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(1) I don't know what the problem is.
(2) I don't know what is the problem.

Is only (1) correct?

(3) Do you know what the problem is?
(4) Do you know what is the problem?

Which one is correct?
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1 and 3 are correct. There's probably a term for what is going on here in the indirect question, but I don't remember what it is (not what is it).
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Hi Philip

Thank you very much. I got more hits in Google for (4) then for (3). That's why I am confused.

How about the following?

(5) I don't know who is singing.
(6) Do you know what is the matter with him?

It's impossible to re-write (5) and it sounds awkward to re-write (6) as
Do you know what the matter is with him?

It seems that I have mixed up something but I don't know what.
Pter I got more hits in Google for (4) then for (3). That's why I am confused.

That's normal. You are supposed to be confused with English grammar!Emotion: wink
Pter(6) Do you know what is the matter with him?

It's impossible to re-write (5) and it sounds awkward to re-write (6) as
Do you know what the matter is with him?

I accept (6) for the simple reason that it is so common. Many things that are very common in English are idiomatic too. Instead of your suggestion I would say:
Do you know what the matter with him is.

I would keep the matter with him together.

CB
PterThat's why I am confused.
Yes. It can get confusing. But there's a simple rule. Do not invert subject and verb in an indirect question. (These are also called embedded questions.) Leave these in the same order as in the statement form. This is contrary to the rule for direct questions, which invert subject and verb unless the subject is being questioned.

The problem is that there are too many people in one room.
Statement form: | The problem -- is | ... (what?)
Direct question: What | is --- the problem?
Indirect question (embedded): I don't know what | the problem -- is.

Jenny is singing.
Who is singing? (No inversion in the direct question because the element being questioned is the subject.)
I don't know who is singing. (Nevertheless, the indirect question has the same subject-verb order as the statement form.)

The one with "matter" follows the same pattern as Jenny is singing.
Something's the matter with my car. (Something is wrong with my car.)
What's the matter with my car? What's wrong with my car?

I don't know what is the matter with my car. I don't know what is wrong with my car.

I hope that helps. Emotion: smile

CJ
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Thank you CB and Jim. I now know what I have mixed up. Some of the questions were about the subject while some others were about the object. That's it!

What is the matter with is particularly problematic because we don't usually use the statement form. I am still thinking what the statement form should be. (<-- Now I am very sure that the indirect question in the preceding sentence is in the correct order!)

Something's the matter with my car. <-- As you suggested.
The matter with my car is that ( clause ) <-- Is this also possible?
PterWhat is the matter with is particularly problematic because we don't usually use the statement form. I am still thinking about what the statement form should be.
the matter used to mean wrong has a highly idiosyncratic grammar.

Besides the question form, only a few statement forms are often used, and these almost exclusively with the indefinite pronouns show below.

What's the matter ...?
Something's the matter ....
Nothing's the matter ....
PterThe matter with my car is that ( clause ) <-- Is this also possible?
It doesn't work for me. There is really no need for that phrasing. If someone asks What is wrong with X? you don't usually repeat thus: What's wrong with X is that PQR. You just say PQR.

-- What's the matter with your car?
-- The tires are flat.

CJ
Thanks, CJ. You are so helpful. And thank you for correcting my sentence.

Actually, I didn't know "Something's the matter ..." and "Nothing's the matter ..." are actually used that often and considered correct. I thought they were just made up during conversations for mimicking what other people say (or should I say parody? Can't find the right word, hope you know what I mean). I thought wrong.
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PterI thought they were just made up during conversations for mimicking what other people say
(This is expressed correctly.)

No. These are not just made up. They are common. Here are some perfectly ordinary exchanges. A few show a common variant with there.

-- Something's the matter with the garage door.
-- Really? What's the matter with it?
-- It gets stuck half-way down.
-- Maybe it needs oil.

-- You look glum today. What's the matter?
-- Nothing's the matter. I'm just tired. I didn't get enough sleep last night.

-- Is there something the matter with Lucy? She seems to be limping.
-- No, not really. She twisted her ankle. She'll be OK by tomorrow, I'm sure.

-- There's something the matter with this printer.
-- Oh? What's the matter with it? It worked fine for me just an hour ago.

-- Ted seemed kind of cranky this morning. What do you think's the matter with him?
-- There's nothing the matter with him. He's just angry the boss didn't pick him to handle the Bennett account.

CJ
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