Solution:

(i) Given: there are five mathematics books and six physics books.

The number of ways to purchase one mathematics book is  ⁵C₁. Similarly, there are ⁶C₁ methods to purchase one physics book. As a result, a student can buy a Mathematics and Physics book in ⁵C₁ × ⁶C₁ = 5 × 6 = 30 different methods.

(ii) Given: there is a total of 11 books.

So, in order to purchase either a Mathematics or a Physics book, only one of the eleven books must be purchased.

As a result, there are ¹¹C₁ = 11 ways for a student to purchase either a Mathematics or a Physics book.