Good Afternoon

Hope you are fine..

As per your query.. you can not take admission in BA 2nd Year.. Jamia Millia Islamia conducts JMI entrance exam to take admission in BA, BA(Hons) and for other courses also.

Jamilia Millia Islamia takes admission through CUET (conducted by NTA) for BA and BA Hons course.

So, It is very difficult to take admission in direct 2nd year, for BA course you have to qualify JMI Entrance Exam or CUET exam.

For more information about BA course in JMI checkout given link below:
https://www.careers360.com/university/jamia-millia-islamia-new-delhi/ba-course

Hope you found it helpful
All the best!!!