Select the most appropriate pair of determiners to fill in the blanks…

The correct answer is Option (3) → any, some

Determiners "any" and "some":

• Any is used in questions and negative sentences, with uncountable nouns (news) as well as plurals.
• Some is used in positive statements for an unstated number or amount.
• This sentence:
  • the first blank is in a question about news, so "Have you had any news?"
  • the second is a positive statement about an unstated number of areas, so "I heard that some areas were badly flooded".
  • Complete sentence: Have you had any news from your family in Mumbai? I heard that some areas were badly flooded.

Why the Other Options are Incorrect?

Option 1: no, both — Incorrect.

• "Have you had no news" turns the friendly question into a surprised one.
• Both refers to two things already named, but no two areas have been mentioned.
  Example: Both my brothers live in Pune.

Option 2: much, few — Incorrect.

• "Much news" can work in a question.
• But few means "hardly any", which plays down the floods instead of reporting them as a worry.
  Example: Few people came to the meeting, so it was cancelled.

Option 4: a, much — Incorrect.

• News is uncountable, so "a news" is wrong.
• Much cannot go with a countable plural like areas.
  Example: We don't have much time left.

Contrast: any goes in questions and negatives. Some goes in positive statements.