How long does it take to become professional in 3ds max?

That's too open-ended a question. Remember that there are many areas to be professional in eg: character animation, texturing, modelling, rigging, lighting etc... If you're super self motivated and self taught like I am, you can become a professional generalist in a couple of months. The software, like all animation software takes years to fully understand and even then, there are still many areas you'll be a beginner in and some you'll be intermediate to advanced in. Like I always say, the learning never stops.

With consistent practice and learning, you can make significant progress in a shorter amount of time. Additionally, it's important to keep in mind that learning 3ds Max is an ongoing process, and as new updates and features are released, you will need to continue to develop your skills to stay up to date.

His depends on how fast your able to grasp.

For Fundamental 3dsmax usage (2--3 month), which entails - modelling and texturing.

For Intermediate lvl 1(5--6 month) to get adv. Modelling, texturing and Fundamental Animation and rigging)

Intermediate lvl 2 (1 yr ) to get adv. Modelling, texturing, Intermediate rigging and Cartoon.

And you're going to go on researching 3dsmax as you keep on working on projects and assignments.

According to my experience.If you want to learn 3DS max professionally then I suggest you to take or join 3DS max training.  

In order to learn the basics for 3Ds Max, it can take up to full 2 months to get proper knowledge of design construction, texture, material, lighting, modeling, etc. 

However, the practice would be the key to becoming a professional in 3Ds Max, which could take a couple of months or even a year. 

In order to become a professional in 3D max, one should have the passion or the love for the craft, skills will be developed in time, it is much important that you have to consistently practice learning the skill.