Economics

If you want to take admission in Economics Honours then you must have maths in class 12th.

Yes, you are eligible for economics honours though you didn't have maths subject in class 12th.

https://www.shiksha.com/humanities-social-sciences/economics/colleges/b-a-colleges-india
Here is the list of the top college of BA Economics, kindly follow the link.

I think, you do not face any problem in pursuing MBA/PGP courses, because you have enough knowledge of Science and Economics. Top management Institutions like IIMS, DMS of IITs and NITs, XLRI, MDI Gurgaon and SPJIMR Mumbai etc. are the few B-Schools can be best suited to your profile. Please start you preparation for CAT and obtain the percentile above 95 for getting these B-Schools.

The eligibility criteria for MA in Economics at PSGCAS is given below.
Educational qualifications : UG Passed with Economics/ Econometrics/ Mathematics/ Statistics/ Business Economics /B.Com/ BBM .
So, from above you can apply here.

Hi
You will have to take a drop in order to switch from mechanical engineering into economics.

Hi
Yes, it is required to have maths in class 12th, else you won't get admission. Check the prospectus of the course to know about the eligibility criteria. https://www.shiksha.com/university/du-delhi-university-24642.

Hi
https://www.shiksha.com/search/?q=Economics&s[]=11&sb[]=34&sa=^0^0^0^34^11^0^0^0^0^0^0^0^sb:34
You must have maths, this is the basic eligibility for many colleges to make the students admitted in the graduation courses.

You will have to check the official website of the college to know more about all the courses that the college is offering.