To determine which categories of people are required to give a notice of six weeks under the Industrial Disputes Act, 1947, it is essential to understand the provisions related to strikes and lock-outs in public utility services. Let's explore each option systematically:

1. Workmen employed in public utility service, before going for a strike: According to the Industrial Disputes Act, 1947, workmen engaged in public utility services must give a notice of six weeks before organizing a strike. This is to ensure there is no abrupt disruption of essential services. Therefore, this option is correct.
2. Employers carrying out public utility service, before declaring lock-out: Similarly, employers of public utility services are required to give a six-weeks notice before declaring a lock-out. This is to allow for any negotiations or settlements that could resolve disputes before they affect critical services. Hence, this option is also correct.
3. Workmen employed in any service, before going for a strike: The mandate of giving a notice applies specifically to public utility services. Workmen in sectors that do not classify as public utility services are not obligated under the Act to provide a six-weeks notice before going on strike. Therefore, this option is incorrect.

Based on the above analysis, the correct answer is 1 and 2.

Thus, the provisions focus on maintaining the stability and continuity of public utility services by mandating notice periods to minimize unexpected disruptions.