Number of different words that can be formed using all the

 letters of the word "DEEPMALA" if two vowels of same 

kind are together and the other two are also together but 

separated from the first two is

| D | P | M | L | can be arranged in 4! ways & the two gaps 

out of 5 gaps can be selected in ${ }^5{\mathrm{C}}_2$  ways.

two A's and two E's can be atranged in $\frac{4!}{2!2!}=6$ ways.

$\therefore$ Total number of arrangements $=4!{\cdot }^5{C}_2\cdot \frac{4!}{2!2!}$

$=1440$