$\begin{array}{1 1}(A)\;1814400\\(B)\;2419200\\(C)\;2419220\\(D)\;2419240\end{array} $

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There are 12 letters in the word PERMUTATIONS which have T two times

Now the vowels $a,e,i,o,u$ are together.Let it be considered in one block

The letters of vowels can be arranged in $5!$ ways

Thus there are 7 letters and 1 block of vowels with T two times

$\therefore$ Number of arrangements =$\large\frac{8!}{2!}$$\times 5!$

$\Rightarrow \large\frac{8!5!}{2}$

$\Rightarrow 2419200$

Hence (B) is the correct answer.

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