The elections are being held to fill the seats for members retiring in April and May this year.
Bypolls for Araria Lok Sabha seat and the Assembly seats of Jehanabad and Bhabhua are scheduled for March 11.
The results will increase the Bharatiya Janata Party (BJP) tally in the Rajya Sabha. Of the 58, the top three states in terms of the number of seats are NDA-ruled-Uttar Pradesh (10 seats), Bihar and Maharashtra (six each).
The Election Commission on Friday announced that polling for 58 Rajya Sabha seats, set to fall vacant in April, will take place on March 23. Six MPs each would have to be chosen from Bihar and Maharashtra, five MPs each from West Bengal and Madhya Pradesh and four MPs each from Karnataka and Gujarat would be elected during the polls to be held in respective State capitals on 23rd March.
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The NDA's numbers are expected to fall in states like Bihar, where it could win three, unlike the six it now holds, while in Gujarat it is unlikely to retain more than two of the four seats.
The seat has fallen vacant following the resignation of Veerendra Kumar. "Electorally, the BJP under Prime Minister Narendra Modi has done well in the last four years and this electoral strength would now be visible in Rajya Sabha", the BJP leader added.
RJD chief Lalu Yadav had offered to send Ms Mayawati to the upper house from Bihar in July past year after she resigned, accusing the BJP of not allowing her to raise the issue of anti-Dalit violence in Uttar Pradesh. With only seven members in the UP Assembly, Congress stands no chance to manage a seat without support. His insistence on fielding a HAM candidate for Jehanabad Assembly seat was brushed aside by NDA and the seat was allotted to JD (U) earlier this month.
The poll panel said March 12 will be the last day to file nominations, and that votes will be counted on the day of the polls.