Mr Kumar's alliance won 143 seats in the 243-member assembly
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The new chief minister for the most crime-ridden state in India, Bihar, has been sworn in having pledged to restore law and order.
The new leader, Nitish Kumar, is a former railway minister and head of the National Democratic Alliance in Bihar.
His victory ended 15 years of rule of the Rashtriya Janata Dal, a key ally of the Congress Party, and its charismatic leader Laloo Prasad Yadav.
Mr Kumar says his success was a victory for people who had voted for change.
Two elections
Mr Kumar was sworn in as chief minister by Bihar's governor, Buta Singh, in a simple ceremony in the state capital, Patna.
Thousands of Mr Kumar's supporters attended.
Mr Kumar heads an alliance of the Janata Dal United party and the Bharatiya Janata Party (BJP) which won a clear majority in the state elections.
Before his inauguration, Mr Kumar expressed confidence in his chances of turning Bihar's fortunes around.
"The myths are being exploded one after another," he told journalists in Delhi.
"This government will be able to restore law and order. We will co-operate with all communities, all castes."
This is Mr Kumar's second spell as chief minister of Bihar.
His first stint was in 2000 but it lasted only seven days as he failed to gather a majority in the legislative assembly.
Sixteen cabinet and 10 junior ministers were also sworn in on Thursday.
They include Sushil Kumar Modi of the BJP who is tipped to become the deputy chief minister.
Those present at the swearing in ceremony included the former prime minister Atal Behari Vajpayee, the BJP president, LK Advani and former federal ministers George Fernandes and Sharad Yadav.
Laloo Prasad Yadav had dominated Bihar until these elections.
He resigned as chief minister in 1996 over corruption charges but ensured his wife, Rabri Devi, took over.
Bihar has had two elections this year. In February, no majority could be achieved and federal rule was imposed.
In the recent election, Mr Kumar's alliance won 143 seats in the 243-member assembly.