grammaticality - "There exists some people..." or "There exist some people..."?

I know the usage of

This is a new car.

This is singular.

These are some books for you.

These is plural.

Shall we use

1. There exists some people who agree with me.




2. There exist some people who agree with me.

Which one is the correct usage and why?

Answer

There exist some people who agree with me.

The subject of the sentence is people, which is plural.

Because of subject-verb-agreement, we need a plural verb to match the plural subject ("people"). The plural form of the verb is exist.