The correct answer is "1 only".

Option 1 states that the Governor of Punjab concurrently serves as the Administrator of Chandigarh. This is true as it has been constitutionally mandated so due to Chandigarh being a union territory.

Option 2 says that the Governor of Kerala concurrently works as the Administrator of Lakshadweep. This, however, is incorrect. Lakshadweep is a union territory and is administered by an Administrator appointed by the President of India, not by the Governor of Kerala.

Option 3, stating that both 1 and 2 are correct, is therefore incorrect because option 2 is not correct.

Option 4, stating that neither of the statements is correct, is also incorrect because option 1 is indeed correct.

In conclusion, only the Governor of Punjab serves concurrently as the Administrator of a Union Territory (Chandigarh), but the Governor of Kerala does not serve in the same capacity for Lakshadweep.