My elder brother is ________ M.A whereas I am only a B.A.

• the
• a
• an
• No article required
Correct Option: C  [ an ]

Remark:

The work took half _______ hour.

• a
• an
• the
• none
Correct Option: B  [ an ]

Remark:

He wrote ________ one-act play.

• the
• an
• a
• no article
Correct Option: C  [ a ]

Remark: "a" is used with "one-act" ( Vowel word with a consonant sound.)
similar: a university, a one-man army, a union

_________ rich and poor, young and old met together.

• a
• an
• the
• zero rticle
Correct Option: D  [ zero rticle ]

Remark:

Let's watch _______ movie; I mean 'Pather Panchali'.

• a
• an
• the
• no article is needed.
Correct Option: C  [ the ]

Remark: "The" used as movie name is specified.(the definite article)

It was ________ unit of measurement.

• the
• an
• a
• no article
Correct Option: C  [ a ]

Remark:

Let us discuss _________ matter seriously.

• the
• an
• a
• no article
Correct Option: A  [ the ]

Remark:

None but _________ brave deserves the fair.

• the
• a
• an
• No article required
Correct Option: A  [ the ]

Remark: here adjective "brave" used as noun. "the brave" means "the brave people".

_____________ rich is not always happy.

• a
• an
• the
• zero article
Correct Option: C  [ the ]

Remark:

My wife and I have _________ appointment.

• an
• a
• the
• none of these.
Correct Option: A  [ an ]

Remark: "an" is used before "appointment" because "appointment" starts with a vowel sound.