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The correct answer is option 3: 1 and 3 only.
Let`s dissect each option to understand why this is the correct answer:
Option 1: The statement says that the Lodge was built by the 17th Viceroy, Earl Dufferin. However, this statement is incorrect. The Viceregal Lodge at Shimla was actually built during the period of Lord Dufferin, who was the 17th Viceroy of India.
Option 2: The statement claims that the present shape of the building was given by the Earl of Marquis of Lansdowne. This statement is not mentioned in the question, so we cannot determine its correctness or incorrectness based on the given information.
Option 3: The statement states that the Viceregal Lodge is famous for holding three meetings before the Independence of India, including the Cabinet Mission. This statement is correct, as mentioned in the question.
Option 4: The statement claims that the Lodge was built by the Earl of Marquis of Lansdowne, which contradicts the information provided in option 2. Therefore, this statement is incorrect.
In conclusion, option 3 is the correct answer as it includes the only correct statement provided in the question.