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
- A \(\frac{7}{18}\)
- B \(\frac{5}{18}\)
- C \(\frac{19}{54}\)
- D \(\frac{17}{54}\)
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 \(\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9\) \(\mathrm{T}_{r+1}={ }^9 \mathrm{C}_{\mathrm{r}}\left(\frac{3 \mathrm{x}^2}{2}\right)^{9-\mathrm{r}}\left(\frac{-1}{3 \mathrm{x}}\right)^{\mathrm{r}}\)…
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