What ketones would be formed from the acid-catalyzed hydration of 3-heptyne?

The answer would be heptan-3-one and heptan-4-one.

The acid-catalyzed hydration of a balanced alkyne gives a ketone.

R-C≡C-R + H₂O → R-CH₂-CO-R

If the alkyne is uneven, you get a combination of two ketones, since the O can increase to either of the alkyne C atoms.

R-C≡C-R' + H₂O → R-CH₂-CO-R' + R-CO-CH₂-R'

So, for CH₃CH₂CH₂-C≡C-CH₂CH₃, the products are

CH₃CH₂CH₂-CH₂-CO-CH₂CH₃ and CH₃CH₂CH₂-CO-CH₂-CH₂CH₃

Their terms are heptan-3-one and heptan-4-one,