Fill in the blanks with the correct pair of words arranged sequential…

The correct answer is Option (1) → am convinced, are

Tense and subject-verb agreement:

• Clue word: "now" shows a present state of mind, so the first blank needs the simple present am convinced.
• The verb agrees with its real subject, not with a noun in a phrase that comes between them.
• The subject of the second clause is "views" (plural); "on how to control pollution" only describes it. So the plural verb are is needed.
• Two-step check: 1. tense of the first blank ("now" → am convinced); 2. agreement in the second blank ("views" → are).
• Complete sentence: I am convinced now that his views on how to control pollution are worth listening to.
  Example: The price of these shoes is too high.

Why the Other Options are Incorrect?

Option 2: am convinced, is — Incorrect.

• Blank 1: "am convinced" is right.
• Blank 2: "is" does not agree with the plural subject "views".

Option 3: was convinced, is — Incorrect.

• Blank 1: "was convinced" puts the belief in the past, against the clue word "now".
• Blank 2: "is" does not agree with "views".

Option 4: have been convinced, is — Incorrect.

• Blank 1: "have been convinced" is less natural with "now" than the simple present "am convinced".
• Blank 2: "is" does not agree with the plural subject "views", so the pair cannot be correct.