Hi,

It is possible to opt psychology after completing bachelor's degree in engineering. The eligibility criteria depends on the university/college you are opting. You can  do MA or MSc in psychology even if you haven't opted psychology as your optional subject during engineering.

Generally, the eligibility criteria in top universities is to have 50% or above in under graduate.

Certain institutes takes an entrance test before you opt psychology includes:

• Banaras Hindu University
• Jammu university
• Delhi University
• Tata institute of social science

And many institutes do not take any such entrance exam and directly provide you admission based on your bachelor's percentage includes:

• IGNOU
• St. Xavier's college, Mumbai
• Hindu college, New Delhi

Please note that direct admissions (without entrance test) are also available in Hindu College.

Top institutes in Bangalore are:

• Indian institute of psychology and research -- It is a private college established in 2003 provides MSc in psychology and psychological counselling.
• Mount Carmel college -- It is a private college only for females established in year 1994 provides course in MSc psychology.
• St. Francis De Sales college -- It is also a private college which is co-educational established in year 2004 provides MSc in Psychology.

All the best.