Elections for 59 seats in Tripura's 60-member House were held on February 18 and the results will be declared on March 3.
Polling in one Assembly seat has been postponed to March 12, following the death of a CPI(M) candidate.
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The TV channel gave the BJP alliance 35-45 seats and said the Left Front will bag 14-23 seats while one seat will be won by others.
On the other hand, Centre for Voting Opinion & Trends in Election Research (CVoter), a Delhi-based agency, hinted at a close fight and predicted the CPI(M) and Left parties to win in 26-34 seats with 44.3 per cent vote share.
It predicted the BJP alliance to win in 24-32 seats with a vote share of 42.8 per cent and said the Congress might win in two seats with 7.2 per cent vote share.
CPI(M) spokesperson Goutam Das declined to comment on the exit poll predictions saying they these were "speculations".
Das said his party would only issue a statement after the results were declared on March 3.
An alliance between the BJP and the Indigenous People's Front of Tripura (IPFT), an anti Left tribal party, has emerged as a major challenger to the ruling Left Front, which has been at the helm for the last 25 years.
BJP state in-charge Sunil Deodhar said exit polls were not always true. He, however, exuded confidence that his party would win with at least two-third majority in the polls.
State Congress Vice-President Tapas De said exit polls are often done "purposefully" although indications are there that the CPI(M) will retain power in the state.
If you look at the poll predictions of two different agencies, you will find that one shows BJP would come to power by defeating Left Front, and the other predicting that the Left Front would retain power, he said.
Kok Tripura, a cable TV channel among the tribals, which broadcasts programme in Kokbarak -- the language of more than 1 million tribals in the state -- predicted 'possible outcome' only in 20 Scheduled Tribe (ST) reserved seats of Tripura.
The channel predicted that the CPI(M) could win only in 4-7 ST reserved seats while the BJP alliance could win in 13-16 seats.
It said, the Congress, TMC and others would have no presence in the reserved seats.
DinRaat, a local cable TV channel, predicted the Left Front to secure a minimum of 40 seats and maximum 49 seats and the BJP and IPFT alliance to win in 10-19 seats.
The channel predicted the Left parties to win in 15 out of 20 ST reserved seats.
Headlines Tripura a local cable TV channel which broadcast the predictions of 'Peoples pulse', a Hyderabad-based agency, said the BJP-IPFT alliance could secure up to 54 per cent votes this time. However, it did not predict the number of seats the parties will win.
In the 2013 Assembly elections, the ruling Left Front polled 52.32 per cent votes while the opposition Congress-Indigenous Nationalist Party of Tripura (INPT) combine secured 44.60 votes.
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