BCA

For MCA admission, the first preference is given to ranking in entrance exams i.e. PGCET or KMAT. There are some colleges offering MCA on merit basis. You can try in BITS. Else Pune or Bangalore is a good option.

BCA+MCA is usually preferable. you can also go for M.Sc, but MCA has more exposure and provides better jobs because in MCA more of practical knowledge will be provided.

Yes, admissions are open for the academic year of 2017-18.

There is nothing like I am weak. It's just our psychology. There are many students whose weak subjects become their whole career. Maths is all about practice. I think in order to test yourself you should be practicing a sum and understanding its concept and then you should try to solve a sum on your own without referring the solution if you come to be correct then maths is your subject. If not then you can opt for BCA. But be confident while solving because if you set this in your mind that I am weak in this subject you will never be able to solve any problems of maths.

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B.Tech (CS) is a four-year engineering degree in computer science but BCA is a Bachelor's degree in computer application.
CS provides you engineering degree which is equivalent to BCA+MCA.

MBA is a business administration course. If you looking for Masters in computers definitely Masters in computer science would help you at after BCA. Choosing Masters in computer science is better than choosing MBA.

IIMT is a good college to pursue BCA but in Greater Noida there are so many good colleges than IIMT like Galgotias, Amity-Noida, IMS-Noida.
Choose wisely.
Good luck.