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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.