Which is correct? `The majority of the applicants is not qualified’ or `The majority of the applicants are’?

The second sentence is grammatically correct. `Majority of’ is invariably followed by a plural noun. For example, we say, `majority of students’, `majority of young mothers’ and `majority of cases’. Since the noun in all the examples is plural, the verb that follows must also be plural.

*The majority of students are unwilling to take part in the strike.

When `the majority’ is not followed by `of’, then the verb that follows can be either singular or plural. For example,
*The majority is of the opinion that we must go on strike. *The majority feel threatened by the possible changes.
Source: ‘Know Your English’ ( The Hindu) – April 3, 2006

Is it OK to say, `None of them have… ‘?

 People who love their grammar would argue that the sentence is wrong. They would want `none’ to be followed by the singular verb `has’. In informal contexts, however, there is a tendency, even among native speakers of English, to use the plural `have’. In American English, it is very common for people to say, `None of the movies were a hit’ and `None of the guys were good looking’.

Sourced from The Hindu ‘Know Your English’ Series, October 24, 2005