The BJP's vote share marked a three percent swing in its favour, while the Congress faced a loss of one percent votes and JD-S two percent, it said.
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Others were expected to win around 2-4 seats, the exit poll said.
The saffron party emerged winners in the first phase of the poll held on May 10 when polling was held in 89 seats, according to the exit poll by the channel on that day.
After exit polls covering 155 seats (more than half of the total of 224), the BJP has been projected to get 73 seats, the Congress 45 and the JD-S 42.
The third and final phase of polling will cover 69 seats.