Which of the following is/are incorrect `IUPAC` name/ (s):

Explanation

To determine which of the provided IUPAC names are incorrect, we will analyze each name step by step.

### Step 1: Analyze the first name - 2-methyl butane-3-ole
1. Identify the functional group: The name suggests a ketone (indicated by "ole").
2. Determine the correct numbering: The ketone should be given the lowest possible number.
- If we number from the left, the ketone is at position 3 (butane-3-ole).
- If we number from the right, the ketone is at position 2 (butane-2-ole).
3. Since the ketone has a higher priority than the methyl group, we should start numbering from the end closest to the ketone.
4. The correct name should be 2-methylpentan-3-one, as the longest chain is 5 carbons (pentane) and the ketone is at position 3.

**Conclusion for Step 1**: The name 2-methyl butane-3-ole is incorrect.

### Step 2: Analyze the second name - 4-ethenyl-1-pentene-4-yne
1. Identify the functional groups: There is a double bond (alkene) and a triple bond (alkyne).
2. Determine the correct numbering: Alkenes have a higher priority than alkynes.
- Start numbering from the end closest to the double bond.
- The correct numbering gives the double bond at position 1 and the triple bond at position 4.
3. The correct name should be 4-ethenyl-1-pentene-4-yne, as it accurately reflects the structure.

**Conclusion for Step 2**: The name 4-ethenyl-1-pentene-4-yne is correct.

### Step 3: Analyze the third name - 2-hydroxy-4-methylpentan-3-one
1. Identify the functional groups: There is an alcohol (hydroxy) and a ketone.
2. Determine the correct priority: The ketone has a higher priority than the alcohol.
3. The correct numbering should start from the end closest to the ketone.
- The longest carbon chain is 5 carbons (pentane).
- The ketone should be at position 3, and the hydroxy group should be at position 2.
4. The correct name should be 2-hydroxy-4-methylpentan-3-one, which reflects the correct priority of functional groups.

**Conclusion for Step 3**: The name 2-hydroxy-4-methylpentan-3-one is incorrect because it treats the alcohol as the primary functional group instead of the ketone.

### Final Conclusion:
The incorrect IUPAC names are:
1. 2-methyl butane-3-ole
2. 2-hydroxy-4-methylpentan-3-one

### Summary of Incorrect Names:
- The first name (2-methyl butane-3-ole) is incorrect due to improper functional group priority.
- The third name (2-hydroxy-4-methylpentan-3-one) is incorrect for the same reason.