Question

Find the coefficient of the middle term of the expansion ${(x-\frac{1}{2y})}^{10}$:

• A. $-\frac{63}{8}$
• B. $24$
• C. $-\frac{33}{4}$
• D. $-33$

Answer 1

The correct option is A $-\frac{63}{8}$

We need to find middle term of ${(x-\frac{1}{2y})}^{10}$

Total number of terms are $11$.
So, middle term will be the $6^{th}$ term.
$\therefore t_{5+1}{=}^{10}{C}_5(-1{)}^5{x}^{10-5}(\frac{1}{2y}{)}^5=-\frac{63x^5}{8y^5}$
Hence, option A is correct.