Polling is scheduled for March 23, but with just six candidates for six seats, it may not be required at all.
In Kerala, MP Veerendra Kumar, who walked out of Nitish Kumar-led Janata Dal (United) a year ago, filed his nomination as an independent candidate.
It was BJP national president Amit Shah who informed Muraleedharan, who is now in Shimoga in connection with the Karnataka Assembly elections, about the party's decision on Sunday.
By backing his candidature, CM Devendra Fadnavis is making sure that Rane stays "occupied" in the national capital and steers clear of state politics. Veerendra Kumar's term would have expired in April 2022.
Katiyar had also claimed that Taj Mahal stands at the site of a temple and suggested that it should be re-named Tejo Mandir.
The BJP nominated businessman Rajeev Chandrasekhar as its candidate from Karnataka on Sunday. BJP General Secretary Saroj Pandey will contest from Chhattisgarh, the party's Media Cell Convenor Anil Baluni from Uttarakhand, and Lt General D.P. Vats (retd) from Haryana.
Madan Lal Saini will be the second BJP candidate from Rajasthan.
The selection of Meena, whose equations with Rajasthan Chief Minister Vasundhara Raje are known to have been strained, is seen as an initiative against perceived anti-incumbency. The second seat will be fought by an independent supported by it, sources said. SP spokesperson Sunil Singh Sajan, when contacted said.
Vijay Pal Singh Tomar, another UP candidate, is a prominent farmers' leader. Both leaders belong to the Bundelkhand region, which could be significant in the assembly polls later this year.
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Law Minister Ravi Shankar Prasad, joined the fray once again from his home state Bihar, while Pradhan, minister for petroleum and natural gas, filed his papers from Madhya Pradesh. Muraleedharan's nomination could please the Ezhavas, who represent a significant section of Hindus in Kerala.
Mr Chandrasekhar alleged that the present rule "is the darkest period" in Karnataka's modern political history.
Finance Minister Arun Jaitley filed his nomination papers for the Biennial Elections for the 58 Rajya Sabha seats on Monday in Lucknow.
The Congress with 77 legislators, besides the four Independents and one Bharatiya Tribal Party member, also has the numbers this time to send two members to the Upper House.
Union ministers Purushottam Rupala and Mansukh Mandavia of BJP filed their nominations from Gujarat. JD (U) spokesperson K C Tyagi might be considered later for the seat held by Sharad Yadav.
Rashtriya Janata Dal (RJD) candidates Manoj Jha and Ashfaque Karim were the first to file their nominations.
With their current strength in the assembly, two candidates of the Congress and one from BJP can get elected comfortably.
Meanwhile, in Gujarat, the BJP fielded three candidates on its mandate to counter a possible move by the Congress.
Enraged over the leader's statements, more than 70 social activists had demanded Rajya Sabha Chairman Venkaiah Naidu in February to revoke the membership of the leader from the Upper House "for violating the Constitution".