Senior BJP leader SS Ahluwalia failed to retain his seat.
Mr Ahluwalia finished third with 20 votes while Congress' Pradip Kumar Balmuchu secured 25 votes. The JMM's Sanjeev Kumar bagged 23.
A total of 68 votes were polled in the 82-member state assembly. Eleven members of Jharkhand Vikas Morcha (Prajatantrik) and the lone MLA of CPI(ML-Liberation) abstained from voting.
There is a nominated member but the seat is vacant.
The BJP is heading the ruling coalition in Jharkhand in partnership with the JMM although both parties have 18 MLAs each.
Today's Rajya Sabha poll was rescheduled after it was countermanded on March 31 in the wake of allegations use of money power and horse-trading which the Election Commission said had "vitiated" the electoral process to the upper house in the state. Rs 2.15 crore was seized from the car of a relative of an independent candidate R K Agarwal.
Mr Ahluwalia was denied nomination by BJP in the earlier round of Rajya Sabha elections when about 50 seats had been decided and he was fielded only after the countermanding of the poll in Jharkhand.
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