The coefficient of ${x^7}$ in the expansion of ${\left( {\frac{{{x^2}}}{2} - \frac{2}{x}} \right)^8}$ is

  • A

    $-56$

  • B

    $56$

  • C

    $-14$

  • D

    $14$

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If $n$ is the degree of the polynomial,

${\left[ {\frac{1}{{\sqrt {5{x^3} + 1}  - \sqrt {5{x^3} - 1} }}} \right]^8} $$+ {\left[ {\frac{1}{{\sqrt {5{x^3} + 1}  + \sqrt {5{x^3} - 1} }}} \right]^8}$ and $m$ is the coefficient of $x^{12}$ in it, then the ordered pair $(n, m)$ is equal to

  • [JEE MAIN 2018]

The middle term in the expansion of ${(1 + x)^{2n}}$ is