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Hello Aniket,
Yes, a commerce student can apply for BCA given that you had maths in class 11th and 12th. Maths (10+2) is compulsory to apply for BCA as entrance exam varies from college to college and universities. There are several entrance exams for this course in various institutes.
SMIT Entrance Exam for Sikkim Manipal
LUCSAT for Lucknow University
Some other colleges you can apply in are:
Christ University, Bangalore
Madras Christian College, Chennai
Presidency College, Bangalore
Symbiosis Institute of Computer Studies and Research, Pune
DAV College, Chandigarh
Check their official sites for more details.
Pailan College of Management & Technology College, Kolkata, West Bengal
Techno India College of Technology, Kolkata, West Bengal
Narula Institute of Technology, Kolkata, West Bengal
Guru Nanak Institute of Technology, Kolkata, West Bengal
George Group of Colleges, Kolkata, West Bengal
Netaji Subhash Engineering College, Kolkata, West Bengal.

Admission to regular BCA course is generally done through a common entrance test conducted by respective universities. IPU CET SET are a few entrance tests conducted by some top institutes for providing admission to the course. Application process for BCA entrance test usually starts in the month of May and June. Students have to apply to respective institutes in both online as well as offline modes. BCA entrance test is generally of objective type and contains questions from the topics mentioned below. The difficulty level is easy to moderate and questions in the test paper are of 10+2 level. The number of questions varies from 150-200 and the duration of the test is generally between 2- 2 1/2 hours. BCA Course: Selection Process:
The selection for admission to BCA is generally based on the performance in the written test. Certain universities like the Christ University, Bangalore, also conduct a personal interview for selection to the programme. The final selection is based on the cumulative performance in written test, personal interview and qualifying examination. Below is a list of institutes which conduct entrance test for admission to BCA programme. Indira Gandhi National Open University
Symbiosis University
Guru Gobind Singh Indraprastha University
Banaras Hindu University
Panjab University
There are certain colleges like BIT Mesra, Amity University etc. Which take admission purely on the basis of marks scored in the 10+2 examination. Regards.