NOC

I am a Scale 1 officer in a public sector bank since January 2010.I recently applied for GIC and NICL Assistant Manager and Administrative Officer respectively. After applying online for the above I sent an intimation letter to my Bank via speed post regarding submission of my candidature.The above intimation was sent via speed post because I am on leave since 27-02-17 due to my mother's illness.The Bank has replied that I have not taken permission from the Bank to apply for the above posts.Also since all my leaves have exhausted I am presently on unauthorised leave.My hometown is in Kanpur and I have been posted in Kolkata.Due to my mother's critical condition I cant resume my duties.Is there some way you can help me out?Though I want to resign from the present organisation,but only after getting employment elsewhere.Is there a way out?Are there any adverse consequences that i'll have to face if i resign from my Bank after clearing my written exam in NICL and GIC(I am well prepared and sure of passing the written exam).In that case do I still need to produce NOC? Will my Bank object on my resignation since it has been brought to their notice that I have applied elsewhere?Kindly guide me urgently.