What is the notice period in probation time? Is there any law?

Hi all, My first question is what is the notice period in probation time? Is there any law? My company said U have to serve the 60 days notice period however their one their also written like " After confirmation, your service is terminable by the company giving one month notice period or payment in lieu thereof" so it is applied to both employees as well employer?

The third is I have ask them for the buyback notice period and they said there is no option However in my offer latter it is clearly mentioned:" in your request, the company agrees to relieve you before serving the notice period, you will liable to pay the company gross salary of the balance notice period."

Please guide me in above questions

Notice period depends mostly on the offer letter / terms of employement. So what you have signed is to be enforced. If there was no terms of employment, then you would need to follow Standing Orders.

It is not necessary to have the same rules for both employer and employee. So they can have a shorter period for themselves.
Lastly, the part you quoted basically says IF they agree to relieve early, you have to pay. Its not your right. But you should share the full letter if you want proper answers