No, they are done outside of the courtroom - usually at the plaintiffs office for the deposition and a court reporter will be there to take down whatever you say in response to their questions.
The interrogatories will be sent to your residence or address being used for the litigation of the matter.
Here's an example of the interrogatories:
$ 3117a-06 Form of Interrogatories
1. If there are any suits, actions, or legal proceedings of any kind against you pending and undetermined, state the full particulars as to each.
2. Are there any judgments on record against you?
a. What amount and where?
b. Have payments been made on account thereof by you or by any third party for you?
c. By what person?
d. Was satisfaction recorded?
e. If answer to item d. is "No," state why.
3. Are supplementary proceedings on any of these judgments pending against you?
4. Has any judgment creditor's action been commenced against you?
5. Have you any interest in real estate in this state or elsewhere?
a. Are you entitled to any reversion, remainder, or contingent interest in real estate; or is any real property held in trust for you?
b. Do you own any leasehold or have you any interest in any lease of real property?
c. Do you lease any real property?
d. Have you a lien on any interest in or under a lien on real property?
6. Have you any interest under any will or trust?
a. Have you recently received any money or property under any will by inheritance?
b. If answer to item a. is "Yes," state disposition.
7. What property have you in this state, real or personal?
a. Have you made any transfers of same and to whom?
b. State circumstances.
8. Give description and location of any property you have outside the state.
9. Have you any mortgages on real or personal property or other investments
, such as stocks, bonds, dividend certificates, interest coupons, certificates of deposit, promissory notes, drafts, or checks?
10. Have you any interest in any pension, patent, copyright, or invention, or in any royalties?
11. Do you own a seat in any stock, commodity, or other commercial exchange?
12. Have you any right or interest or any prospect of pecuniary advantage under any contract
or any interest in any suit in the courts of this or any other state, or in the federal courts?
13. Are there any judgments in your favor in any action by or against you, or have any judgments been assigned to you?
14. Have you any insurance on your life?
a. To whom was same made payable?
b. When were the beneficiaries changed?
15. Are you the beneficiary under a policy on the life of any other person?
16. What property did you have at the time when the debt for which this judgment was secured was contracted? Trace the disposition of this property.
17. Where do you live?
a. How long have you lived there?
b. How much do you pay for rent, board, services, etc.?
18. Are you a member of any club?
a. What are the dues?
b. Are they paid?
19. What salary or income have you?
20. Have you any uncollected debts or other money coming to you?
21. What is your occupation?
22. Are you married?
a. Have you a family?
b. How large?
c. How many are dependent on you?
d. With whom do you live?
23. What money have you received within the last sixty days from any source, and what have you done with it?
24. Have you a bank account?
a. When did you make your last deposit?
b. When did you draw your last check?
25. Have you anything in pawn?
26. Do you own or rent the place where you live?
a. Who owns the furniture in it?
b. What does it consist of?
27. Have you made a will?
b. State property devised.
28. What money have you spent since the service of this order?
29. Had you at the time of the service of this order any rights, real or personal property, money, debts, claims, mortgages, leases, choses in action, judgments, insurance, watches, jewelry, checks, notes, bills of exchange, bonds, stocks, or certificates; any interest in a contract, patent, copyright, invention or royalties, which you are not now possessed of, or in which you now have no interest, or a lesser interest?
Dated ________, 20___.