The two, accompanied by former deputy chief minister Sushil Kumar Modi, Leader of Opposition in Bihar Assembly Nand Kishore Yadav and a large number of legislators, submitted their nomination papers to the Assembly Secretary.
BJP has chosen to re-nominate Thakur and selected Sinha, who has his roots in RSS, for the Rajya Sabha.
With its strength of 91 MLAs, the party would have no problem in sending the two to the Rajya Sabha.
Thakur served as Union Health Minister in the NDA government of Atal Bihari Vajpayee.
Tuesday is the last date for filling nominations for the biennial election slated for February 7.
The three JD-U candidates -- Ramnath Thakur, son of the late veteran socialist leader Karpoori Thakur, Kahkasha Parveen and journalist Haribansh are yet to file their nominations.