Either is correct:
elect him as chairman
elect him chairman
The word may be capitalized Chairman because it is the proper name of a position in a particular context.
*elect him as a chairman *
is also possible, but that makes the capitalization less likely to be correct.
I would prefer the second option,
participated in the online webinar ‘Engineering Projects Management’
The first example isn't wrong, but it needs at least a comma after webinar. Better yet would be the word named instead of a comma,
participated in an online webinar named ‘Engineering Projects Management’
In the second option, the name of the course is ...
When comparing two or more things using than, you use a comparative, for example better or more dangerous:
The Burj Khalifa is taller than any other building. -many things,
The Willis Tower is taller than the Empire State Building. -two things
When comparing more than two things and you don't use than, you use the definite article followed by the ...
In the case the referent is specific. and so if an article is used it should be definite. But
The Hilbert twenty-fourth problem
is incorrect. (as FumbleFingers says in a comment, this is because a "number" adjective should come before the noun in normal use.) It could be rephrased as
The twenty-fourth Hilbert problem
Hilbert's twenty-fourth ...
If there is more than one document current in a particular context, meaning, for example, that there are documents that have not expired, you can certainly refer to any one of them as "a current document".
You can even use it in a general sense:
A current document will have a date in the upper right hand corner that is not earlier than today's ...
Both of these work in your context:
I took last week off.
I took the last week off.
The difference in meaning is very slight, and is irrelevant in your current case, because it's Monday. But on different days, the meaning is different.
Imagine that you sent this on Wednesday instead of Monday. Now the meanings are different. "I took last week off&...
Confusingly, other similar-looking maxims have a different thrust, saying that even a small amount of something (and 'a little X' means 'a small amount of X' not 'a small X' where X is non-count) can be beneficial:
A little [bit of] love goes a long way.
A little effort goes a long way.
A little kindness goes a long way.
This is different again from the ...
It could absolutely be "an airport"; a shortcoming of many tests is to expect only one of several valid possibilities. If you answered "an" and the test is being graded by a human, I think you can absolutely argue that your answer should be counted as correct.
That said, there are some idiomatic usages about articles with some public ...
"A people" is a very common way of referring to a specific group of people.
It is a particularly useful term when referring to a group that may be harder to define - in this case, it is not a whole nation, nor a single tribe, but a group of tribes commonly affected by something.
Macmillan dictionary notes that opportunity is either countable or uncountable, giving the example:
opportunity for: The job pays well, but there’s not much opportunity for career advancement.
It does sound a bit odd to use it this way without more qualifying words ("It provides plenty of opportunity for..."), but it's valid.
"Elect him as a chairman" sounds fine to me grammatically, though in this case it should probably be "the", since there's only one chairman. ("A chairman" would be fine in a case where chairmen of multiple committees are being elected.)
I think you are confusing two usages here.
He can only maintain an erection while laying on his back.
This is fine except that it should be lying, not laying as MichaelHarvey kindly pointed out in a comment, and it is singular because he can only have one erection at a time
He can only maintain erection while laying on his back.
Perhaps you were thinking ...
If you have experience of something, you have spent time doing that job or being in that situation, and probably know how to do the job or cope with the situation.
I have had five years' experience as a hairdresser.
I have had experience of being in hospital for long periods.
An experience is a single instance of something happening to you.
Riding behind ...
The rule with articles, as always, is that the definite article is used with something specific, and the indefinite article is used with something non-specific.
Although each person only has one life, different sections of a person's life marked by major changes may be referred to as different lives.
If you are speaking about a 'life' that is unique to a ...
The word people in that sense is singular, and "a people" is correct.
The sense is referring to a group of individuals with nationality or ethnicity in common.
It can even be pluralized: the peoples of Europe, an example that appears in this discussion:
Stack Exchange English Language & Usage people are/is
(in the last answer)
The standard "saying" does include the article, and the standard meaning is...
a small amount of knowledge can mislead people into thinking that they are more expert than they really are, which can lead to mistakes being made.
It's not particularly idiomatic to discard that leading article in OP's exact case, but consider...
1: Little of my ...
The definite article is justified in phrases like this because we are talking about a specific kind of manipulation: the of part specifies what kind. The definite article is justified, but not required, in phrases like this. It is justified in this particular sentence, but the definite article is not always justified in "[the] noun1 of noun2" ...
Even though I don't know the specifics of your case, I would suggest this:
The tensile tests were performed at a XX strain rate for the sample with the XX mm gauge part.
The first indefinite article could be used since there may be infinite instances of such "XX strain rate".
That sample is indeed a specific one.
That "XX mm gauge part" ...
Either will do (and will be appreciated).
"The great team" is a little stronger. It suggests (without explicitly claiming) "the greatest team" among all the teams, while "a great team" is one great team among many.
I would keep both the's for more parallel construction especially given academic writing:
The proton and the electron are parts of an atom.
Protons and electrons are parts of an atom.
Protons and electrons are parts of atoms.