The answer to this question is option 'D', which means that there are 4 generators in a cyclic group of order 10. To understand why this is the correct answer, let's break it down step by step.

A cyclic group is a group that is generated by a single element. In other words, all the elements in the group can be obtained by repeatedly applying the group operation to the generator.

- Definition of a generator:
A generator of a group G is an element g in G such that every element of G can be expressed as a power of g. In other words, for any element x in G, there exists an integer k such that x = g^k.

- Order of an element:
The order of an element x in a group G is the smallest positive integer n such that x^n = e, where e is the identity element of G. In a cyclic group of order n, every element has an order that divides n.

- Number of generators in a cyclic group:
For a cyclic group of order n, the number of generators is equal to the number of positive integers less than n that are coprime to n. Two numbers are said to be coprime if their greatest common divisor (GCD) is 1.

- Calculating the number of generators for a cyclic group of order 10:
The order of the group is 10. Now, we need to find the positive integers less than 10 that are coprime to 10. These numbers are 1, 3, 7, and 9. Therefore, there are 4 generators in the cyclic group of order 10.

In summary, the answer to the question is option 'D' because there are 4 positive integers less than 10 that are coprime to 10, and each of these integers can act as a generator for the cyclic group of order 10.