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TS EAMCET · Maths · Binomial Theorem

The term independent of \(x\) in the expansion of \(\left(1-3 x+2 x^3\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9\) is

  1. A \(\frac{7}{18}\)
  2. B \(\frac{5}{18}\)
  3. C \(\frac{19}{54}\)
  4. D \(\frac{17}{54}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{17}{54}\)

Step-by-step Solution

Detailed explanation

\(\left(1-3 x+2 x^3\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9\) for \(\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9\) \(\mathrm{T}_{r+1}={ }^9 \mathrm{C}_{\mathrm{r}}\left(\frac{3 \mathrm{x}^2}{2}\right)^{9-\mathrm{r}}\left(\frac{-1}{3 \mathrm{x}}\right)^{\mathrm{r}}\)…