is it valid to write "the directors resolution be passed with majority present and at least with 2 executive directors in by law of the company

First, you have used two separate terms to describe directors: "directors" and "executive directors." Do such distinct titles or offices exist under your company's Articles of Incorporation or Bylaws, or does your company have just one class of directors? Companies with large boards sometimes have an executive committee to provide guidance to the officers and answer their questions between meetings of the larger board. Is that what you mean by "executive directors?" If so, then the answer is no. At a meeting of directors, all directors are equal. The absence of directors who are members of an executive committee cannot prevent the other directors from taking action. In order for the board of directors to take any action a quorum must be present. Most bylaws provide that a quorum is half the total number of directors. Some provide that it is half the total number of directors offices including vacancies. Resolutions are approved by majority vote. If there are 3-6 directors, then the quorum would be either 2 or 3 directors, and the votes of two of them would be enough to pass a resolution. Smaller quorums for meetings of shareholders are sometimes provided in the bylaws and may be appropriate, especially for corporations with a large number of shareholders, and many actions for which shareholder approval is required. I cannot think of any situation in which a smaller quorum for meetings of directors would be appropriate. That you should discuss with an experienced corporate attorney. Please call me if you would like to discuss this further. Dana Sack 510-286-2200