Answer (with explanation):
a. in
Come in the classroom. You walk into the classroom, so it's 'in'.
b. at
They will stay at the hotel. The 'they' will stay at a place. So, you say 'at' not in.
c. in
Milk stays in or inside the jug, we don't want it to be outside or it would spill. So, it's 'in'.
d. in
Similar to (b.), the sentence is talking about a place. The 'man' will be living in a place. So, the answer is 'in'.
e. by <--(this sentence doesn't make any sense for any of the choices...)
In American or U.S.A English, we don't have this kind of sentence (we don't talk like this). The answers I provided you are all 100% actual English. However, my best guess is 'by' but the use is outdated.
We would usually say: "His name is not Hari."