$\frac{1}{81^{\mathrm{n}}}-{ }^{2 \mathrm{n}} \mathrm{C}_1 \frac{10}{81^{\mathrm{n}}}+{ }^{2 \mathrm{n}} \mathrm{C}_2 \frac{10^2}{81^{\mathrm{n}}}-\ldots+\frac{10^{2 \mathrm{n}}}{81^{\mathrm{n}}}=$

• A

  $0$
• B

  $(-1)^{\mathrm{n}}$
• Correct answer
  C

  $1$
• D

  $81$

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