I found out NTC has GSM 900. Does a cell phone with  GSM/GPRS Tri-Band 850/1900/1800  work in Nepal? Your help is appreciated. 

no.. u need a quad-band.. phone..

I think, GSM/GPRS Tri-Band 850/1900/1800 cell doesn't work in Nepal because Nepal use European std which is 900/1800 frequency band. Among this, 900 MHz is for GSM and 1800MHz is for CDMA phones. In 900 MHz GSM, 935 to 960 Mhz for downlink and 890 to 915 Mhz for uplink which is totally different from 850 MHz GSM where 824 to 849 MHz for uplink and 869 to 894 MHz for downlink.
     

May not work with NTC but will work Mero Mobile
Mero Mobile GSM band 900/1800

Thank you all, that was helpful.

Technicall, I say these cells doesn't work in Nepal. Both NTC and mero mobile do have 1800Mhz but this type of network planning is common in all place. e.g In some places where both NTC and mero mobile only use 850Mhz. So, when you take your cell in such places, probably your cell doesn't work.
      I am only talking technical aspects, I don't have practical experince in this issue.

I think following frequencies are being used in Nepal

oops! I posted the wrong link

http://www.gsmworld.com/roaming/gsminfo/cou_np.shtml