As per section 269 (1), a public company or private company which is subsidiary of a public company, having paid up share capital of Rs. 5 crore or more shall have a managing director or whole time director or manager.
Therefore, a private company is not required to have managing or whole time director or manager.
If you are not appointing any of them within time then there are many of sections of Companies Act, 1956 you will contravene, like section 161, section 215 etc…
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