Q65 / 170 · Manipal (MET) 2017 · Mathematics

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

  • Correct answer
    A
    -20
  • B
    -1
  • C
    1
  • D
    None of these

Solution

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 $\begin{aligned} \therefore T_4 & ={ }^6 C_3(\sqrt{x})^3\left(-\frac{1}{\sqrt{x}}\right)^{6-3} \\ & =\frac{6!}{3!3!}(\sqrt{x})^3 \frac{(-1)^3}{(\sqrt{x})^3} \\ & =\frac{-6 \times 5 \times 4}{6} \\ & =-20 \end{aligned}$

Hence, the correct answer is option: 'A'.

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