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

Option: 1

{ }^9 C_3 \cdot \frac{1}{6^3}


Option: 2

{ }^9 C_3\left(\frac{3}{2}\right)^3


Option: 3

{ }^9 C_3


Option: 4

None of these


Answers (1)

best_answer

In the expansion of  \left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9, the general term is T_{r+1}={ }^9 C_r \cdot\left(\frac{3 x^2}{2}\right)^{9-r}\left(-\frac{1}{3 x}\right)^r

For the term independent of x, 18 – 3r = 0 ⇒ r = 6

This gives the independent term

T_{6+1}={ }^9 C_6\left(\frac{3}{2}\right)^{9-6}\left(-\frac{1}{3}\right)^6={ }^9 C_3 \cdot \frac{1}{6^3}

 

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