Science

You are an Engineer Graduate. Generally, the eligibility criteria for M.Sc. Agriculture are B.Sc. With Zoology, Botany and Chemistry / Biochemistry or B.Sc. Agriculture or life sciences with 55% marks. We suggest that you reconfirm from the institute you wish to do the course regarding the eligibility.

M. B.A. In hospital management is bound to the only hospital sector. But as per the current scenario, the hospital sector is growing. Also, more advantage is you are belonging form nursing background. You know whats the problem and the solutions regarding the hospital management system. An MBA in HR is not bound to the specific sector.

Is it for Bachelors or Masters? Masters is doubtful as you are from arts field. But Bachelors seems okay 0.

See there is no limit in the number of attempts you can give in WBJEE exam but it is useless to give attempts more than 2. Be wise and don't go for more than 2 attempts.

Which college or university?

Yes, maths is actually not required in this BCA degree. You will get to know about this.

Use this link:
https://www.shiksha.com/college-predictor

Check with the college academics directly.

Refer the link:
https://www.shiksha.com/university/andhra-university-visakhapatnam/aucet-exam