The appointments were approved by the PM Manmohan Singh-led appointments committee of cabinet.
Sinha, a 1977-batch IAS officer of the Uttar Pradesh cadre, is at present secretary in the ministry of shipping. The vacancy was necessitated following superannuation of incumbent P Uma Shankar on Friday.
A 1979-batch IAS officer of West Bengal cadre, Sarkar has been appointed in place of PK Mishra (1976-batch IAS officer of the UP cadre).
Sarkar, at present secretary in the water resources ministry, has earlier served as additional secretary in the DoPT.
Trivedi, a 1977-batch IAS officer of the Madhya Pradesh cadre, has replaced Sinha following his new appointment. He is currently chairman, Inland Waterways Authority of India.
Senior IAS officer Alok Rawat has been appointed as secretary in the ministry of water resources, a government press release said.
The 1977-batch officer of the Sikkim cadre is secretary (coordination and public grievances), in the Cabinet Secretariat.