viswamy2k,
I could not replicate the issue at my end. I could see the Java compiler and Java build path options in Project properties.
Can you please switch to a new workspace and create a sample project and check whether Java compiler and Java build path options are present in project properties page ?
If you are still facing issues, can you please answer some more queries to help us investigate further :
1) Can you please mention how did you install MyEclipse 2013 ?
2) Can you please share your OS version and details ?
3) Can you please share us the details of the project ? Is it a Web project / EAR project / EJB project / Java project / anything else.
4) Can you please attach the screenshot of your project properties page to help us visualize the issue ?