Is there any Maximum amount of dollar limitation that can be transfer to India from USA without declaring it in US or India in a year. I hear that if I send more than $10,000 in one year, I need to declare it to IRS. Is this true?

I am working in US on H1b visa. I have already sent $10,000 this year, but I need to send another $10,000. I use my local US bank to transfer the money to my Indian bank account. Is there anything I need to do to transfer this second $10k to India? Do I need to declare or fill up some form with IRS or Indian income tax for the same. Will there be any tax charged on the money that I have transferred?

There may be a declaration requirement for India, but for the U.S. the reporting threshold for Form 3520 is $100,000, to which you are nowhere close.