The correct answer is option 2 - Calcutta. The first university in modern India was founded in Calcutta, now known as Kolkata. It was established as the University of Calcutta on 24th January 1857. The university was founded by the British East India Company as a means to provide education to the Indian elite and train bureaucrats for colonial administration.
Option 1 - Bombay: Although the University of Bombay (now University of Mumbai) was established in 1857, it was founded after the University of Calcutta.
Option 3 - Lahore: The University of the Punjab, now located in Lahore, Pakistan, was also established in 1882. Therefore, it was not the first university in modern India.
Option 4 - Madras: The University of Madras, located in Chennai, Tamil Nadu, was founded in 1857, the same year as the University of Calcutta. However, the University of Calcutta was established before the University of Madras, making it the first university in modern India.
In conclusion, the first university in modern India was founded in Calcutta, making option 2 the correct answer.