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The BJP-led NDA candidate won the election comfortably with 528 votes against Ms Alva's 182, the voting for which took place earlier in the day. The Vice President is also the ex officio Chairman of the Rajya Sabha.
Mr Dhankhar secured 74.36 per cent. He has the highest winning margin in the last six vice presidential elections held since 1997.
The returning officer of the vice presidential election said of the total 780 electors, 725 cast their ballots but 15 votes were found to be invalid. The turnout was 92.94 per cent, he said, adding that a candidate needed 356 votes to get elected.
The Trinamool Congress, which has a total of 36 MPs, including 23 in Lok Sabha, had abstained from the election. However, two of its MPs had cast their ballots. As many as 55 MPs did not vote in the vice presidential election held from 10 am to 5 pm on Saturday.
Margaret Alva congratulated Mr Dhankhar on the win. She also thanked leaders of the Opposition, and MPs from across parties who voted for her in this election. "This election is over. The battle for protecting our Constitution, strengthening our democracy & restoring the dignity of Parliament, will continue," she posted on Twitter.
Prime Minister Narendra Modi, along with BJP chief JP Nadda, went to congratulate Mr Dhankhar on on his election as the Vice President.
Mr Dhankhar had the support of several other non-NDA parties - Naveen Patnaik's Biju Janata Dal, Jaganmohan Reddy's YSR Congress, Mayawati's Bahujan Samaj Party, Chandrababu Naidu's Telugu Desam Party, the Jharkhand Mukti Morcha, Akali Dal and the Eknath Shinde faction of the Shiv Sena.
Telangana Rashtra Samithi, Aam Aadmi Party and the nine MPs of Shiv Sena's Uddhav Thackeray faction supported Ms Alva.
Mr Dhankhar will be the second vice president from Rajasthan after Bhairon Singh Shekhawat who held the office between 2002 and 2007.
Joyous scenes were also reported from Rajasthan's Jhunjhunu, the hometown of Mr Dhankhar. Celebrations also took place at the state BJP headquarters in Jaipur where people danced to the beats of dhols and distributed sweets.
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