Dear Richa,
Of course the opinion of our learned friend Nelson is correct in consonance with the principles of the notice clause in the contract of employment pertaining to resignation.
Let me also try to explain it - If fully served by the employee, notice period is included in the total service rendered by him/her in the organization; here the expiry of the notice period and the day of actual relief are coincidental. In case the employee is unable to serve the notice period due to whatever reason and opts for buy-out which is accepted by the employer OR the notice period is graciously waived by the employer due to reason like illness of the employee, the service of the employee in the organization comes to an end exactly on the very date of his relieving.
Therefore, first, it is not administratively necessary to issue the relieving orders after two months; second, considering the statutory time limits prescribed for the payment of employment dues on termination such as wages/salary due for the last spell of service, gratuity and the like, two months is too long a period and the full and final settlement should be completed within 30 days from the date of relieving. Better, get it confirmed whether the employer is going to waive the notice period on medical grounds or intends to recover salary for the notice period since you were relieved immediately. If their intention is to recover notice salary from you, better pay it forth with to speed up the process of F&F Settlement.