NEW DELHI, January 29 (Reuters) - Two of Prime Minister Narendra Modi's main political opponents opened their joint campaign on Sunday to win a crucial election in Uttar Pradesh, India's most populous state, which heads to the polls next month. Home to 200 million people and India's most important region politically, Uttar Pradesh will help shape Modi and his Bharatiya Janata Party's (BJP) chances of winning a second term in national elections in 2019. The chief minister of Uttar Pradesh and president of the Samajwadi Party, Akhilesh Yadav, and the vice-president of the Congress party, Rahul Gandhi, smiled and hugged for the cameras in a show of personal and political unity. "We are going to fight united and we are going to defeat the BJP," Gandhi, 46, told reporters in the state capital, Lucknow, before the two headed off for their first campaign roadshow. In Uttar Pradesh, a poor and agrarian state, people tend to vote along social and religious lines. With no one community dominant, political parties struggle to win unless they can convince more than one social group to back them. The alliance brings together two parties that have previously won a large share of Muslim voters. Muslims account for 19 percent of Uttar Pradesh's population. Another party in the state, led by politician Mayawati, is also wooing their vote. BJP minister Mahesh Sharma said the Congress and Samajwadi party tie-up was a "desperate and opportunistic alliance". Modi has invested huge political capital in winning Uttar Pradesh, holding a series of rallies and trumpeting the benefits of his controversial decision to abolish high-denomination banknotes in November. Congress, run by the Nehru-Gandhi dynasty that has ruled India for most of its existence, has watched its voter base shrink in recent years. The alliance offers it a chance for a limited comeback. Akhilesh Yadav, 43, is a relatively popular leader and regarded as the modern face of his party after he triumphed in a bruising battle with his father for control of their party. Voting in Uttar Pradesh begins on Feb. 11. The election is set to be the world's largest democratic exercise this year. Four other Indian states also head to the polls, with results due on March 11.