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.

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:

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

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

Remark:

My Father, along with others, ___________ worried.

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

Remark:

The team _______ playing well.

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

Remark: "team" is a collective noun and should be treated as a singular entity. Therefore, the verb "is" (singular) used.

Not Amit but his brothers ______ to the store

• walk
• walks
• are walk
• have walk
Correct Option: A  [ walk ]

Remark: If plural subjects are joined by "or," "nor," or "but," the verb must only agree with the subject that is closest to it.

Every girl and every boy ________ given a silver medal.

• are
• was
• has
• have
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.

Ashok as well his brothers _________ coming today.

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

Remark:

While eating he _______ a lot.

• talk
• talks
• talked
• taking
Correct Option: B  [ talks ]

Remark: Singular subject takes singular verb.