Can CEO be appointed by a Private Limited company

A Startup Private Limited Company where there is an angel round of funding and who does not fall under mandatory class of appointment of Key Managerial Personnel can appoint CEO in its Company.
Well, definitely its a welcome step for a Company to appoint a CEO defining the roles and a Private Company can do so by passing a resolution in the Board Meeting. However, assuming the responsibility given, being a Company which has been invested by the Investors, it is always suggestible to have their consent whether the Shareholders agreement dictate or not.
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