AP EAMCET · Maths · Binomial Theorem
The independent term in the expansion of \(\left(1+x+2 x^2\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9\) is
- A \(\frac{18}{7}\)
- B \(\frac{7}{18}\)
- C \(-\frac{7}{18}\)
- D \(-\frac{18}{7}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{18}\)
Step-by-step Solution
Detailed explanation
\(\because\) The general term in the expansion of \(\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9\) is \(T_{r+1}={ }^9 C_r\left(\frac{3 x^2}{2}\right)^{9-r}\left(\frac{-1}{3 x}\right)^r={ }^9 C_r\left(\frac{3}{2}\right)^{9-r}\left(\frac{-1}{3}\right)^r x^{18-3 r}\) Now, the…
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