You can use だ and か together. I think だか is short for であるか. For native speakers, であるか sounds like a formal speech. So we often use だか.
For example, of course you can say
but you can also say
so your textbook is wrong, and
is also Okay, but this is a little bit formal. (maybe young people don't say so.)
Another example, you can say both of
There's no difference between them. However
is strange. Because in the latter part, it uses であるか so this sentence should be formal, but in the former, は or が is omitted. So
is Okay, but I don't usually say so to my friends.
Now, turn back to the main topic. As far as I have mentioned, it seems there is no difference between だ and だか, but unfortunately it is not true. Actually, you can say
but you cannot say
This is difficult to explain, but probably because many people feel a sentence doesn't end by だか. Actually, if I heard the latter, I would think "What is Hondaka?". To sum up, these are basically the same but don't end a sentence with だか.