JNTU Hyderabad, School of Management Studies (JNTUHSMS)

The minimum requirements for admission to the M.Sc in Environmental Sciences programme at JNTUH are:A Bachelor's degree in any discipline with a minimum of 50% marks.A valid score in the National Eligibility Test (NET) or the Graduate Aptitude Test in Engineering (GATE). A good academic record.A valid passport.A medical certificate.

Yes, you can do Diploma MEC through distance. Good luck.

For MBA in JNTU, you have to get 170 + marks in ICET and a rank of 1-20 because JNTU is an 'A' Grade college. If you got 40-80 marks you will get D Grade colleges like, Sir Crores Reddy College of Engineering, Sri Vishnu college, Vignan's Lara, etc.
If you want more information about the cutoffs, feel free to ask.

Please click on the link below for the admission process:
https://bit.ly/2HvErpX

There are several colleges in Hyderabad which provide integrated B.Tech+MBA through TS EAMCET. JNTUH College of Engineering, Hyderabad is one of them. https://www.shiksha.com/b-tech/resources/ts-eamcet-college-predictor
The link above may help you better.