A Governor can make recommendations to the President on certain issues. Option 1, which states "Dismissal of the State Council of Ministers," is correct. The Governor has the power to recommend the dismissal of the State Council of Ministers if they are not functioning in accordance with the constitution or if they are not able to prove their majority in the State Legislative Assembly.

Option 2, "Removal of the Judges of the High Court," is incorrect. The Governor does not have the power to recommend the removal of High Court judges. This power lies with the President or in some cases, the Chief Justice of India.

Option 3, "Dissolution of the State Legislative Assembly," is correct. The Governor can recommend the dissolution of the State Legislative Assembly if a situation arises where a government cannot be formed or if the existing government is unable to function.

Option 4, "Declaration of the breakdown of the Constitutional machinery in the State," is correct. The Governor can recommend the declaration of the breakdown of the Constitutional machinery in the state if there is a situation of complete breakdown of law and order, or if the state government is unable to function properly.

Therefore, the correct answer is (a) 1, 3, and 4.