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  • The term independent of x in the expansion of <img alt="\left(2 x-\frac{3}{x}\right)^6" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%282%20x-%5Cfrac%7B3%7D%7Bx%7D%5Cright%29%5E

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

Option: 1

4320


Option: 2

216


Option: 3

-216


Option: 4

-4320


Answers (1)

best_answer

\begin{aligned} &T_{r+1}={ }^6 C_r(2 x)^{6-r}\left(-\frac{3}{x}\right)^r= \end{aligned} { }^6 C_r(2)^{6-r}(-3)^r(x)^{6-2 r}

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

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

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manish

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