India

Hello,
Yes, you can apply for government job exams, because there is no area restriction. Any Indian can apply for competitive Exams.
There are many jobs available for graduates in IBPS PO, SSC CGL and railways.
You can refer the link mentioned below for more details:
https://ask.shiksha.com/i-wanna-a-govt-job-and-which-course-is-best-for-me-in-business-line-qna-3792155
Best of luck.

Based on all India ranking, following are the top 10 private MBA B-Schools in India:
XLRI - Xavier School of Management;
S.P. Jain Institute of Management and Research (SPJIMR);
NMIMS University School of Business Management;
Jamnalal Bajaj Institute of Management Studies (JBIMS);
Institute of Management Technology, Ghaziabad (IMT);
Symbiosis Institute of Business Management, Pune (SIBM);
XIMB - Xavier University;
T. A. Pai Management Institute (TAPMI);
Symbiosis Centre for Management and Human Resource Development (SCMHRD);
International Management Institute, Delhi (IMI)

Aerospace engineering is mainly offered at PG level in India in most of the reputed colleges. You can look for IISC for it. Abroad also, your first year is general courses related to engineering and you choose specialization or majors after a year. Germany, USA, Canada are the places to be.

There are so many good business schools or universities, where you can do MBA or BBA.

Many engineers do that but you have to learn all finance basics. I would rather suggest you to go for MBA in operations.

You can click the below mentioned link:
http://career.webindia123.com/career/institutes/list_colleges_Institutes.asp?group=320&cat=Audio_Sound_Engineering_Institutes&state=Kerala