Select the most appropriate word to fill in the blank.

All his endeavors to win his teacher's favour proved ______ and did not bring the desired results.

futile

The most appropriate word to fill in the blank is futile.

The word "futile" means useless, ineffective, or pointless. It is the most appropriate word to use in this context, as it conveys the meaning of the student's efforts being unsuccessful and not achieving the desired outcome.

The other options are not as appropriate.

• Perpetual means lasting or continuing for an indefinitely long time. This is not the right word to use, as it does not make sense to say that the student's endeavors were perpetual.
• Apparent means easily seen or understood. This is not the right word to use, as it does not make sense to say that the student's endeavors were apparent.
• Prosperous means successful and thriving. This is not the right word to use, as it does not make sense to say that the student's endeavors were prosperous.