Yes, you can apply for both at the same time but according my experience you might land in trouble at the end when you will get seat on both sides.

For instance, you took admission on merit in a good college however, after a week JAT results are out and you got good rank there too.

Now, if your mind dwindles and you think you might get good college by JAT rank.

Mind you i said "you might" then you have to leave the merit seat i.e complete cancellation and stand for JAT without any certainly.

They may allow simultaneous filing of form but they will never allow simultaneous admissions.

If you are confident enough to get through any one of them you may fill because at last whrn everybody will ve getting admission then it feels little left out. Indeed, you may go for the two but make sure what you are willing to pursue.