Hello!
You can try for:
1. IOCL
2. Powergrid corporation of India limited
3. BBNL (Bharat broadband network limited)
4. BARC
5. Gail
6. Mineral exploration corporation limited (MECL)
7. PSPCL
8. Steel authority of india(SAIL)
9. FCI (food corporation of India)

Yes they are available but only less vacancies.

It's very difficult to get them

Morever private companies offer better package than those

Through gate exam securing 150 rank or below.

Drdo , ISRO

Have junior computer engineer post

But getting into MNCs are better