Neither John nor Alex __________ scored the century.

• have
• was
• has
• is
Correct Option: C  [ has ]

Remark: in case "Neither-Nor" the verb must agree with the second subject (the subject closer to the verb).

The horse and the coach ________ arrived.

• have
• have been
• would
• has
Correct Option: A  [ have ]

Remark: When two singular nouns joined by "and" refer to the same person or thing, the verb is singular.
But here article "the" used twice before each noun to indicate two different subjects, thus "have" used.

Everyone _______ at the party.

• dance
• dances
• are dances
• have dances
Correct Option: B  [ dances ]

Remark: "everyone" is considered a singular pronoun (subject), singular verb should be used.

Each of the students ________ responsible for keeping this room clean.

• are
• has
• is
• have
Correct Option: C  [ is ]

Remark:

Unless we ______ now we can't be on time.

• will start
• start
• starts
• will be starting
Correct Option: B  [ start ]

Remark:

The jury _______ divided in their opinion.

• were
• was
• have been
• have
Correct Option: B  [ was ]

Remark: "jury" is treated as a collective noun, and when referring to the group as a whole, generally we use a singular verb "was."

Ashok as well his brothers _________ coming today.

• are
• were
• had been
• is
Correct Option: D  [ is ]

Remark:

A bouquet of flowers ___ on the table.

• is
• are
• was
• were
Correct Option: A  [ is ]

Remark: The subject "bouquet" is singular, so it takes a singular verb.

Most of the labourers _____________ on the strike.

• is
• has
• are
• have
Correct Option: C  [ are ]

Remark:

The members of the committee ___ divided in their opinions.

• is
• are
• have
• has
Correct Option: B  [ are ]

Remark: When the members of a collective noun act individually, the plural verb is used.