Dear,
Regarding the Notice Period, it depends on the company policy as it varies from company to company. When an employee is under the probation period, a one-month notice period is enough. After the completion of the probation period, a two-month notice period is mandatory for handing over the work and completing the tasks assigned.
Similarly, if a manager feels that the assigned tasks are already completed or will be finished within 10-15 days, the manager can waive off the remaining notice period.
My suggestion here is, first of all, you have to check your internal processes to understand the type of work you generally do. Then, have a session with the top management and based on the conclusions drawn, proceed accordingly.
Take care and regards,
Rupendra Mehta