B.Tech

There is no guarantee of 100% placements in India for B.Tech / B.Sc IT because in India there are large number of IT engineers and B.Tech is better among B.Tech and B.Sc IT.

It depends on person to person. If you have good technical knowledge then go for a job otherwise civil services.

Maths is a basic part of engineering. Every stream involves maths but if you are not interested in maths then you can choose CSE or IT which has a little part of maths but maths will be involved in programming languages.

I would recommend UEM, Kolkata:
https://www.shiksha.com/university/university-of-engineering-and-management-kolkata-47398
For further study and build career in electrical engineering with the best engineering college in West Bengal.

It is good to start civil service examination early but make sure that you do not spoil your academics of graduation degree. You may prepare with small and short effort during your spare time and take concentrated preparation just one year before you are planning to appear for the examination.

The Civil Services Examination is a nationwide competitive examination in India conducted by the Union Public Service Commission (UPSC) for recruitment to various Civil Services of the Government of India, including the Indian Administrative Service (IAS), Indian Foreign Service (IFS), Indian Police