These questions seem to be about diastereomers and contain some ambiguity about the specifications. For the reaction of 2,5-dimethylcyclopentanol with sulfuric and addition of HCl to the resulting alkene, I am going to presume we get a single intermediate, 3-methylcyclopentene. Addition of HCl to that will give 1-chloro-1,3-dimethylcyclopentane. However, there are now two chirality centers, neither of which should have been stereospecific, therefore a diastereomeric mixture of products result.
For question two, although it states the product is optically active, it does not preclude that it is also a diastereomeric mixture. If it were a single compound, then distillation should give a single fraction. If the answer is there are two fractions, then it is indicating the material was an optically active diastereomeric mixture of alcohols. If I were writing this question, I might ask students to explain how this optically active material could give two fractions and see if anyone could realize that the material had to have been a diastereomeric mixture.
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