Dubai,

I think you may have left a word out by mistake?

The sentences "Did you used/use/using sports when you were young?" make no sense.

You need a verb i.e. "Did you use/used/ using:-
(to like/to play/to excel/to take part in/to join in/to enjoyetc.) sports when you were young?" (It's a question. You must use a question mark.)

The problem still remains.

Did you use sports?

Is nonsense.
You don't 'use' sports. Not the way it is written in this sentence.




If that is what the question says then stop using those questions because they are rubbish.

There is the way you express habits in the past.
Eg
I used to play football when I was young.

'used to' behaves exactly as a regular verb when there is a question or negative.

The auxiliary verb becomes the inflected verb. There is only one inflected verb so the main verb becomes a bare infinitive.


But this question, without verb like 'to play', is completely wrong, as Rom said.

If the question really is

Did you ___ sport when you were young?
Then stop using the resource.


If it is
Did you ___ to play sports when you were young?

Then think about what happens to a simple past verb when you add an auxiliary.


Eg

I liked to play sport.
I didn't like to play sport.
Did you like to play sport?


'used to do something' is a particular construction but its grammar is completely regular.

I used to...
I did use to...
I didn't use to...
Do you use to...?