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.

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.

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.

While eating he _______ a lot.

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

Remark: Singular subject takes singular verb.

The news ___ very surprising.

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

Remark: "News" is an uncountable noun and always takes a singular verb.

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

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

Remark:

That woman ____________vegetables.

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

Remark:

Mathematics ___ my favorite subject.

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

Remark: "Mathematics" is treated as a singular subject even though it ends in "s".

None of the students ___________ responded.

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

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.