The expressions half of and none (of) may take either a singular or a plural verb when the noun they modify is countable. Otherwise, the verb must be singular.
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None of our graduates has had problems gaining a grant for further studies. |
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None of our graduates have had problems gaining a grant for further studies. |
The expression the majority (of) takes a plural verb if the following noun is a collection of individuals.
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The majority of our graduates have had no problem gaining a grant for further studies. |
When a number (of) means several, it takes a plural verb.
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A number of applications are still to come. |
Meanwhile, the number (of) takes a singular verb.
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The number of applications is small. |