It is correct to use "they" in reference to a singular noun because you don't know if the teacher is a man or a woman.
Someone has left their umbrella in the changing room.
One person left an umbrella. Unless I know for sure that this person is a woman or a man, I wouldn't say "his" or "her".
In English, "his" cannot refer to a woman or girl. When I read that sentence, I understand it to mean that Narendra Modi's own 69th birthday was on Tuesday (not his mother's birthday). If that is not what the article meant, then there is a typo in it.
Generally speaking, we always use all of when it's followed by a pronoun:
Yes, I've seen all of them
I've seen all of his books
Can you fit all of us in your car?
The of is optional when it's followed by a noun, for example
I want all [of] the news about your wedding
The dog ate all [of] the food
For a small number of the words, it is never ...
Yes, this sentence is correct. "His" has "PM Narendra Modi" as its antecedent, which is the noun it needs to match in terms of gender.
As long as the antecedent is male, his mother (his father, his friend, his daughter, his son, his wife) are all correct regardless of the gender of the following noun.
I can think of two ways of interpreting the second sentence, but it is still different from the first in either interpretation.
Depending on context, the following interpretations are possible:
1. Give me another two shirts.
a) Give me two more of the same type of shirt.
→ If you've already given me two shirts, I will now have four shirts.
"I" is a subject, "me" is an object. In other words, use "I" when you are causing some action and use "me" when something is being done to you.
For example: "I (subject) am going to the store (object). Would you (subject) like to come with me (object)?"
The excerpt you provided is a really good example of why this distinction is so important. If they were ...
I would pronounce this:
as f of x.
And I would pronounce this:
as u sub a.
Therefore, I would pronounce your expression as: u sub a of x.
Note: This assumes that ua is a function. If ua was a variable and not a function, then I suppose this could be a multiplication expression instead. In that case, I would say: u sub a times x
There is nothing wrong with the sentence. The subject is locations, which is plural and which is in accord with the verb.
The use of it as the first word in the sentence is a red herring. This is an example of a cleft sentence; it is not the subject.
It is the locations that make the tournament special.
→ The locations [are what] make the ...
"Another two shirts" has two interpretations:
two additional shirts (as Jason Bassford said)
two shirts instead
Neither of these imply that the desired shirts must be of the same kind as any previously mentioned shirts -- nor that they must be of a different kind. For all we know, the speaker might already have 3 shirts but want 5 in total, and doesn't ...
Do you know some writers?
could be used in that way, and is not ungrammatical. It is slightly ambiguous, in that "some" can be taken in any of several ways, and this sentence does not particularly indicate any of them more than any other. It could mean "more than one" for example.
In this context "this" is referring to the actions of the previous paragraphs. In the preceding paragraphs Harry was cleaning up and sorting his possessions. After doing that, there was a stack of newspapers left over. In other words, "this" (the organizing) caused a stack of newspapers to be left over.