B.Sc

Did not get your query, you want admission in to a Masters programme without a B.Sc degree? No university in the world will allow you to do so.

It depends on the college reputation if its a very good college you wont get but you will get in a normal college.
Again, its upon the course you select.
B.Sc has many Branches, if you are a biology student you will get life science, cut-off for life science is less and further you can go in research or teaching profession
If you are a Maths student or a It student you can take B.Sc-IT, it has a great scope.
All the best.

You should opt for vocational courses.

For IAS, BA would be a better choice.

MBA require Graduation in any stream as eligibility criteria. So graduation in which subject is not important. But if you take BBA, then it will be continuation of your graduate studies.
Apart from traditional specializations such as HR, Systems, Marketing and Finance, several sectoral programs also available at MBA like
Media and Entertainment Management
Project Management
Pharma Management
Marine Management
Logistics and Supply Chain Management etc.
If you want to specialize in Agricultural Marketing / Management, it is better to choose B.Sc-Agriculture