In relation to sec 181 and 182

As such there is no condition of having clause for donation or charity either u/s 181 or 182 of the Companies Act, 2013. 

However some company may adopt modal article for making law more stringent to itself so it is OK 

Conclusion - no requirement of object clause under MOA of the Company rather in MOA the active or ordinary course of business  for which company is incorporated has been described. 

NO , not required as the contribution to Charitable Trust / Others shall be vest with the power of BoD via Board Resolution