Why do I have to use the in following phrase?
What are the problems ....
For example
What are the problems John is facing while riding a bike?
What are the problems Smith is facing while solving a puzzle?
What are the problems Jeff is facing while reconciling his financials?
John is a poor man who has a lot of problems. Some of his problems have to do with riding a bike. Some of his problems have to do with money, some with his children, some with his boring job, and some problems he has because he would rather live in the countryside than the crowded, smoggy city, which also happens to set off his asthma. Luckily, John's wife is the apple of his eye and the light of his life. So he has no problems with her. Her only problem with him is that he loves her so much.
Of all those problems, which ones do you want to know about?
Those he must face while riding a bike? Then that is a specific set of problems represented by the word the. For a small word, it is very important.
If you don't want to hear about all of his many problems, ask only about those problems he has while riding a bike (not the red bike, but any bike.)
I am interested in knowing about the problems John has while riding a bike.
All of the bold-type words are determiners. A determiner is a modifying word that determines the kind of reference a noun or noun group has: a? the? some? all? none? one? these? those? his? her? their? no? Here is a list of determiners.
John is facing a specific set of problems while riding a bike, and you are asking for that specific set. You are interested in the problems John is facing while riding a bike.
Now, while "What are problems John is facing while riding a bike" is ungrammatical, do note that you could ask "What are some [of the] problems John is facing while riding a bike". Just keep in mind that the corresponding answer would then be a partial list.
Ditto many other answers.
Another way to put it is, "The word 'the' is necessary because it is a convention in English." It may not actually convey any information or make the sentence more clear, but it is required by the language. That's just how it is. It's like, Why do men wear a tie when they want to look more formal and dressed up? What useful purpose does a tie serve? Probably none, it's just a convention.
If you use "What is the problem" vs "What is a problem" it might be clearer. In the one without the "the" you're asking for a definition of the word problem. In the other one you're asking for the problem one might have.
