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Prove that there is no term involving x6 in the expansion of \((2x^2-\frac{3}{x})^{11}\) ,r10

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General term of \((2x^2-\frac{3}{x})^{11}\)

Tr + 1 = 11Cr (2x2 )11 – r  \((\frac{-3}{x})^{r}\)

= 11Cr (-1)r 211-r 3r x22-3r

For term contain x6 

22 – 3r = 6

R = \(\frac{16}{3}\)

∴ r is not natural number

∴ Expansion of \((2x^2-\frac{3}{x})^{11}\) is not contain x6 term

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