For hotels try

http://www.booking.com

Have used this site quite a few times and definitely is the best choice (at least for me has been the best choice)

As per airlines try searching on the internet

http://www.bing.com/search?q=budget+airlines+from+india+to+singapore&src...

This is the result I got, now it is up to you to check times, and costs.

Regards!!