am sure experts will reply. In the mean while, here are my 2 cents.

Collective noun takes a singular verb when the collection is thought of a one whole and it takes a plural verb when the individuals of which it is composed are thought of.

The committee has issued its report
The committee are divided on one minor point

As far as article A/The is concerned:

The is definitive article used to point a particular thing or person.
A is indefinite article.

source: the good old High School English Grammar by Wren and Martin.

So, based on the context, one decides whether the Subject is acting as a whole or individual parts and use singular or plural verb accordingly.

HTH!!

gmat_perfect wrote:
A majority of railway commuters reads or listens to music while traveling - is correct

The majority of the students in this class are hard workers - is correct

The majority of students are smart.
A majority of students are smart.
The majority of physics students are smart.
A majority of physics students are smart.

In all above cases "majority of physics students" is acting as a plural subject and hence takes plural verb

some more examples:

A majority of railway commuters are listeners of sufi music.... context changed, now subject is acting as plural
The majority of railway commuters are monthly pass holders.
A majority of railway commuters drinks starbucks coffee
A majority of railway commuters is young singles

context is the key.

HTH!!