As you have take CSE in 11th and 12th so you must have good knowledge of programming. You can take CSE branch. Well as you mentioned you are not  good in coding. But in  CSE branch you must have good maths and you have good maths as you mentioned. As you are good in creating logic which is must for CSE branch. You can learn programming by doing practice. As coding should be good for CSE and for this logic must be created first and you have good command in logic. So you can take CSE/IT branch as per your choice. As there are many jobs in private sector in CSE/IT branch.
As in Electronics and Communication branch there is maths and programming. There is some less programming as compared to CSE/IT so you can take even this branch. But for this you must have interest in integrated circuit, digital circuit... means for this you must have interest in Electrical. As ECE is a evergreen branch. You can get many opportunities in private and government sector as well. As it is a good branch for getting job opportunity in foreign countries also. So go through it.
These are the branch (CSE/IT/ECE) you can take as per your interest and command . These three branch are suitable according to your interest. For ME... you must have interest in physics..... As you have studied CSE in 11th and 12th you have some knowledge of coding definitely. And even you can improve your coding skills by practicing too much programming. You must keep try to develop logic for program. So you have to work hard for getting CSE/IT branch in good College

There are many branches which you can choose like Mathematics and computational engineering (MCE) , production and industrial engineering (pie), environmental engineering (Ene), biotechnology, etc. In various colleges like iits NITs and in DTU. For further information please go through this link:
http://www.careers360.com/list-of-engineering-courses-offering-be-btech-degree-in-india
You can find your interest in the list given in this link.