They are used in similar ways to a lot of and lots of, but they are more formal.
A great deal of and a large amount of are generally used with uncountable nouns.
- I have spent a great deal of time thinking of the design.
- You have got rid of a large amount of old clothing.
A large number of is used before plurals, and the verb that follows is plural.
- Despite the instructions, a large number of people didn’t know what to do.
It is true that in standard English speech, it is quite common to use a plural noun after a great deal of and a large amount of, however when taking an exam, it is better to follow their usage rule.