Dear Chatgaya1,
The condition of serving a notice period upon submission of the letter of resignation is always mentioned in the appointment letter. Now, whether it is legally admissible to change the condition or not, other members will explain. However, my explanation is limited to the Indian Contract Act, 1872.
Principle of Equal Consideration
The principle of equal consideration is one of the basic principles of the law of contracts. Its essence lies in finding a fair balance in the exchange between parties when establishing bilateral (consensual) contracts.
In your proposal regarding the length of the notice period, a fair balance does not exist between an employer and an employee.
Thanks,
Dinesh Divekar