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Dear student,
I don't have much idea about SSC CGL apart from what I see on Google (Staff Selection Commission - Combined Graduate Level examination, often referred to as SSC CGL is an examination conducted to recruit staff to various posts in ministries, departments and organisations of the Government of India).
But first, you'll have to decide which way you want to go.
I have appeared for CAT 2016 and I would like to suggest you to appear for CAT as it will not only be a good foundation for your higher education but it will help you develop critical thinking capabilities, writing skills, increase knowledge, reading habits and much more. Most of the B-schools in India give preference to CAT than any other entrance test. If you could score some really good marks in CAT, doors for your career will be wide open.

Since you have made the basis as placements only, I researched through the placement data of most of the top institutes of the country to draw my conclusions. But first I will start with a pie chart of various fields in which the students of IIT Delhi were recruited in 2012-2013 session. As one can see that only 24% of the graduates were actually absorbed in their respective core technical fields along with 22% in IT, while for being recruited in the other fields, your branch really doesn't matter. So keeping this in mind, let's go towards the top three branches according to placement opportunities in their core sectors. Computer Science/ Information Technology
Both these branches are pretty similar in their curriculum and job opportunities. In the present day scenario, there is no doubt that CS/IT engineers are the highest paid and most placed graduates in the country and this situation is not going to change in at least the coming decade as we are moving towards an era where software will be the controlling factor of our lives. So the present demand for these engineers is only going to increase and the pay packages will become heftier for really good and knowledgeable ones.
2. Electronics and Communication (ECE)/ Electrical and Electronics (EEE)/ Aviation Electronics (Avionics)
I have clubbed these three branches together, again due to their similarity in curriculum, with ECE and Avionics being almost same and EEE with few different core subjects. These three branches make up the bulk of core technical placements. Since these branches are continually evolving and they provide the hardware which is the backbone of almost every industry on the planet, so the demand for good electronics and electrical engineers is always going to be there in the coming years.
3. Mechanical/ Chemical
I have clubbed two very dissimilar branches together on the sole criteria of placements and job opportunities. While researching, I came across this interesting fact that more Chemical engineers have been placed in their core fields than Mechanical. With more Pharma, Oil and Cosmetic companies coming up, Chemical engineering is clearly making its mark. As for the Mechanical graduates, although placements have been dismal for them in their core sectors, the sheer demand for them in the government sector helped this branch to make it to my list of top three branches. Conclusion:
I was disheartened to see the question asking me to place the branches only on the basis.