Distance

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.

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

EMBA is good only from the knowledge point of view. There is no guarantee of placement. My suggestion would be to pursue online MBA as it will have added features of online video lectures, live streaming, problem redressal via email, etc.

Babaria institute of technology, Ahmedabad institute of technology, are two top distance learning center for Engineering in Gujarat.

To pursue MBA through distance, Sikkim Manipal University, NIBM and Symbiosis are the best choices.

Generally, Hotel Management colleges prefer students who have completed their 12th exam as a regular student. But some colleges may have no issue with the distance education. You have to check with the college directly.

Dear Kiran Kowshik,
Indira Gandhi National Open University is the top and best in the country. Secondly, you can prefer, Pondicherry Central University, Hyderabad Central University and even private institutes like Symbiosis, and Welingkar also offer distance MBA.
All the best.