Accidentally plugged in the wrong power adapater to my Aspire 5742. Is the motherboard now fried?

well it depends, if it was a higher wattage, it doesnt matter. i can charge my dell 65 watt laptop with a 90 watt adapter... doesnt bother a thing, only pulls what it needs from the adapter. BUT if the VOLTS or polarity are different on the adapters, there are several things that could happen. most new laptops have a fuse in the charging system, which will blow at this point, if not, it will short out the charging system, and yes, at this point without skill of replacing parts on the motherboard, you will need the motherboard replaced. 

the power jack may have been damaged if the pins/plug wasnt exactly the same..

so worst case scenario yes, the board needs repalced, best scenario is to do a power cycle, take out battery unplug it etc. and press power button for 30 seconds, hook it all back up and try it. if it doesnt work, then most likely the power jack, then the mobo. 

eaither way, unless the power cycle fixes it, then the computer needs work. which if you dont do it yourself, can get quite expensive. 

good luck!