Number of isomers of C8H10 that give only aromatic dicarboxylic acid:
To determine the number of isomers of C8H10 that give only aromatic dicarboxylic acid when reacted with hot alkaline KMnO4, we need to understand the reaction mechanism.

1. Oxidation of xylene:
The first step in the reaction is the oxidation of xylene (C8H10) by hot alkaline KMnO4. Xylene has three isomers: ortho-xylene, meta-xylene, and para-xylene.

2. Formation of aromatic dicarboxylic acid:
When oxidized, ortho-xylene gives ortho-phthalic acid, meta-xylene gives isophthalic acid, and para-xylene gives terephthalic acid. These are the three aromatic dicarboxylic acids that can be obtained from the respective isomers of xylene.

3. Isomers that do not give aromatic dicarboxylic acid:
There are other isomers of C8H10 that do not give aromatic dicarboxylic acid when reacted with hot alkaline KMnO4. These isomers may give different products or may not undergo complete oxidation.

Number of isomers of C4H8 that give carbon dioxide:
To determine the number of isomers of C4H8 that give carbon dioxide when reacted with hot alkaline KMnO4, we need to understand the reaction mechanism.

1. Oxidation of butene:
The first step in the reaction is the oxidation of butene (C4H8) by hot alkaline KMnO4. Butene has two isomers: 1-butene and 2-butene.

2. Formation of carbon dioxide:
When oxidized, both isomers of butene give carbon dioxide as the product. This is because the double bond in butene is completely oxidized, resulting in the formation of two carbonyl groups.

Sum of x and y:
The sum of x and y is 5 because there are 3 isomers of C8H10 (ortho-xylene, meta-xylene, and para-xylene) that give aromatic dicarboxylic acid and 2 isomers of C4H8 (1-butene and 2-butene) that give carbon dioxide. Therefore, 3 + 2 = 5.

In summary, the number of isomers of C8H10 that give only aromatic dicarboxylic acid is 3, and the number of isomers of C4H8 that give carbon dioxide is 2. The sum of these isomers, x and y, is 5.