36. Is it possible to disable the core required modules through drupal admin ?

No, it is not possible to disable the core required modules.

35. Which are the core required modules in drupal 6.x ?

1. Block --- Controls the boxes that are displayed around the main content.
2. Filter --- Handles the filtering of content in preparation for display.
3. Node --- Allows content to be submitted to the site and displayed on pages.
4. System --- Handles general site configuration for administrators.
5. User --- Manages the user registration and login system.