Choose the grammatically correct sentence:

The correct answer is Option (4) → One of my friends has moved to Pune with his family.

"One of" + plural noun takes a singular verb:

• In "one of my friends", the subject is one, not "friends". "One" is singular, so the verb is singular: has moved.
• "His" is also correct, as it stands for one friend.

Why the Other Options are Incorrect?

Option 1: Neither the coach nor the players was happy with the result. — Incorrect. With "neither ... nor", the verb agrees with the subject nearer to it. Here that is "players", which is plural.
Corrected: Neither the coach nor the players were happy with the result.

Option 2: She is senior than me in the school choir. — Incorrect. "Senior" is followed by "to", not "than". Junior, superior and inferior also take "to".
Corrected: She is senior to me in the school choir.

Option 3: The news of the results were announced in the morning assembly. — Incorrect. "News" ends in -s, but it is a singular noun. So the verb must be singular.
Corrected: The news of the results was announced in the morning assembly.