Exceptional = extraordinary, remarkable, unusual.

• Shaun is an exceptionally intelligent student.
• Such loans will be granted only in exceptional cases.
• Vaikom Vijayalakshmy is a gifted and exceptionally talented singer.
• He has a garden with exceptional beauty.
• Modifications in the original plan can be sanctioned only in exceptional cases.

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Exceptionable = objectionable, causing disapproval or offence.

• His recent writings on individual freedom are highly unpleasant and exceptionable.
• You should be careful not to seem exceptionable in your language and manners.
• Their exceptionable remarks may arouse religious sentiments and that may disrupt the otherwise calm social atmosphere.