Sinha, Mansingh, Mohapatra and Shakal were last week nominated to the Upper House.
Mansingh, who is among the foremost Indian classical dancers and performs Bharatnatyam and Odissi, took oath in Hindi, while internationally renowed authority on stone carving and architect, Mohapatra, took oath in Odia.
RSS ideologue Sinha, who is the founder and honorary director of the Delhi-based think tank India Policy Foundation, and Shakal took oath in Hindi.
Also taking oath were three newly elected members from Kerala - CPI(M) leader and CITU state general secretary Elamaram Kareem, CPI's Binoy Viswam and Jose K Mani of Kerala Congress (Mani).
Members thumped desks to welcome the newly elected members.