M.Sc Mathematics

Yes, you can definitely pursue M.Sc in Mathematics as correspondence along with any regular course.
Eligibility is Graduation: 50%
Additional Details:
Mandatory Course: B.Sc (Mathematics)
Candidates must be Graduate with a Major, or Honours in Mathematics with mentioned aggregate.
If the seats at a center remain vacant then:
Graduate with a mentioned degree/ BA with Mathematics as one of the three main subjects with equal weightage, having at least 50% in aggregate and 55% in aggregate in the Mathematics courses will be considered for admission.

Sure, it is possible to do that. You need to have scored a good grades in B.Tech of ECE Field and also needs to be clear with all the tics and tactics to be evolved in the field that is most ravishing and dealing with the equations. But, it differs from university to university. There are Entrance exam for some of the universities.
Rule of admission:
Any candidate who has obtained Bachelor degree in any subject and has qualified at least 3 courses each of one year duration or 6 courses each of one semester duration in Mathematics securing at least 45% marks in aggregate will be eligible to appear in the Entrance test.
Best of luck.

MBA will be a better option since they have better career opportunities and a good brand value.

You can check the official website of the university in which you want to take distance education.

Loyola College,Miranda House.Hansraj College
Fergusson College.Madras Christian
College (MCC). HinduCollege.Sri Venkateswara College.
Ramjas College.

Hi, Please find the link below for detailed information:
https://www.shiksha.com/science/articles/top-bsc-msc-entrance-exams-in-india-blogId-13484.

Hi, Please find the link below:
https://www.shiksha.com/university/tata-institute-of-fundamental-research-Mumbai/exams/tifr-gs/dates.

Hello, To appear in IIT JAM Exam, you don't require minimum marks for class 12th. But, you need to score minimum 55% marks for General & OBC and 50% marks for SC, ST categories in your graduation. Click here http://bit.ly/2HxUej2 to check the complete eligibility criteria of IIT JAM Exam. You need to satisfy all the eligibility criteria if you want to appear in the exam. Best of Luck.

Check the eligibility here:
https://www.shiksha.com/university/devi-ahilya-vishwavidyalaya-indore-51562