Hydroxylation of trans-but-2-ene results in the formation of

Racemic mixture of Butan-2, 3-diol

The correct answer is option 4. Racemic mixture of Butan-2, 3-diol. 

In trans-but-2-ene, the carbon-carbon double bond is between carbon atoms 2 and 3. When hydroxylation occurs, a hydroxyl group \((-OH)\) is added across this double bond. As a result of hydroxylation, two hydroxyl groups \((-OH)\) are added to the carbon atoms 2 and 3 of the but-2-ene molecule. This results in the formation of butan-2,3-diol. The addition of the hydroxyl group creates a chiral center at carbon atom 2, as this carbon now has four different substituents attached to it: the hydrogen atom, the methyl group, and two hydroxyl groups. A racemic mixture consists of equal amounts of both enantiomers of a chiral molecule. In the case of butan-2,3-diol, the molecule exists as two enantiomers: (2R,3S)-butan-2,3-diol and (2S,3R)-butan-2,3-diol. These enantiomers are non-superimposable mirror images of each other. Option 4 states that the correct product is a racemic mixture of butan-2,3-diol. This means that both enantiomers, (2R,3S)-butan-2,3-diol and (2S,3R)-butan-2,3-diol, are formed in equal amounts during the hydroxylation of trans-but-2-ene. So, the correct answer is option 4, a racemic mixture of butan-2,3-diol, because hydroxylation of trans-but-2-ene results in the formation of a chiral molecule, leading to the formation of equal amounts of its enantiomers.