Computers & IT (Non-Engg)

B.Sc (Hons.) Computer Science is a 3-year full-time undergraduate course divided into 6 semesters, with each semester lasting a period of 6 months. The minimum eligibility for the course is a Higher Secondary Certificate (10+2) qualification with a minimum aggregate score of 45%. If you fulfill this eligibility criteria, you can apply for B.Sc in Computer Science.

For being a product manager in technology, MBA in IT and operation management are suitable.
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To be eligible to apply in Christ University for BCA course, the basic eligibility for the programme is to pass at +2 level (Karnataka PUC / ISC / CBSE / NIOS / State Boards) from any recognised Board in India. Students pursuing International curriculum must have AIU approval and must obtain a grade of not less than 'C' or it's equivalent.
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You can go for short term as well as long term courses in game designing and development. There are many institutions which provide these courses. Choose upon your area and budget!
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Data Science is the study of scientific methods and systems used to extract information from both structured and unstructured groups of data. Throughout M.Sc Programme, students often learn how to apply information technologies to business administration.
Visit the link given below to get complete details:
https://www.manchester.ac.uk/study/masters/courses/list/11424/msc-data-science/course-details/.

There is no such a core domain in medical after MCA. But, you can go for medical degrees, like MBBS, BDS, MS etc.
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For better understanding, kindly mention the college name where you wish to get admission. You can also check for the course and college name on Shiksha and check for the eligibility for the course.

Please click the link below to check for lateral entry colleges in M.Sc IT course in India. https://bit.ly/2ALUxpT
https://www.shiksha.com/it-software/colleges/m-sc-colleges-Delhi-ncr
You will have to check with the following colleges to know more about lateral entry options.

Som-Lalit Institute of Management Studies (SLIMS), which offers 2 years full time / 3 years part-time Post Graduate Programme leading to the degree of PGDBM (Post Graduate Diploma in Business Management) approved by AICTE. Further, Som-Lalit Institute of Business Management (SLIBM), which offers 2 years full time Post Graduate Programme leading to the degree of MBA (Master in Business Administration) approved by AICTE and affiliated to Gujarat Technological University. Hence, about programme you asked is not there.

Kindly mention the qualifications that you currently have, so that I can have a better understanding.