In how many different ways can the letters of the word OPERATE be arranged?

Answer: Option C

The given words contains 8 letters out of which U is taken 2 times and all other letters are different.
∴ Required number of ways
$$\begin{array}{rl}& =\frac{8!}{2!}\\ & =\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{2}\\ & =20160\end{array}$$