Question

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

• A. 7/12
• B. 7/18
• C. – 7/12
• D. – 7/16

Answer 1

Answer: (B)

7/18

Answer 2

n =9, $\alpha = 2$, $\beta = 1$. Then $r = \frac{9(2)}{1 + 2} = 6$.

Hence, $T_{7} =^{9} ⥂ C_{6}\left( \frac{3}{2} \right)^{3}\left( - \frac{1}{3} \right)^{6} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1}.\frac{1}{2^{3}.3^{3}} = \frac{7}{18}$.