Consider the following statements:
1. The Legislative Council of a state in India can be larger in size than half of the Legislative Assembly of that particular state.
2. The Governor of a State nominates the Chairman of the Legislative Council of that particular state.
Which of the statements given above is/are correct?

The correct option is Neither 1 nor 2.

Let us analyze each statement step-by-step to understand why both are incorrect:

Analysis of Statement 1:
According to Article 171(1) of the Constitution of India, the total number of members in the Legislative Council (Vidhan Parishad) of a State shall not exceed one-third of the total number of members in the Legislative Assembly (Vidhan Sabha) of that State. Furthermore, the total number of members in the Legislative Council of a State shall in no case be less than 40. Since the size of the Legislative Council is constitutionally limited to a maximum of one-third (and not half) of the Legislative Assembly, Statement 1 is incorrect.

Analysis of Statement 2:
According to Article 182 of the Constitution of India, the Legislative Council itself chooses two members of the Council to be respectively Chairman and Deputy Chairman thereof. The Governor of the State does not nominate the Chairman of the Legislative Council. Therefore, Statement 2 is also incorrect.

Since both Statement 1 and Statement 2 are incorrect, the correct option is "Neither 1 nor 2".