Yes, you can change your preferred branch of engineering after the JEE Advanced exam. Here's how:

1. Research and Identify:
First, research and identify the branches of engineering that you are interested in. Consider your strengths, career aspirations, and future prospects of each branch. Make a list of your preferred branches in descending order of priority.

2. Check the Availability:
Check if the branches you are interested in are available in the institutes where you have qualified for admission through JEE Advanced. You can refer to the official website of the respective institutes or the JEE Advanced counseling portal for this information.

3. Counseling Process:
After the JEE Advanced exam, there is a counseling process for seat allocation in various engineering colleges. Register for the counseling process by filling out the counseling form and providing your preferred branches of engineering.

4. Seat Allotment:
Based on your JEE Advanced rank, availability of seats, and your preferred branches, you will be allotted a seat in one of the engineering colleges. The seat allotment process is usually conducted in multiple rounds.

5. Accept or Upgrade:
Once you are allotted a seat in a particular branch, you have the option to either accept it or upgrade to a different branch in subsequent rounds. If a seat in your preferred branch is available in the later rounds, you can choose to upgrade and secure that seat.

6. Document Verification and Admission:
After accepting a seat, you will have to go through the document verification process and complete the admission formalities at the respective institute. Make sure to carry all the necessary documents and pay the admission fees within the given timeline.

7. Branch Change within the Institute:
Once you join an engineering institute, there might be provisions for branch change within the institute. The eligibility criteria and procedure for branch change vary from institute to institute. You can inquire about the branch change policy from the academic department or the concerned authority of your institute.

Conclusion:
In summary, you can change your preferred branch of engineering after the JEE Advanced exam by participating in the counseling process and upgrading to a different branch in subsequent rounds if available. Additionally, some institutes may have provisions for branch change within the institute after admission. It is important to thoroughly research and consider your options before making a decision to ensure that you make the most suitable choice for your future career.