As per your queries, appointment of director where director of the company is less than the quorum fixed by article for the meeting of the Board. In your case the, the quorum is not, because of the resignation of one director out of the two director.
In such case you must follow the provision of your company articles read with clause 75 of the Schedule I- Table A of the Companies Act, 1956.
16 January 2013
Clause 75 of the Schedule to Table A:
In case the no of director reduced below to the quorum fix by the Act for a meeting of the Board, the continue remaining continuing director may act for the purpose of increasing the number directors to that fixed for the quorum or for summoning of the general meeting of the company, but not for any other purpose. {Clause 75 of Table A of Schedule I of Companies Act, 1956}
So in your case, you can appoint one more director for complying quorum of the meeting of Board as per the above mention clause.
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