Distance

You can consider IGNOU.

IIMs do not offer MBA by distance learning. IIMs offer certificate courses in the field of management which are delivered through partner network in distance learning mode. You are eligible for certificate courses after B.Tech with industry experience.

Your choice is good if you are working with any organisation or their are many institute whose providing distance learning in engineering or your given option so you can check in your nearest distance learning centre for Engineering.

There are lots of courses after graduation:
Sales and Marketing
Management
CS/ CA/ CFA/CWA
Computer Courses: MCA/Animation/Web Design
Mass Communication And Journalism/Advertising
Hotel Management
Travel and Tourism
Civil Aviation: Air Hostess/ Commercial Pilot
Social Work
Law
Banking & Finance
Library Science
Teaching: B.Ed
Designing(Garment/Jewellery/Foot Wear/Interior designer)
Content/Technical Content Writing
BPO/KPO
Entrepreneurship
MBA Courses
Animation Courses
Banking and Finance Courses
Computer Courses

If your B.Tech degree is from a recognised university even if it's by distance learning, you are eligible to appear for CAT examination to seek admission in MBA in IIMs if you have minimum of 50% marks in B.Tech.

Yes, Amity University provides you the best placements although you will pursue distance learning PGDBA or Executive MBA Online. Amity curriculum not only provide you the insights about corporate culture but also enhances your personal and professional development. Companies like Trident, E&Y, Accenture, Tata Tech, Mahindra and Mahindra visit campus for placements in Amity University, Noida.

There is no procedure to get lateral entry admission in distance mode.

You can pursue MBA distance learning after joining Civil Services. These degrees are designed for working professionals.