theorem

easy

The term independent of $x$ in the expansion of ${\left( {2x - \frac{3}{x}} \right)^6}$ is

A

$4320$

B

$216$

C

$-216$

D

$-4320$

Solution

(d) ${T_{r + 1}} = \,{}^6{C_r}{(2x)^{6 – r}}{\left( { – \frac{3}{x}} \right)^r}$

= ${}^6{C_r}{(2)^{6 – r}}{( – 3)^r}{(x)^{6 – 2r}}$

For term independent of $x$, $6 -2r = 0$ i.e. $r = 3$

$\therefore {T_4} = {\,^6}{C_3}\,{2^{6 – 3}}{( – 3)^3}$ $= -4320$.

Standard 11

Mathematics

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