Question

The middle term of $\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{6}$ is

• A. -20
• B. -1
• C. 1
• D. None of these

Answer 1

Answer: (A)

Middle term is $\left(\frac{n}{2}+1\right)$ th term for $n$ even
$\therefore $ Middle term $=\left(\frac{6}{2}+1\right)=4$ th term
$T_{4}={ }^{6} C_{3}(\sqrt{x})^{3}\left(-\frac{1}{\sqrt{x}}\right)^{6-3}$
$=\frac{6 !}{3 ! 3 !}(\sqrt{x})^{3} \frac{(-1)^{3}}{(\sqrt{x})^{3}}$
$=\frac{-6 \times 5 \times 4}{6}=-20$