Maximum No. of Companies in which a person can be MD

Managing director

For private company there is no restriction

For public company not more than 2 without the approval of central government

Director

15 companies excluding :-

private company 

section 25 company 

foreign company 

MD is also a director so if a person is MD in 2 public companies then he can be a director in 13(total 15) other public companies

yes right, but with due respect, this section doesn't restrict managing directorship in private companies 

For unanimous approval* of the board :-if he is seeking second appointment in a public company then an unanimous approval is needed even if the first company(in which he is appointed already) is private or public

*(unanimous approval means all the director present shall vote in favor of the decision and if even one member doesn't vote resolution can't be passed) 

For govt approval :-for 2 or more public companies qovt approval is needed

and there is no restriction placed by section 316(the section is silent in this case) in case of private company if all the companies are private