Hi,
Prioritize your current needs. Are you in need of a job? Can you do without being employed, take up further studies, and then go ahead for a job, etc. It's good that you got placed in TCS. Opportunities will flow in when you do an MBA as you will have double professional qualifications (degrees, I meant). There are people who work after BE and take part-time MBA courses (one of my colleagues was pursuing from NMIMS).
It's up to you to decide if you want to give it a try to work in TCS and simultaneously pursue a part-time MBA. If there are no personal issues or problems like financial constraints, then you can wait a while. Otherwise, you will have to prepare yourself to work very hard, manage the job, and studies as well.
Some companies prefer candidates who have done a full-time MBA, while some consider just the degree (part-time/full-time/correspondence; doesn't matter). See if you can seek part-time admission, take up the job, and if you feel you cannot manage it, you can always leave the job. The final decision is yours.
Best of luck.
Ambika Kamath