The given question is:

Which one of the following statements is not correct about the nature of India’s federal system?

The options and their respective correctness are:

1. There is no equality of representation of States in the Council of States. - This statement is correct as the representation of states in the Council of States (Rajya Sabha) is not based on equal representation, rather it is based on the population of the state.

2. Sikkim was not initially included in the Union as a full-fledged State. - This statement is correct as Sikkim was initially included in the Indian Union as a protectorate and later became a full-fledged state in 1975.

3. Special provisions have been laid down in the Constitution of India for Andhra Pradesh under Article 371 D. - This statement is correct as Article 371D provides for special provisions with respect to the administration of Andhra Pradesh.

4. The Constitution of India enables the federal government to acquire the strength of a unitary system during emergencies. - This statement is not correct as the Indian Constitution does not allow the federal government to acquire the strength of a unitary system during emergencies. The Constitution of India provides for a federal system with a distribution of powers between the central government and the state governments.

Therefore, the correct answer is option 4.