WRONG
There is a number of possible solutions that we can discuss.
RIGHT
There are a number of possible solutions that we can discuss.
WRONG
A number of protesters was seen outside the premises.
RIGHT
A number of protesters were seen outside the premises.
The phrase “a number of” is always followed by a plural verb, NOT a singular verb.
This is rather exceptional because “a number” is singular while the verb it goes with is in the plural. We do this because “a number of” means “several”, so refers to the plural. We use the plural verb to match the plural meaning of the phrase, NOT its singular grammar.
Common Mistakes in Business English 
This confusing because the book I’m reading presently says it goes with a singular verb.
Quite confused right now.
The book I read said it goes with a verb in the plural! I say in the post that it is exceptional, and I also say that we use a plural verb to match the plural meaning, rather than a singular verb to match the singular grammar. It is an example of when meaning trumps grammar in terms of word agreement. But – as seems to be the case with your book – not everyone agrees. There are numerous examples of that too.
If you are communicating with native English speakers I suggest you use the rule I’ve given here. If you are taking an exam written by non-native speakers, you might be better off using a singular verb.