COMEDK · Maths · 7. Binomial Theorem
The ninth term of the expansion \(\left(3 x-\frac{1}{2 x}\right)^{8}\) is
- A \(\frac{-1}{512 x^{9}}\)
- B \(\frac{1}{5 ! 2 x^{9}}\)
- C \(\frac{1}{256 \cdot x^{8}}\)
- D \(\frac{-1}{256 \cdot x^{8}}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{256 \cdot x^{8}}\)
Step-by-step Solution
Detailed explanation
\(T_{9}=T_{8+1}\) \[ \begin{aligned} &={ }^{8} C_{g}(3 x)^{8-8}\left(\frac{-1}{2 x}\right)^{8} \\ &={ }^{8} C_{8}(3 x)^{10}\left(\frac{-1}{2 x}\right)^{8} \\ &=1 \times 1 \times \frac{1}{2^{8} x^{8}}=\frac{1}{256 x^{8}} \end{aligned} \]
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