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The correct answer to the question is option 1: The Supreme Court of India.
The Supreme Court of India is the highest judicial authority in the country and has the power to inquire and decide in case of doubts and disputes arising out of the election of the President and Vice President of India.
Option 2, the Election Commission of India, is responsible for conducting elections and ensuring their fairness, but it is not the constitutional authority that decides disputes related to the election of the President and Vice President.
Option 3, the Parliamentary Committee, is a group of members of parliament that reviews and analyzes various matters, but it does not have the authority to decide disputes related to the election of the President and Vice President.
Option 4, the High Court of Delhi, is a high court that has jurisdiction over the National Capital Territory of Delhi, but it does not have the authority to decide disputes related to the election of the President and Vice President of India.
Overall, the Supreme Court of India is the constitutional authority that has the power to inquire and decide in case of doubts and disputes arising out of the election of the President and Vice President of India.