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:

None of the students ___________ responded.

• have
• were
• is
• has
Correct Option: A  [ have ]

Remark:

Sir, our list of grievances here ________ a long one.

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

Remark: "list" is a singular noun, and when referring to a singular entity, the verb should also be singular.

The modern student _________ the importance of physical exercise.

• understood
• understand
• have understand
• understands
Correct Option: D  [ understands ]

Remark: singular subject (i.e student) takes singular verb (i.e understands).
Note: generally verb ends with "s" is singular.

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 public _______ the thief red-handed.

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

Remark:

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

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

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.

All the planets ________ around the earth.

• moving
• moves
• move
• has moves
Correct Option: C  [ move ]

Remark:

Each of the students _______ given a task to complete.

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

Remark: If a subject is modified by the words "each" or "every" that subject is singular and will take a singular verb.