check and correct

[Allifathima]

1. The effectiveness of teaching and learning depends on several
factors.
2. One of the most serious problems that some students have is
lack of motivation.
3. It was always the brightest students who was asked to answer
the question.
4. The police is investigating the incident.
5. Ten years are a investigating the incident.
6. Some of the fruit were going bad.
7. Every one of us was given a prize.
8. Neither of the governments is willing to give way.
9. Bread and butter was all we had to eat.
10. Either the landlord or his wife was telling the truth.
11. Neither Ram nor Shyam was present.
12. Neither the principal nor the teachers is in favour of the proposal.
Could anyone check the above sentences, please.

[Beeesneees]

3. It was always the brightest students who were asked to answer the questions.
4. The police service is investigating the incident. / The police are investigating the incident.
5. does not make sense at all.
6. Some of the fruits were going bad. / Some of the fruit was going bad.
10. is correct but in casual modern English you are just as likely to hear 'were' used.
12. Neither the principle nor the teachers are in favour of the proposal. (Here, there is not the same issue as we see in 10, because the nearest noun to the verb is plural).

The rest are good.
_________________
Cheers m' dears!

[Allifathima]

1. Both men have not come.
2. Both answers are not correct.
Please correct.

[Beeesneees]

Neither man has come.
Neither answer is correct.
_________________
Cheers m' dears!

[Allifathima]

Neither of the children wants to go to bed.
Neither of the children want to go to bed.
Which one is correct?

[Beeesneees]

Strictly speaking, 'neither' takes a singular verb, however, you will note in 12 above that where the idea of plurality is very strong, exceptions are often made.

Here are examples from the BBC World Service (I don't know whether you can access the actual BBC pages from your location, so I've pasted more than I usually would).

subject-verb agreement with ‘quantity’ determiners
The quantity determiners any, either, neither and none are sometimes used with a singular verb and sometimes used with a plural verb when they function as the subject of the clause.

Although the singular verb may be formally correct, in usage there is no strong preference for one or the other. So I think you may feel free to choose whichever you think best, depending, perhaps, on how strong you think the idea of plurality is.
Compare the following pairs and see which you prefer:
I invited four policemen to my wedding but none was present.
I invited four policemen to my wedding but none were present.
I have two sisters but neither of them is married.
I have two sisters but neither of them are married.
I don’t think either of them deserves a husband.
I don’t think either of them deserve a husband.
I don’t think any of the children is invited to the wedding reception.
I don’t think any of the children are invited to the wedding reception.

The idea of plurality is also very strong in the following pair of sentences so either singular or plural verb form is possible:
The audience was applauding like mad and stamping their feet in excitement.
The audience were applauding like mad and stamping their feet in excitement.

http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv128.shtml

Neither of them is or neither of them are?
Although this of-pronoun is normally considered singular, it is normally followed by plural nouns or pronouns. Thus, the boundary between singular and plural is blurred and effectively it can go with either a singular or plural verb form. Strictly speaking, it should be singular, but you will hear both formulations with no clear preference for one or the other:

Neither of them are coming. They both have to work next weekend.
Neither of them is coming. They both have to work next weekend.
Which of these umbrellas is yours? ~ Neither of them are. That one's mine.
Which of these umbrellas is yours? ~ Neither is. That's mine.
There is similar confusion, I think, when neither...nor are employed as conjunctions, meaning not one and not the other. Consider the following:
Neither Francoise nor Helmut likes to eat English breakfasts, even at weekends.
Neither Franciose nor Helmut like to eat English breakfasts, even at weekends
Neither Emma nor Susan gets on with Chloe.
Neither Emma nor Susan get on with Chloe.

http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv113.shtml
_________________
Cheers m' dears!

[Allifathima]

Beeesneees,
Thanks a lot for quoting from the BBC World Service.