Yes, Under the limitations of UGC, every college can regulate and formulate a different set of requirements that they think is appropriate for admissions.

It is difficult to tell that about Madras University, but in IGNOU you cannot pursue an MA in Psychology without a BA or B.Sc degree in Psychology.

If you are only interested in the course and do not mind what the degree provides, then you can download the IGNOU books for free and read and learn from them.

But if you are interested in a Masters degree in Psychology (or any other applied courses) for making a career, then it is suggested you do the course which is full-time.

If you want to add another degree to your calibre but do not want to make a career, then you can opt for any other average University that accepts BE or B.Tech.