Hii Piyush..

Go through this link for the eligibility criteria:-https://dqxeclau.top/nuclear-engineering-course

First of all, these three institutes are purely science institutes. While both IISc and IISER take through JEE Advanced or KVPY (IISc also takes JEE Main scores), NISER takes through NEST. There are no good institutes for nuclear engineering otherwise as it is a niche field considering that only IIT Bombay offers it and that is a 5 year course. JEE Advanced has to be cleared. IIT Bombay offers Energy Engineering with M.Tech. in Energy Systems Engineering (5 Years, Bachelor and Master of Technology (Dual Degree)) and not nuclear engineering as such.  

You parents are right as the class 11 & 12 th marks are important. However entry to good institutes are through entrance tests so you will have to prepare for them. It is not a necessity that you should take coaching. 

• Sastra University
• IIT Bombay
• IIT Madras
• BARC Mumbai
• Pandit Deendayal Petroleum university
• Amity Noida

You can refer top NITs below

National Institute of Technology Tiruchirappalli

National Institute of Technology Warangal

National Institute of Technology Karnataka, Surathkal

National Institute of Technology Rourkela

Visvesvaraya National Institute of Technology Nagpur

National Institute of Technology Durgapur

Malaviya National Institute of Technology Jaipur

National Institute of Technology Srinagar

Good Luck!!

You can check the list of NITs below

National Institute of Technology Tiruchirappalli

National Institute of Technology Warangal

National Institute of Technology Karnataka, Surathkal

National Institute of Technology Rourkela

National Institute of Technology Durgapur

Malaviya National Institute of Technology Jaipur

National Institute of Technology Jamshedpur

National Institute of Technology Srinagar

Good Luck!!

You can check the top universities below for Nuclear Engineering

IIT-Kanpur

IIT-Bombay

UPES- Dehradun

Delhi Technological University- New Delhi

SRM University- Chennai

Jawaharlal Nehru Technological University- Kakinada

Pandit Deendayal Petroleum University- Gandhinagar

Aryabhatta Knowledge University- Patna

Amity University- Noida

Good Luck!!

NUCLEAR engineering is the branch of engineering which deals with the study of atomic breaking, atomic collision, atomic applications based on the principles of nuclear physics. In simple it deals with study of atoms. The nuclear engineer develops the reactors, radiators and necessary content. The engineer should be involved in operating and maintaining the reactors at industries.  For further relevant details refer the below link,

https://dqxeclau.top/careers/nuclear-engineer

Thank you.