In how many different ways can the letters of the word ‘TRANSPIRATION’ be arranged so that the vowels always come together?

Answer: Option B

The word ‘TRANSPIRATION’ has 13 letters in which each of T, R, A, N and I has come two times
We have to arrange TT RR NN PS (AA II O)
There are five vowels in the given words.
∴ We consider these give vowels as one letter.
∴ Required number of arrangements
$$\begin{array}{rl}& =\frac{9!\times 5!}{2!2!2!2!2!}\\ & =\frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 5\times 4\times 3\times 2}{2\times 2\times 2\times 2\times 2}\\ & =1360800\end{array}$$