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Definitely, you can study Chartered Accountancy course after completion of BBA.
The minimum qualification required for admission in Chartered Accountancy course is 10+2.
The CA course comprises of CPT, IPCC, Articled Training and Final Course.
Candidates are exempted from CPT, subject to any one of the qualifications given below.
1. Graduation in commerce stream with 55% or more marks in aggregate.
or
2. Graduation in non-commerce stream with 60% or more marks in aggregate.
or
3. Intermediate level qualification of Company Secretary couse or Cost and Work Accounts course.
If you have completed BBA with more than 60% marks then you will be exempted from CPT and you can directly register for IPCC.
The exams of IPCC are conducted in May and November months every year.
After qualifying IPCC exams you will have to undergo 3-year Articled Training and after completion of that, you will become eligible for Final course exams.

Eligibility Of the Master of Computer Applications [M.C.A]
Graduation in any stream is the basic eligibility for MCA. The eligibility for qualifying marks in graduation differs from institute to institute. Most of the institutes require 45 to 50 % aggregate in qualifying exam for taking admission. Reserved categories get some relaxation in aggregate percentage.
Apart from this there is another prerequisite for taking admission in MCA degree; one must have studied Mathematics in 10+2 as a compulsory subject.
How to Get Admission in Master of Computer Applications [M.C.A]
Admission to MCA can be obtained either on the basis of entrance exams or directly on qualifying exam merit basis. Following are the general ways of admission in MCA program
Direct Admission- Direct admissions are done on the basis of merit in qualifying exam. Some institutes also provide admission on management quota, which is also way of direct admission. Management quota seats in every college are reserved. Fee is generally higher for these seats than general seats.
Entrance Test- After taking entrance test conducted by various universities, qualified students are called for counselling. Counselling is conducted for seat allotment in various colleges under that university. Admission is done after allotment of seat in counselling.
Entrance tests for MCA admissions
There are several state level/university level entrance tests for admissions.
IPUCET- Conducted by GGSIP University for admission to university and its affiliated colleges in Delhi.
TANCET- Conducted by Anna University for admission to university campus and other colleges in Tamil Nadu.
NIMCET- NIMCET is NIT MCA Common Entrance test, a National Level Test conducted by NITs for admission in to their MCA programs.
BIT MCA Entrance Test- Conducted by BIT Mesra for admissions to its MCA program.
WBJEE- Conducted by West Bengal Joint Entrance Exam Board for admission in all technical institutes of West Bengal
UPSEE- Conducted by Dr. APJ Abdul Kalam University (Formerly UPTU) for admissions to various colleges in Uttar Pradesh.