The correct answer is Option 4: Raja Rammohan Roy.

Raja Rammohan Roy, a renowned Indian social reformer, was one of the key figures involved in the establishment of the Hindu College in Calcutta. The college, which later became known as the Hindu College of Calcutta, played a significant role in the development of modern education in India.

Raja Rammohan Roy, along with his associates David Hare and Alexander Duff, was instrumental in the establishment of the Hindu College in 1817. The primary objective of the college was to provide Western-style education to the Indian youth while also incorporating elements of traditional Indian learning.

Raja Rammohan Roy was a strong advocate for social reform and believed in the importance of education as a means to uplift the Indian society. He recognized the need for a college that would provide quality education to Indian students, enabling them to acquire knowledge and skills that were necessary for social and intellectual progress.

David Hare, a philanthropist and educationist, collaborated with Raja Rammohan Roy in his efforts to establish the Hindu College. Hare shared a similar vision and was deeply committed to the cause of education in India. His financial support and dedication played a crucial role in making the establishment of the college possible.

Alexander Duff, a Scottish Christian missionary, also contributed to the establishment of the Hindu College. He advocated for the spread of Western education in India and played a significant role in shaping the college`s curriculum and pedagogy. Duff`s association with Raja Rammohan Roy and David Hare helped bring together their collective efforts in establishing the college.

It is worth noting that while Henry Louis Vivian Derozio was a prominent educator and poet in India during the 19th century, he was not involved in the establishment of the Hindu College. Ishwar Chandra Vidyasagar, another notable social reformer and educator, made significant contributions to education in India but was not directly associated with the establishment of the Hindu College. Keshab Chandra Sen, a religious and social reformer, was born several years after the establishment of the college and was not involved in its founding.

In conclusion, Raja Rammohan Roy, in collaboration with David Hare and Alexander Duff, established the Hindu College at Calcutta. Their collective efforts aimed to provide modern education infused with traditional Indian values and played a vital role in shaping the educational landscape of India during that time.