Dear Shiba Prasad Bhattarcharjee, what has happened with your mother is unfortunate. I wish her a speedy recovery.
Adhering to terms of separation
Whatever may be the reasons, the terms and conditions of separation specified in the appointment letter must be adhered to. Therefore, return the salary advance, submit a letter of resignation, complete the notice period, and leave the company without hassles.
Applying for Leave Without Pay (LWP)
As you need to tend to your mother, if you are unable to work, then you may apply for Leave Without Pay (LWP). However, there is no guarantee that the company authorities will approve it. It is just a matter of taking a chance.
Facing setbacks in life
Setbacks in life are common. Everyone faces some setback or another. However, never ever think of abandoning employment. It could aggravate the problems further.
Thanks,
Dinesh Divekar