Prove that there is no term involving x6 in the expansion of \((2x^2-

1.	Prove that there is no term involving x6 in the expansion of \((2x^2-\frac{3}{x})^{11}\) ,r10
Answer» General term of \((2x^2-\frac{3}{x})^{11}\) T_{r + 1} = ¹¹C_r (2x² )^{11 – r} \((\frac{-3}{x})^{r}\) =¹¹C_r (-1)^r 2^11-r3^r x^22-3r 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

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

Answer»

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

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

=¹¹C_r (-1)^r 2^11-r3^r x^22-3r

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