The prominent freedom fighter and socialist leader who escaped from Hazaribagh Jail was:

Jayaprakash Narayan
Ram Manohar Lohia
B.P. Mandal
Karpoori Thakur

The correct answer is Jayaprakash Narayan.

Jayaprakash Narayan (1902-1979), also known as JP, was an Indian independence activist, socialist leader, and politician. He was a prominent figure in the Indian independence movement, and he played a key role in the Quit India Movement of 1942. After independence, he became a leading socialist leader, and he founded the Socialist Party of India in 1948. He was also a strong advocate for social justice, and he played a key role in the Bhoodan movement, which aimed to redistribute land to the landless.

In 1974, JP led the JP Movement, which was a mass movement against the government of Indira Gandhi. The movement was successful in forcing Gandhi to resign, and it led to the establishment of a Janata government in 1977. JP is considered to be one of the most important figures in Indian history, and he is often referred to as the “Father of Modern India”.

Ram Manohar Lohia (1910-1967) was an Indian politician and socialist leader. He was a member of the Indian National Congress, and he served as a minister in the government of Jawaharlal Nehru. However, he left the Congress in 1954 to form the Socialist Party of India. He was a strong advocate for social justice, and he played a key role in the Bhoodan movement, which aimed to redistribute land to the landless.

B.P. Mandal (1918-1990) was an Indian politician and social reformer. He was a member of the Indian National Congress, and he served as a minister in the government of Indira Gandhi. However, he left the Congress in 1977 to form the Janata Party. He was a strong advocate for the rights of the Scheduled Castes and Scheduled Tribes, and he played a key role in the Mandal Commission, which recommended affirmative action for these groups.

Karpoori Thakur (1921-1988) was an Indian politician and social reformer. He was a member of the Indian National Congress, and he served as the Chief Minister of Bihar from 1977 to 1979. He was a strong advocate for the rights of the poor and the marginalized, and he played a key role in the Bhoodan movement, which aimed to redistribute land to the landless.