In your case section 262 is applicable. If there were only 2 directors and now only one director is remaining then that single director can appoint second director to comply with section 252 i.e. minimum number of director.
Simply show a board meeting and pass a board resolution u/s 262 and file form 32 for appointment of new director. After approval of this form 32 file another form 32 for cessation of director due to death.
25 June 2010
Sample resolution for appointment of director to fill casual vacancy
RESOLVED THAT pursuant to the provisions of Section 262 of the Companies Act, 1956 and Article No.______ of the Articles of Association of the Company, the casual vacancy in the office of director caused by the death of Mr. Rahul Singh be filled by the appointment of Mr. Harshit Aggarwal who shall hold office upto the date Mr. Rahul Singh would have held office had it not been vacated.
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