Question

}$13^{th term in the expansion of\displaystyle \left ( 9x - \frac{1}{ 3 \sqrt{x}} \right)^{18}, x \neq 0$ is

• A. $15654$
• B. $18465$
• C. $18564$
• D. $65481$

Answer 1

The correct option is C $18564$

13th term, $T_{13}=T_{12+1}{=}^{18}{C}_{12}(9x{)}^{18-12}{(-\frac{1}{3\sqrt{x}})}^{12}$
${=}^{18}{C}_6{9}^6\cdot x^6(-1{)}^{12}\cdot \frac{1}{3^{12}}\times \frac{1}{x^6}=18564\times (3^2{)}^6\cdot \frac{1}{3^{P}12}\times \frac{x^6}{x^6}$
$=18564\times \frac{3^{12}}{3^{12}}=18564$