Question

Let the coefficient of $5^{th}$ term from the end of an expansion be $a$ and $b$ be the power.
Expansion:${(\frac{x^3}{2}-\frac{2}{x^2})}^9$
Find $a\times b$.

• A. $424$
• B. $-252$
• C. $-504$
• D. $335$

Answer 1

The correct option is C $-504$

$5^{th}$ from the end is the $6^{th}$ term.
$(r+1{)}^{th}$ term is $t_{r+1}{=}^n{C}_r{a}^{n-r}{b}^r$
So, for $6^{th}$ term, $r=5$.
$\therefore t_6=t_{5+1}{=}^9{C}_4(-1{)}^5(\frac{x^3}{2}{)}^{9-5}(\frac{2}{x^2}{)}^5$
$\therefore t_6=\frac{-252}{x^2}$
So, $a=-252,b=2$
Ans-Option $C$.