Question

The constant term in the expansion of $\left(2+5x+a{x}^3\right){\left(\frac{3x^2}{2}-\frac{1}{3x}\right)}^9$ is 1 . The value of a is

• A. 3
• B. 4
• C. 5
• D. -6

Answer 1

Answer: (D)

The term independent of $x$ is
$2\cdot {}^9{C}_3{\left(\frac{3}{2}\right)}^3{\left(\frac{-1}{3}\right)}^6+a\cdot {}^9{C}_2{\left(\frac{3}{2}\right)}^2{\left(\frac{-1}{3}\right)}^7=\frac{7}{9}-\frac{a}{27}=1,$
$\text{ giving }a=-6$