Raja,

Life can become easy if you use Common Anode type displays. Also Oleg is right, you need some resistor between port pin and ULN2003 input pins (although ULN2003 has internal resistors but that is around 2.7K).

This is because when you try to turn on many segments, you are basically turning on transistors inside ULN2003. If the total current drawn from the port is more than the specified (in datasheet) you will be in trouble.

Once again, diving the CA type is easy.