hi Shruti,

Basically,

Software Engineering is the branch which includes the study of h ow software is built . It includes topics such as software design, software testing and quality assurance.

Computer Science is the branch which includes the study of how computers work from mostly the theoretical and mathematical perspective.

To become a software engineer you may choose any one them because they are quite similar.

Careers in Computer Science:-

1. Web Developer/Architect

2. Programmer

3. Mobile/Cloud developer

4.  Software Engineering

5. Software Development

6. Product Manager

Careers in Software Engineering:-

1. Software Developer

2. Software Manager

3. Software Engineer

4. Technical Product Manager

5. Software Designer

6. Implementation Consultant

You should choose Computer science if you like math or logic, want to get into a specialized field of security, graphics, machine learning or Artificial Intelligence(AI).

On the other hand, you should choose Software Engineering if you are more interested in a hand-on approach, learning overall life cycle of  a software like how software systems are built and maintained.

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If you require to know colleges for which you are eligible then you should go to the link mentioned below.

Link - JEE Main College Predictor

Hope this helps you.

Good Luck!