Indian languages not suppoted in Ubuntu 16.04?

Use the Language Support in System Settings:

Click on the 'Install/Remove Languages' button:

Click the checkbox next to the language of your choice and click 'Apply'.

You can install related fonts. Like in your case you would need Indian fonts. From terminal:

sudo apt-get install fonts-indic

(Disclaimer: I'm not familiar with these languages)

Try system settings > language support, and check if the languages you need is fully installed. Sometimes some language packages may not be installed.

If that does not work, try to install fonts-knda for Kannada language and fonts-telu and see if that fix it. You can install from Synaptic or use this terminal command:

sudo apt install fonts-knda fonts-telu

For new Ubuntu 16.04 installation

Follow the steps given by @Bharadwaj Raju (installing Language Pack from SystemSetting > LanguageSupport > Install/RemoveLanguage > find and MARK kannada language pack for installation > apply system wide > restart ubuntu)

PS : Please update your system before going for language package installation or removal.

Upgraded from previous versions to Ubuntu 16.04

If you have upgraded from previous versions to Ubuntu 16.04 (like me), language packages will be there itself (if you choose to leave currently installed applications there itself while upgrading).

You just have to remove kannada language pack > apply system wide > restart ubuntu > add language pack again

For me installing Synaptic Package Manager and installing fonts-knda as mentioned by @user541021 worked well, followed by a system restart.

[If you want to type like in Nudi,after getting kannada language pack installed;

SystemSetting > Text Entry > plus icon > add Kannada (kgp (m17n)) (ibus) > system restart

Next time you switch languages using shortcut key or clicking EN button on the top right corner, you'll be easily able to input kannada language (since it's unicode, it'll work even on browser without any issue) ]

I cannot find which language the left side marked one is, probably telugu. Can someone confirm?)