Meghwal, a Lok Sabha MP, will handle the party's affairs in the Lok Sabha, while Goel will be in charge of the Rajya Sabha.
The ministers assumed charge in the presence of Union Parliamentary Affairs Minister Ananth Kumar.
Goel, who was the minister of state for sports with independent charge, has been shifted to the parliamentary affairs ministry in the recent Cabinet reshuffle.
He has also been given additional charge of Statistics and Programme Implementation.
Besides parliamentary affairs, Meghwal, who was the minister of state for finance and corporate affairs, has been given additional charge of water resources, river development and Ganga Rejuvenation.
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