Explanation:

- The original sentence has an error in the placement and form of the adverb "careful." It should describe the verb "examined," so it needs to be in its adverbial form.

- Option 1: carefully examined

This option correctly uses the adverb "carefully" to describe how Viren examined the possibilities.

This is the correct choice.

- Option 2: No improvement required

The sentence requires improvement, so this option isn’t correct.

- Option 3: examine careful

This option maintains the incorrect form of "careful" and adds another error in verb tense.

- Option 4: careful examined

This uses the incorrect form "careful" and incorrect word order.