Explanation:

India celebrated $75$ years of its independence in $2022$. To commemorate this significant milestone, the Government of India launched a special initiative. \nOption (A) Azadi Ka Amrit Mahotsav: 'Azadi Ka Amrit Mahotsav' is the official initiative launched by the Government of India to celebrate and commemorate $75$ years of progressive India and the glorious history of its people, culture, and achievements. The Mahotsav commenced on $12$ March $2021$ and concluded on $15$ August $2023$. 'Amrit' signifies nectar, symbolizing the invaluable contributions and sacrifices that led to India's independence. Therefore, this option is correct. \nOption (B) Azadi Ka Swarnim Mahotsav: 'Swarnim' means golden. While 'Swarnim Vijay Varsh' was celebrated to mark $50$ years of India's victory in the $1971$ war, 'Azadi Ka Swarnim Mahotsav' is not the official name for the $75^{th}$ independence anniversary celebrations. Therefore, this option is incorrect. \nOption (C) Azadi Ka Parv: 'Parv' means festival. While the celebration is indeed a festival of independence, 'Azadi Ka Parv' is not the official name given to the event series. Therefore, this option is incorrect. \nOption (D) Azadi Ki Yatra: 'Yatra' means journey. While India's journey since independence is celebrated, 'Azadi Ki Yatra' is not the official name for the event series commemorating $75$ years of independence. Therefore, this option is incorrect. \nTherefore, 'Azadi Ka Amrit Mahotsav' is the correct event series inaugurated to mark $75$ years of India's Independence.