We have to get the correct alkyne which after undergoing an acid-catalyzed hydration, would be expected to produce two different ketones in nearly equivalent yields.
The answer is: 2-hexyne
Acid catalyzed hydration of alkyne produces ketone (except acetylene, as only acetylene gives aldehyde on hydration).
2-Hexyne on hydrolysis produces 2-hexanone and 3-hexanone where they both are ketones and they both are different ketones.
4-methyl-1-pentyne gives 4-methyl-2-pentanone and 4-methyl-1-pentanal (non equivalent mixture), where both are not ketones, one aldehyde and one ketone.
1-hexyne gives 2-hexanone and 1-hexanal where one is ketone and other one is aldehyde.
3-methyl-1-pentyne gives 3-methyl-2-pentanone and 3-methyl-1-pentanal (non equivalent mixture), where both are not ketones, one aldehyde and one ketone.
3-hexyne gives two equivalent amount of 3-hexanone.