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He is to solve these questions.
He is about to solve these questions.
What are the differences between these two sentences in terms of meaning? Would any of you mind directing me to a question ,if there is one, related to the structure of "noun+be+to+verb+"?
be to do something (formal)
a) used to talk about arrangements for the future:
Audrey and Jimmy are to be married in June.
Two men are to appear in court on charges of armed robbery.
b) used to give an order or to tell someone about a rule:
You are to wait here in this room until I return.
All staff are to wear uniforms.
c) used to say or ask what someone should do or what should happen:
What am I to tell her?
He is not to be blamed.
d) used to ask how something can be done:
How are we to get out of the present mess?
Source :Longman Dictionaries
And also you can check out
http://www.macmillandictionary.com/dictionary/british/be-to-do-something
be about to do something
Intend to do something, or be close to doing something, very soon:
The ceremony was about to begin
Source : Oxford Dictionaries
Based on what I've been studying and according to Avanced grammar in use by Martin Hewings, I guess in the first sentence he is likely in to solve the questions in the near future, on the other hand, in the second one, he is likely to solve the question in the "very" near future, so he will do it almost immediately.
