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I'm a Computer Science student in Bangalore, India, doing a part time MTech at an autonomous university.

My classmates were avoiding working with me, and formed their own groups. I tried approaching one group but they were not willing to reveal their topic idea. So I spoke with students of three different branches: Electronics, Civil and Automotive, to see if I could work with them. While they were initially okay with it, they later backed out citing lack of time from company work.

A Civil dept teacher said I could do the project alone, so I told my department head that I would be doing the project alone. He mentioned by email that university norms require 4 people working on a group project and the Academic Registrar's permission would be required to do it alone. I replied (CC'ing my mentor) asking if I would have to meet the registrar. I received no reply. Subsequently I created my pre-project presentation and initial demo and showed it to my mentor and the department head. I got an okay for the project topic. Yesterday I presented the completed project. My mentor and two other faculty members loved it. My mentor asked if I got the Registrar's permission. I said I thought department head sir was going to handle that. I asked if it would be a problem and she said it might not be a problem.

Today my department head emails this:

I recall that your topic was okayed but not that you alone would work on the group project as it was mentioned that university has its norms.
So if your project is not accepted by university for the reasons that you are not in a group, your project may not be considered. Please be aware that this may happen. This was also about working in a group.

How do I reply to this? During the entire two months my mentor, the department head and even classmates were aware that I was doing the project alone. Is this a way of setting a precedent for other students? Can the university reject the project? I'm a working professional. Working in groups is an everyday job. Even companies have realized that certain people perform better when not in a group and are hired as "individual contributors". What is a university's purpose in forcing people to work together.

I'm scared now. What would be the right way to respond to him without sounding defensive? (I have cordial relations with all my teachers and department head. They know me as a good student)

Update 29th May: acknowledging my error was crucial. I did that and the HoD, my mentor and the registrar gave a retrospective approval, knowing that my not obtaining permission was not due to disobedience and that I had genuinely tried hard to find and convince project partners. Big relief. Thank you all for your help. And y'all were right. There was a good chance the university could have rejected the project.

It seems like this will come down to your university's rules and the personalities involved. Still, let's consider:

He mentioned by email that university norms require 4 people working on a group project and the Academic Registrar's permission would be required to do it alone.

So you were very specifically told, in writing, that you would need to get approval from the registrar.

I replied (cc'ing my mentor) asking if I would have to meet the registrar. I received no reply.

And you didn't get approval from the registrar. As a "working professional", you should know that you can't just send one e-mail and then drop the matter -- it's your responsibility to run this to ground.

My mentor asked if I got the Registrar's permission.

Well that was predictable

During the entire two months my mentor, the HoD and even classmates were aware that I was doing the project alone.

They probably assumed that you had gotten approval from the registrar as they had told you to. It would have been nice if they had followed up on this, but this is not their responsibility.

I'm a working professional. Working in groups is an everyday job. Even companies have realized that certain people perform better when not in a group and are hired as "individual contributors". What is a university's purpose in forcing people to work together.

This is very much not the point. The program can impose whatever (reasonable) requirements it wants. Learning to work in groups is a reasonable goal, regardless of whether you personally already have background working in groups.

What would be the right way to respond to him without sounding defensive?

This is the part that comes down to your university's rules and the personalities involved. It may be that this is a strict rule and there is nothing that anyone can do. Or, it may be that there is a process for an appeal or exception. I would start by recognizing that you are in the wrong.

What is a university's purpose in forcing people to work together.

The main objective of a group project is to learn how to work as a group. The technical content is less important.

We only have one side of the story (yours) about why you didn't join a group, but the bottom line is that by doing an individual project you have not taken part in the main objective.

To be honest, I think the University is quite right to reject your individual project, however technically excellent it might be, simply because it was not done as a group project.

Even companies have realized that certain people perform better when
not in a group and are hired as "individual contributors".

That is true, but irrelevant. An "individual contributor" who can only work by doing everything on his/her own won't achieve much. Most real world "projects" are too big for one person to do in a reasonable time, and too important to come to a complete stop if that one person becomes ill, etc. And even if someone is working "alone," they need to convince other people in the company that what they are doing is useful, otherwise it has no value to the company.