If we use a dual in package comparator Example LM2903 and do use only one comparator, what should be done with the other one. It is sure that paralleling the two comparator will cause instability and we cannot leave that comparator unconnected too. Are there any inputs how it can be connected?
The LM2903 is a bipolar comparator and you can safely leave all the unused connections open.
If it's a CMOS-input comparator then it would be best to tie the inputs to some known voltage within the power supply range.
If you are doing something especially critical (sub-mV) you may wish to bias the inputs so the output is in a known state (which means the inputs are at different voltages within the common-mode range)- because the bias networks tend to share a few parts there might be a slight effect of one comparator on the others. Unused output(s) can always be left open, whether open drain/collector or push-pull. You can ground unused open drain/collector outputs if you want, but it doesn't matter.
For LM339/2901 and 393/2903 parts the data book says: " All pins of unused comparators should be grounded." (The exception they don't mention is when the V- pin is not ground, then the pins should be connected to the V- pin.) Just grounding the inputs can leave the output floating, so it should be connected to ground as well. Any unconnected , floating pin will act as an antenna, coupling signals from one part of the circuit to another. By connecting it to a low impedance point it will be a shield. With Opamps like LM324/358 the suggested connection is to ground the plus input and connect the minus input to the output, thus creating a buffer with zero volts output. This general idea of turning potential antennas in to shields can be applied to any IC or component and it is the engineers task to determine how.