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The correct answer is option 1, which states that only statement 1 is correct.
Statement 1 asserts that Muhammad Hamdulla Sayeed, elected from Lakshadweep parliamentary constituency, is the youngest MP in the 15th Lok Sabha. This statement is correct as Muhammad Hamdulla Sayeed was indeed elected as the Member of Parliament from Lakshadweep and held this position at a young age during the 15th Lok Sabha.
On the other hand, statement 2 claims that Agatha K. Sangma is the youngest Union Minister in the 15th Lok Sabha who represents Shillong parliamentary constituency. However, this statement is incorrect. Agatha K. Sangma did serve as a Member of Parliament from the Shillong parliamentary constituency but she was not the youngest Union Minister in the 15th Lok Sabha.
In summary, statement 1 is correct, but statement 2 is incorrect. Therefore, the correct answer is option 1.