Q: How to remove password for the recovery mode wizard which you get by pressing command   r while booting mac with mac os 10.10?

No password is required to boot from the Recovery HD.

Describe what exactly do you see when you are trying to start your Mac to Recovery Mode.

If you have set a firmware password on your Mac and you do not remeber it, then a trip to an Apple Retail Store or Apple Authorized Service Provider will be necessary...

What is a firmware password and how do I set one up? - Apple Support

MacBook Air (Late 2010) and later, MacBook Pro (Early 2011) and later, iMac (Mid 2011) and later, Mac mini (Mid 2011), M…

You set a firmware password. You can't remove it yourself if you've forgotten the password. Make a "Genius" appointment at an Apple Store. You may be asked for proof of ownership.

It's possible you set a firmware password, see if the password dialog is similar to the one on this site…

http://osxdaily.com/2014/01/06/set-firmware-password-mac/

Those passwords prevent ALL startup key combinations. Confirm it also happens when you boot holding T (target disk mode - How to use and troubleshoot FireWire target disk mode - Apple Support) If that goes to the password dialog you have a firmware password set.

Apple suggest you take it to an Apple store to get it reset, you can't remove the battery or remove RAM to reset this, so only Apple should reset it.