I face this problem with some other websites also. What should i do how can i resolve this problem?
This is a problem of the web site and not Opera for Android. I tested the site with Opera, Chrome, Firefox, UC Web and Dolphin and neither of them showed anything in the drop down. If you go into Settings in Opera and change the "User agent" field to Desktop then you get their desktop version of the page and then it probably works (though there's no drop down any longer).
I'd suggest emailing the site owner and asking them to look into making their site mobile friendly. It probably has more effect if you do since you're a customer of theirs and I'm not.
If the drop down in discussion is on cleartrip calendar area then it works for me.
It does not work for me also.