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.

The boy in the bus ________ like your brother.

• look
• looks
• looking
• have been looked
Correct Option: B  [ looks ]

Remark:

Neither the books nor the magazine ________ on the shelf.

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

Remark: The verb agrees with the closer part of the subject, which is "magazine" in this case. Here "Magazine" is singular subject, so "was" used.

The public _______ the thief red-handed.

• catch
• caught
• is caught
• catching
Correct Option: B  [ caught ]

Remark:

Neither of the two stores _________ open.

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

Remark: Sentence begins with "neither" or "either" without the "or/nor" combination, the verb is singular.

The student, as well as his teacher ________ going on the excursion.

• have
• has
• were
• was
Correct Option: D  [ was ]

Remark:

One person __________ and several others were injured as the police opened fire on protesters.

• were killed
• was killed
• had killed
• was killing
Correct Option: B  [ was killed ]

Remark:

The Prime Minister with all the members of his cabinet __________ arrived.

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

Remark:

That woman ____________vegetables.

• sells
• sell
• have sold
• selling
Correct Option: A  [ sells ]

Remark:

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.