College students attend college for various reasons, but the big goal is to come out with an undergraduate degree. As you know, each student has his or her own passions and interests, which is common with many individuals. It isn't surprising for this overlap to happen, but whatever it is, you will typically choose your major(s) based on something you're passionate about.
With respect to "The Big Bang Theory," some of the scenes in the show will correlate very well to the majors listed below.
1. Chemistry
(Beginning through 1:24)
When Leonard is mixing the combustible gel to create that thrust, he doesn't properly adjust the formula (confirmed by Sheldon), and as you can see, bad things happen when you don't use the correct formula. Especially in your own apartment and in an elevator. Don't try this at home, kids.
2. Communications
There is clearly some disconnect between Raj and Sheldon, and Sheldon is displeased with Raj's insufficient understanding based on his body language. As a result, Raj decides to wait inside the door rather than outside (He also came in without Sheldon telling him to come in). Not only that, Raj thinks that he has a job offer waiting for him, but it didn't really come yet until Sheldon played a practical joke on him.
DISCLAIMER: In all honesty, any scene where Sheldon yells 'Bazinga!" there's a communication problem because most of the cast takes Sheldon too seriously.
3. Biology
As you can see here, biology students can have a challenging experience with multiple labs in a day, and being able to maintain a high level of success and focus in their research is anything but easy.
4. Psychology
Penny is a frequent visitor to Leonard and Sheldon's apartment (start at 1:04), and at times she can be a bit extra. Sheldon is able to keep that in control by using operant conditioning.
5. Education
Teachers expect their students to take class seriously, so when Penny doesn't do so, Sheldon becomes a bit more impatient. (Start at 0:22)
6. Engineering
Amy Farrah Fowler is in the middle of a research project and in her case, she needs an engineer to help with the project. It's the perfect project for Howard, whose skillset and background matches up.
7. Mathematics
Using number theory, Sheldon is able to identify a complex relationship between numbers in both prime number format, but also in binary.
8. Athletic Training
Penny gives a perfect explanation on how NOT to train.
9. Physics
Sheldon is working on a physics problem and he ponders it as he goes to bed. When he wakes up in the morning and notices that somebody solved the equation for him, he reacted negatively, but the equation ends up being correct. In physics, it's important to model things correctly because inaccuracy can prove to be a critical mistake.