For how many days Govt of India keep travelers under observation who have transit in Singapore and travelling from Australia to India via singapore? [duplicate]

They don't. Per IATA, as of March 5th, measures for travellers from Singapore are limited to medical screening on arrival:

Passengers arriving from China (People's Rep.), Hong Kong (SAR China), Indonesia, Iran, Italy, Japan, Kore (Rep.), Macao (SAR China), Malaysia, Nepal, Singapore, Thailand or Viet Nam must go thorough medical screening upon arrival.

Source: https://www.iatatravelcentre.com/international-travel-document-news/1580226297.htm

...and this is obviously subject to change at any time, although Singapore seems to have things pretty well under control.

I have been to India from Singapore recently. They won't isolate or quarantine healthy travelers without symptoms from Singapore. This is the process they follow.

1. As soon as you depart from the plane, from the Jetway itself, you will be given a form.
2. Fill the form with details including your flight number, seat number, address, phone, email and so on.
3. A security personal will screen each passenger for fever using a non-contact IR thermometer.
4. Another person will stamp the form and advice you to avoid crowded places.
5. You have to walk through a separate immigration counter.

If you have a fever, you will be isolated and medical personal will take over.

Note: India is tightening the process, more restrictions can be placed in future.