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

Answer: Option D

The given word contains 7 letters out of which E is taken 2 times and all other letters are different .
∴ Required number of ways
$$\begin{array}{rl}& =\frac{7!}{2!}\\ & =\frac{7\times 6\times 5\times 4\times 3\times 2\times 1}{2}\\ & =2520\end{array}$$